Network alignment, which aims at learning a matching between the same entities across multiple information networks, often suffers challenges from feature inconsistency, high-dimensional features, to unstable alignment results. This article presents a novel network alignment framework, Unsupervised Adversarial learning based Network Alignment(UANA), that combines generative adversarial network (GAN) and reinforcement learning (RL) techniques to tackle the above critical challenges. First, we propose a bidirectional adversarial network distribution matching model to perform the bidirectional cross-network alignment translations between two networks, such that the distributions of real and translated networks completely overlap together. In addition, two cross-network alignment translation cycles are constructed for training the unsupervised alignment without the need of prior alignment knowledge. Second, in order to address the feature inconsistency issue, we integrate a dual adversarial autoencoder module with an adversarial binary classification model together to project two copies of the same vertices with high-dimensional inconsistent features into the same low-dimensional embedding space. This facilitates the translations of the distributions of two networks in the adversarial network distribution matching model. Finally, we develop an RL based optimization approach to solve the vertex matching problem in the discrete space of the GAN model, i.e., directly select the vertices in target networks most relevant to the vertices in source networks, without unstable similarity computation that is sensitive to discriminative features and similarity metrics. Extensive evaluation on real-world graph datasets demonstrates the outstanding capability of UANA to address the unsupervised network alignment problem, in terms of both effectiveness and scalability.
1 Introduction
With the proliferation of social media platforms, such as Facebook, LinkedIn, and Instagram, each user usually participates in multiple social worlds, each with unique structures and semantics. Network alignment has received increasing attention in recent years [13, 53, 56, 59, 67, 91, 94, 114, 122, 132]. Network alignment can provide a comprehensive view of entities by integrating multiple aligned networks into one more complete/compact network as well as new insights about how entities interact with and influence each other on different information networks, enabling knowledge transferring across networks. Network alignment techniques have gained huge successes on a wide variety of real-world problems in different domains, such as biological or protein network analysis [14, 35, 36, 56, 81], image matching in computer vision [15, 26], ontology matching [32, 79], user account linking in different social networks [25, 46, 48, 65, 78, 127, 128], and knowledge translation in multilingual knowledge bases [51, 107, 157]. Despite the great success of existing network alignment techniques, the flood of big networks still poses several unsolved computational challenges.
Feature inconsistency. Traditional network alignment techniques are based on the fundamental assumption of topological and/or attribute consistency [3, 9, 21, 26, 31, 39, 81, 117, 119, 122]: Two vertices in different networks are more likely to have a higher matching score if they share similar topological and/or attribute features in respective networks. However, it is often observed that the same entities in different networks have very diverse neighbors and behaviors and thus have quite different structural and attribute features. Figure 1 presents an illustrating example of network alignment for two social networks \(G^1\) and \(G^2\). The actual offline names of users in two networks are anonymized and only their virtual online usernames are available. The goal of network alignment is to align different copies of the same users across two networks, denoted by red dashed lines. Due to various functionalities of different networks, say Facebook for socializing with friends vs. LinkedIn for job seeking, the users in \(G^1\) and \(G^2\) have different features, e.g., four users in \(G^1\) and five users in \(G^2\), attributes Locations in \(G^1\) and Affiliations in \(G^2\). In this situation, different copies of the same vertices across two networks are not often most similar to each other. Without handling feature inconsistency, choosing the vertex pairs with the maximum similarity scores in two networks as the alignment results usually leads to biased or incorrect results. A natural way to address the feature inconsistency issue is to compare pairwise vertices by utilizing common features but ignoring inconsistent features, e.g., MEgo2Vec [112] considers the common neighbors of each pair of vertices from two networks. This strategy is useful for two networks with similar structures. However, two copies of the same vertices on two different networks often share few or no common neighbors. It is challenging to get a clear consensus from different networks with unique characteristics.
Fig. 1.
Fig. 1. Network alignment with high-dimensional inconsistent features.
High-dimensional features. Real-world graph data typically have high-dimensional features. The huge memory consumption dramatically limits the applicability of network alignment methods on large-scale network data. A practical solution is to employ network embedding techniques to learn low-dimensional representation of big networks and preserve the original correlations between vertices in the embedding space, and thus achieve acceptable network alignment results over the network embeddings while further improving the memory performance [13, 31, 48, 53, 60, 88, 112, 132]. PALE [60], FRUI-P [132], and UUIL [48] perform the individual embeddings on two networks. In this case, the feature inconsistency issue still maintains in the individual embedding space of two networks to be aligned. MAH [88], IONE [53], SNNA [47], and CrossMNA [13] project the anchor node pairs with known matching information into the same embedding vectors in a semi-supervised manner. REGAL [31] jointly embeds two graphs based on the similarity computation with the assumption of topological and attribute consistency. MEgo2Vec [112] generates candidate user pairs with considering only the user pairs with similar usernames before executing the network embedding. Can we develop a joint network embedding model to project two networks into the same embedding space for alleviating the feature inconsistency issue without the help of prior alignment and side information in an unsupervised way?
Unsupervised learning. The majority of existing network alignment algorithms are supervised methods [4, 26, 37, 58, 60, 65, 108, 109, 128] or semi-supervised approaches [38, 47, 53, 88, 108, 122, 127], which utilize known anchor links connecting aligned vertices or additional alignment constraints to guide the alignment process. On the other hand, the unsupervised methods are able to provide more generic network alignment solutions with the absence of prior alignment knowledge [3, 9, 31, 39, 48, 115, 116, 128]. However, the unsupervised methods often rely heavily on highly discriminative features for ensuring the effectiveness of network alignment and thus limit their applicability under different scenarios. In addition, the quality of the network alignment results is sensitive to the similarity computation between vertices across different networks. This may result in unstable network alignment results, due to inadequate discriminative features and user-defined similarity metrics.
With these fundamental challenges in mind, we develop a dual Generative adversarial network (GAN) and reinforcement learning (RL) based network alignment approach, Unsupervised Adversarial learning based Network Alignment (UANA), with three original contributions.
A bidirectional cycle-based adversarial network distribution matching model is proposed to train the network alignment task in an unsupervised way. We jointly translate the pairwise copies of the same vertices from one network to another, move the cross-network translated distributions of two networks from two directions, and make the distribution of one network translated from another one as close as possible to the distribution of this network itself. This makes the distributions of real and translated networks completely overlap together. Two cross-network alignment translation cycles are built for training the unsupervised alignment without prior alignment knowledge.
With the goal of alleviating the feature inconsistency issue, a dual adversarial autoencoder module is plugged into an adversarial binary classification model to project two copies of the same vertices with high-dimensional inconsistent features into the same low-dimensional embedding space, such that they are closest to each other for facilitating the translations of the distributions of two networks in the adversarial network distribution matching model.
To avoid the unstable similarity computation that is sensitive to discriminative features and similarity metrics, based on the matched distributions of real and translated networks, a policy gradient-based optimization approach is developed to solve the vertex matching problem in the discrete space of the GAN model, which cannot be optimized by the stochastic gradient descent (SGD) method. The proposed method can directly select the vertices in target networks most relevant to the vertices in source networks.
Extensive evaluation on real graph datasets demonstrate the strength of UANA to address the network alignment problem in terms of both effectiveness and scalability.
2 Problem Definition
We formally define our research problem as follows. In this article, we are given two networks \(G^1 = (V^1, E^1, A^1, \mathbf {A}^1, \mathbf {B}^1)\) and \(G^2 = (V^2, E^2, A^2, \mathbf {A}^2, \mathbf {B}^2)\). Each network is denoted as \(G^k = (V^k, E^k, A^k, \mathbf {A}^k, \mathbf {B}^k)\)\((1 \le k \le 2)\), where \(V^k = \lbrace v_1^k, \ldots , v_{N_k}^k\rbrace\) is the set of \(N_k\) vertices, \(E^k = \lbrace (v_i^k, v_j^k) : 1 \le i, j \le N_k, i \ne j\rbrace\) is the set of \(L_k\) edges, and \(A^k = \lbrace a_1^k, \ldots , a_{M_k}^k\rbrace\) is the set of \(M_k\) attributes. \(\mathbf {A}^k\) denotes the \(N_k \times N_k\) adjacency matrix of \(G^k\). \(\mathbf {A}_{ij}^k\) specifies the value of the edge between two vertices \(v_i^k\) and \(v_j^k\) in \(V^k\). \(\mathbf {B}^k\) specifies the \(N_k \times M_k\) attribute matrix of \(G^k\). \(\mathbf {B}_{ij}^k\) denotes the attribute value of vertex \(v_i^k\) on attribute \(a_j^k\). We use symbols \(\mathbf {A}_{i:}^k\) and \(\mathbf {B}_{i:}^k\) to denote the \(i{\mathrm{th}}\) row vectors of \(\mathbf {A}^k\) and \(\mathbf {B}^k,\) respectively. The concatenation of \(\mathbf {A}_{i:}^k\) and \(\mathbf {B}_{i:}^k\), denoted by \(\mathbf {A}_{i:}^k \oplus \mathbf {B}_{i:}^k\), is used to specify the original representation of the copy \(v_i^k \in V^k\) in \(G^k\) of a vertex \(v_i\), consisting of both structural and attribute features. For ease of presentation, we use \(v_i^k\) to denote the vertex copy itself and its original representation \(\mathbf {A}_{i:}^k \oplus \mathbf {B}_{i:}^k\). The problem of UANA contains three analysis objectives.
(1) Consensus network embedding: Map the original representation \(\mathbf {A}_{i:}^k \oplus \mathbf {B}_{i:}^k\) of each vertex \(v_i^k\) in \(G^k (1 \le k \le 2)\) to a low-dimensional representation \(u_i^k\) with the minimum reconstruction error between the output and the input, i.e., and \(d\lt \lt (N_k+M_k)\). In addition, two different copies \(v_i^1\) in \(G^1\) and \(v_i^2\) in \(G^2\) of any vertex \(v_i\), should be projected into the same embedding space for alleviating the feature inconsistency issue, i.e., \(u_i^1 = u_i^2\).
(2) Network distribution matching: Match the distribution of real networks \(G^k\) and the distribution of translated networks \(\tilde{G}^k\) through the alignment translation from \(G^l\)\((1 \le k, l \le 2, k \ne l)\), i.e., continuously move and twist the distributions of \(G^k\) and \(\tilde{G}^k\) and make two distributions as close as possible until two distributions completely overlap together, for ensuring a good network alignment from \(G^l\) to \(G^k\). By following the same idea in existing efforts [46, 47, 106], this article matches the distribution of real networks and the distribution of translated networks by minimizing the Wasserstein distance between two distributions. It is a symmetric distance metric that is equal to zero when two distributions completely overlap together.
(3) Bidirectional vertex matching: Directly select the most relevant embedding \(u_i^k\) of the copy \(v_i^k\) in \(G^k\) of the same vertex \(v_i\) for the given embedding \(u_i^l\) of the copy \(v_i^l\) in \(G^l\) of \(v_i\)\((1 \le k, l \le 2, k \ne l)\) without unstable similarity computation. In addition, the unsupervised bidirectional network alignment should be supported, i.e., given \(v_i^1\) in \(G^1\), the counterpart \(v_i^2\) in \(G^2\) can be retrieved without the need of ground truth, and vice versa. Although we do not utilize any ground truth (i.e., pre-aligned vertex pairs) in the entire learning process, we still use the ground truth information for evaluation only.
The GAN technique was proposed to generate photographs that look authentic to human observers [29, 77]. In the GAN model, a generator \(\mathbf {G}\) tries to fool a discriminator \(\mathbf {D}\) by generating real-looking fake images but \(\mathbf {D}\) aims at distinguishing between real and fake images. As a result of the GAN training, \(\mathbf {D}\) cannot differentiate real images from fake images generated by \(\mathbf {G}\). This implies that the generated fake images become identical to the real images. In other words, the fake images have the same distribution as the real images.
This motivates us to extend the basic GAN model to a dual GAN model to learn the bidirectional matchings between the distributions of two networks for alleviating the feature inconsistency issue as well as train the unsupervised network alignment task. Figure 2 exhibits a toy example of adversarial network alignment. There are the distributions of two networks \(G^1\) and \(G^2\), where each dot denotes a vertex in \(G^1\) or \(G^2\) and two vertices within each network are close/distant if they have similar/dissimilar structural and attribute features. For example, \(v^1_1\) and \(v^2_1\), \(v^1_2\) and \(v^2_2\), and \(v^1_3\) and \(v^2_3\) are three pairs of aligned nodes in \(G^1\) and \(G^2,\) respectively. Two similar nodes \(v^1_1\) and \(v^1_2\) are very close but \(v^1_1\) and \(v^1_3\) are quite distant. As shown in Figure 2(a), two distributions initially have quite different shapes, due to their inconsistent structural and attribute features. In Figure 2(b), an adversarial classification model in Equation (8), containing two encoders \(\mathbf {E_1}\) for \(G^1\) and \(\mathbf {E_2}\) for \(G^2\) and a binary classifier \(\mathbf {C}\), is designed to jointly project \(G^1\) and \(G^2\) into the approximately same embedding space for facilitating the translations of the embeddings of \(G^1\) and \(G^2\). In order to avoid the unstable similarity computation, an adversarial network distribution matching model in Equation (4), consisting of two alignmenters \(\mathbf {M_{12}}\) (or \(\mathbf {M_{21}}\)) for the translation from \(G^1\) to \(G^2\) (or from \(G^2\) to \(G^1\)), is developed to learn the bidirectional alignments between pairwise vertices in \(G^1\) and \(G^2\). Therefore, translated \(\tilde{G}^2\) (or \(\tilde{G}^1\)) from \(G^1\) (or \(G^2\)) are moved close to real \(G^2\) (or \(G^1\)) in Figure 2(c) until the distributions of two networks completely overlap together in Figure 2(d), which implies that \(\mathbf {M_{12}}\) (or \(\mathbf {M_{21}}\)) can produce a good network alignment from \(G^1\) to \(G^2\) (or from \(G^2\) to \(G^1\)). By combining the bidirectional alignments \(G^1\stackrel{\mathbf {M_{12}}}{\longrightarrow }\tilde{G}^2\) and \(G^2\stackrel{\mathbf {M_{21}}}{\longrightarrow }\tilde{G}^1 \approx G^1\) together, the network alignment tasks can be trained in an unsupervised way, since we can translate \(G^1\) into \(\tilde{G}^2\) with \(\mathbf {M_{12}}\) and return back to \(\tilde{G}^1 \approx G^1\) with \(\mathbf {M_{21}}\), i.e., \(G^1\stackrel{\mathbf {M_{12}}}{\longrightarrow }\tilde{G}^2\stackrel{\mathbf {M_{21}}}{\longrightarrow }\tilde{G}^1 \approx G^1\), denoted by red line in Figure 2, and vice versa. Therefore, we do not need any prior aligned vertex pairs as the ground truth for the training.
Figure 3 presents the model architecture, which contains three analytics components. For ease of presentation, we ignore the vertex subscripts and use \(v\) to denote any same vertex in two networks \(G^1\) and \(G^2\). \(v^1\) and \(v^2\) are used to denote two copies in \(G^1\) and \(G^2\) of \(v\) and their original representations, respectively. Two pairs of encoders and decoders are shared by all three components. Concretely, encoders \(u^k = \mathbf {E_k}(v^k)\) and decoders \(\hat{v}^k = \mathbf {\tilde{E}_k}(u^k)\) for \(G^k\)\((1 \le k \le 2)\) output the embedding \(u^k\) and the reconstruction \(\hat{v}^k\) of \(v^k\) in \(G^k\).
Fig. 3.
Fig. 3. Bidirectional cycle-based adversarial training architecture.
Three analytics components consist of (1) bidirectional cycle-based adversarial network distribution matching aims at learning the bidirectional matchings between the distributions of real \(G^1\) (or \(G^2\)) and translated \(\tilde{G}^1\) (or \(\tilde{G}^2\)) from \(G^2\) (or \(G^1\)) with the alignmenter \(\mathbf {M_{21}}\) (or \(\mathbf {M_{12}}\)), such that two distributions completely overlap together. Two cross-network alignment translation cycles are built for training the unsupervised alignment without prior knowledge, e.g., one red cycle \(u^1\stackrel{\mathbf {M_{12}}}{\longrightarrow }\tilde{u}^2\stackrel{\mathbf {M_{21}}}{\longrightarrow }\tilde{u}^1 \approx u^1\) and one cyan cycle \(u^2\stackrel{\mathbf {M_{21}}}{\longrightarrow }\tilde{u}^1\stackrel{\mathbf {M_{12}}}{\longrightarrow }\tilde{u}^2 \approx u^2\) in Figure 3. (2) Adversarial binary classification tries to achieve the consensus network embedding of \(G^1\) and \(G^2\): project two copies \(v^1\) in \(G^1\) and \(v^2\) in \(G^2\) of the same vertex \(v\) into the same embedding space, i.e., \(u^1 = u^2\). And (3) policy gradient-based optimization of the alignmenters aims at optimizing \(\mathbf {M_{21}}\) (or \(\mathbf {M_{12}}\)) in the discrete space of the GAN model, i.e., select the most relevant \(\tilde{u}^1\) (or \(\tilde{u}^2\)) in \(\tilde{G}^1\) (or \(\tilde{G}^2\)) for the given \(u^2\) (or \(u^1\)) in \(G^2\) (or \(G^1\)), based on the matched distributions of real and translated networks.
3.2 Bidirectional Cycle-Based Adversarial Network Distribution Matching
A straightforward GAN model for adversarial network distribution matching is defined as follows:
(1)
At each GAN training, \(\mathbf {D_k}\) is trained to maximize the probability of the embedding \(u^k\) of the copy \(v^k\) of \(v\) in \(G^k\), i.e., \(\mathbf {D_k}(u^k)\). In addition, \(\mathbf {D_k}\) is fooled by using the embedding \(u^l\) of the copy \(v^l\) of \(v\) in \(G^l\) as input to maximize \(\mathbf {D_k}(u^l)\)\((1 \le k, l \le 2, k \ne l)\). The GAN training continuously moves and twists the distributions of \(G^k\) and \(G^l\) and makes two distributions as close as possible until the two distributions completely overlap together, i.e., \(p_{\mathbf {E_l}}(v^l,u^l) = p_{\mathbf {E_k}}(v^k,u^k)\).
The following theorems show that the distributions of two networks can be matched in terms of the embedding features:
Theorem 1.
Given fixed encoders \(\mathbf {E_1}\) and \(\mathbf {E_2}\), the optimal discriminators \(\mathbf {D_1}, \mathbf {D_2}\) for \(\max \limits _{\mathbf {D_1}, \mathbf {D_2}} \mathcal {V}(\mathbf {D_1}, \mathbf {D_2}, \mathbf {E_1}, \mathbf {E_2})\) are \(\mathbf {D_1}^*(u) = f_{12}(v,u)\) and \(\mathbf {D_2}^*(u) = f_{21}(v,u)\), where \(f_{12}\) and \(f_{21}\) are two Radon–Nikodym derivatives.
Proof.
We define the average of two probability measures \(p_{\mathbf {E_1}}\) and \(p_{\mathbf {E_2}}\) as \(p_{\mathbf {E}} = \frac{p_{\mathbf {E_1}} + p_{\mathbf {E_2}}}{2}\). As both \(p_{\mathbf {E_1}}\) and \(p_{\mathbf {E_2}}\) are absolutely continuous w.r.t. \(p_{\mathbf {E}}\), there exist two Radon–Nikodym derivatives: \(f_{12} = \frac{dp_{\mathbf {E_1}}}{d(p_{\mathbf {E_1}} + p_{\mathbf {E_2}})} = \frac{dp_{\mathbf {E_1}}}{2dp_{\mathbf {E}}}\), and \(f_{21} = \frac{dp_{\mathbf {E_2}}}{d(p_{\mathbf {E_1}} + p_{\mathbf {E_2}})} = \frac{dp_{\mathbf {E_2}}}{2dp_{\mathbf {E}}}\), such that their sum is equal to 1, i.e., \(f_{12} + f_{21} = 1\). As the last two terms in Equation (1) are irrelevant to the solving of \(\mathbf {D_1}^*(u)\), we ignore them and rewrite the first two terms in Equation (1) as follows:
(2)
We know that a function \(a \log x + (1 - a) \log (1 - x)\) achieves the maximum when \(x = a\). Thus, \(\mathbf {D_1}^*(u) = f_{12}(v,u)\). Similarly, we can prove that \(\mathbf {D_2}^*(u) = f_{21}(v,u)\).□
Theorem 2.
The global minimum of \(\max \limits _{\mathbf {D_1}, \mathbf {D_2}} \mathcal {V}(\mathbf {D_1}, \mathbf {D_2}, \mathbf {E_1}, \mathbf {E_2})\), i.e., \(\min \limits _{\mathbf {E_1}, \mathbf {E_2}} \max \limits _{\mathbf {D_1}, \mathbf {D_2}} \mathcal {V}(\mathbf {D_1}, \mathbf {D_2}, \mathbf {E_1}, \mathbf {E_2})\), is \(-\log 16\) and achieved iff \(p_{\mathbf {E_1}}(v,u) = p_{\mathbf {E_2}}(v,u)\) with \(\mathbf {D_1}^*(u) = \frac{1}{2}\) and \(\mathbf {D_2}^*(u) = \frac{1}{2}\).
Proof.
Without loss of generality, we only demonstrate the proof of the minimum of the first two terms in Equation (1). The minimum of the last two terms in Equation (1) can be generated by using the similar method. According to Theorem 1, given the optimal \(\mathbf {D_1}^*(u)\), we reformulate the GAN objective below:
(3)
The JS divergence is always non-negative. The first two terms in Equation (1) achieve the minimum \(-\log 4\) when the JS divergence is equal to zero iff \(p_{\mathbf {E_1}}(v,u) = p_{\mathbf {E_2}}(v,u)\). Similarly, the last two terms in Equation (1) achieve the minimum \(-\log 4\) iff \(p_{\mathbf {E_1}}(v,u) = p_{\mathbf {E_2}}(v,u)\) too. In this case, \(f_{12}(v,u) = \frac{dp_{\mathbf {E_1}}}{d2p_{\mathbf {E_1}}} = \frac{1}{2}\) and \(f_{12}(v,u) = \frac{dp_{\mathbf {E_2}}}{d2p_{\mathbf {E_2}}} = \frac{1}{2}\).
Therefore, \(\min \limits _{\mathbf {E_1}, \mathbf {E_2}} \max \limits _{\mathbf {D_1}, \mathbf {D_2}} \mathcal {V}(\mathbf {D_1}, \mathbf {D_2}, \mathbf {E_1}, \mathbf {E_2})\) is equal to \((-\log 4) + (-\log 4) = -\log 16\). This concludes the proof.□
The original GAN problem in Equation (1) is easy to solve and optimize, but cannot directly offer the answer of network alignment. We still need to calculate the similarities between vertices across two networks to produce the alignment results. In order to avoid the unstable similarity computation, we convert the original GAN problem in Equation (1) to another equivalent GAN problem for matching the vertices by introducing two alignmenters \(\tilde{u}^1 = \mathbf {M_{21}}(u^2)\) and \(\tilde{u}^2 = \mathbf {M_{12}}(u^1)\).
Theorem 3.
The original GAN problem in Equation (1) is equivalent to the following GAN problem under suitable regularity conditions:
(4)
Proof.
Since the first and third terms in Equation (4) are the same as the corresponding terms in Equation (1), and the second and fourth terms in Equation (4) are similar to each other, we only show the proof of the second term in Equation (4).
Notice that we have \(\int _{\tilde{u}^1} p_{\mathbf {M_{21}}}(\tilde{u}^1|u^2) du^1 = 1\) in Equation (5) since the integral of a probability density function over the entire space is equal to 1. This concludes the proof.□
In the equivalent GAN problem in Equation (4), a discriminator \(\mathbf {D_1}\) outputs the probability of a sample vertex embedding from the true distribution \(p_{\mathbf {E_1}}(u^1|v^1)\) rather than the fake distribution \(p_{\mathbf {E_2}}(u^2|v^2)\) through the translation \(p_{\mathbf {M_{21}}}(\tilde{u}^1|u^2)\), i.e., distinguishes real \(v^1\) in \(G^1\) from fake \(\tilde{v}^1\) through the alignment translation of \(v^2\) in \(G^2\). Given a sample \(u^2\) in \(G^2\), an alignmenter \(\tilde{u}^1 = \mathbf {M_{21}}(u^2)\) selects the most relevant \(\tilde{u}^1\) in \(\tilde{G}^1\) (i.e., the alignment from \(G^2\) to \(G^1\)), in terms of the conditional distribution \(p_{\mathbf {M_{21}}}(\tilde{u}^1|u^2)\), and then the selected \(\tilde{u}^1\) is fed into \(\mathbf {D_1}\) for differentiation. \(\mathbf {D_2}(u^2)\) and \(\tilde{u}^2 = \mathbf {M_{12}}(u^1)\) are the counterparts for the network alignment from \(G^1\) to \(G^2\) with similar meanings.
We train \(\mathbf {D_1}\) (or \(\mathbf {D_2}\)) to maximize the probability of a sample from real \(u^1\) (or \(u^2\)) in \(G^1\) (or \(G^2\)), while optimizing \(\mathbf {M_{21}}\) (or \(\mathbf {M_{12}}\)) to fool \(\mathbf {D_1}\) (or \(\mathbf {D_2}\)) by selecting translated \(\tilde{u}^1\) (or \(\tilde{u}^2\)) from \(u^2\) (or \(u^1\)) in \(G^2\) (or \(G^1\)) with maximizing \(\mathbf {D_1}(\mathbf {M_{21}}(\mathbf {E_2}(v^2))\) (or \(\mathbf {D_2}(\mathbf {M_{12}}(\mathbf {E_1}(v^1))\)). As a result, the GAN training will make the distribution of one network translated from another network as close as possible to the distribution of this network itself until the distributions of real and translated networks completely overlap together. Thus, \(\mathbf {D_1}\) (or \(\mathbf {D_2}\)) cannot differentiate real \(u^1\) (or \(u^2\)) in \(G^1\) (or \(G^2\)) from translated \(\tilde{u}^1\) (or \(\tilde{u}^2\)) from \(u^2\) (or \(u^1\)) in \(G^2\) (or \(G^1\)). It implies that \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\) can produce good bidirectional network alignment results from \(G^1\) to \(G^2\) and from \(G^2\) to \(G^1\).
Given two close vertices \(v_i^1\) and \(v_j^1\) in \(G^1\) and two close vertices \(v_s^2\) and \(v_t^2\) in \(G^2\) in terms of both structural and attribute features, we have large values of \(\mathbf {A}_{ij}^1\), \(\mathbf {A}_{st}^2\), \(\mathbf {B}_{i:}^1 \cdot \mathbf {B}_{j:}^1\), and \(\mathbf {B}_{s:}^2 \cdot \mathbf {B}_{t:}^2\), where \(\cdot\) denotes the inner product between two attribute vectors. Intuitively, if \(v_i^1\) and \(v_s^2\) are the alignment, which implies \(\mathbf {E_1}(v_i^1) \approx \mathbf {E_2}(v_s^2)\) based on the adversarial classification model in Equation (8), then it is highly possible that their close neighbors \(v_j^1\) and \(v_t^2\) are the alignment too, i.e., \(\mathbf {E_1}(v_j^1) \approx \mathbf {E_2}(v_t^2)\). The following homophily consistency loss aims at maintaining the vertex homophily consistency between pairwise vertices in both the original and embedding spaces. Namely, strong structural correlations and similar attribute features between pairwise vertices correspond to similar embedding features between them.
where \(v_i^1 \leftrightarrow v_s^2\) and \(v_j^1 \leftrightarrow v_t^2\) represent two alignments.
A cycle loss is introduced to guarantee the quality of the unsupervised bidirectional network alignment with two alignment translation cycles, as shown in Equation (7). Intuitively, if a vertex embedding \(u^1\) in \(G^1\) can be translated into the counterpart \(\tilde{u}^2\) in \(\tilde{G}^2\) with \(\mathbf {M_{12}}\) and translated back to \(\tilde{u}^1 \approx u^1\) itself with \(\mathbf {M_{21}}\), i.e., \(u^1\) can be returned back to itself through the cycle of \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\), then it is unnecessary to have the prior alignment knowledge between \(u^1\) and \(u^2\) as the ground truth for training. The only focus is whether the original \(u^1\) is the same as the translated \(\tilde{u}^1\) through the translation cycle.
(7)
3.3 Adversarial Binary Classification
Due to inconsistent structural and attribute features, different copies of the same vertices across two networks are not often most similar to each other. Training two independent embedding models for two networks with inconsistent features are hard to eliminate the feature inconsistency issue in the individual embedding space of two networks. Thus, an adversarial binary classification model is designed to jointly train the embedding models of two networks, such that two copies of the same vertices in different networks are projected into the same embedding space.
(8)
where \(\mathbf {C}\) is a binary classifier to predict the probability of a sample vertex embedding \(\mathbf {E_1}(v^1)\) (or \(\mathbf {E_2}(v^2)\)) belonging to class \(\mathbf {1}\) (i.e., \(G^1\)) or class \(\mathbf {2}\) (i.e., \(G^2\)). \(H\) is the cross-entropy for adversarial classification.
We train \(\mathbf {C}\) to maximize the probability of a sample \(\mathbf {E_1}(v^1)\) belonging to class \(\mathbf {1}\) or \(\mathbf {E_2}(v^2)\) on class \(\mathbf {2}\) by minimizing \(H\), while optimizing \(\mathbf {E_1}\) and \(\mathbf {E_2}\) by maximizing \(H\) to fool \(\mathbf {C}\). Compared with the basic GAN model, \(\mathbf {C}\) is like the discriminator and \(\mathbf {E_1}\) and \(\mathbf {E_2}\) are like the generators. As a result, \(\mathbf {C}\) cannot differentiate the embeddings \(\mathbf {E_1}(v^1)\) and \(\mathbf {E_2}(v^2)\) in two networks of the same vertices \(v\). This implies that \(v^1\) and \(v^2\) are projected into the same embedding space, i.e., \(\mathbf {E_1}(v^1) \approx \mathbf {E_2}(v^2)\).
The following theorems exhibit our adversarial classification model can alleviate the feature inconsistency issue:
Theorem 4.
Given fixed encoders \(\mathbf {E_1}\) and \(\mathbf {E_2}\), the optimal classifier \(\mathbf {C}\) for \(\max \limits _{\mathbf {C}} \mathcal {W}(\mathbf {C}, \mathbf {E_1}, \mathbf {E_2})\) is \(\mathbf {C}^*(u) = \frac{p_{\mathbf {E_1}}(v,u)}{p_{\mathbf {E_1}}(v,u) + p_{\mathbf {E_2}}(v,u)}\) for class \(\mathbf {1}\) and \(\mathbf {C}^*(u) = \frac{p_{\mathbf {E_2}}(v,u)}{p_{\mathbf {E_1}}(v,u) + p_{\mathbf {E_2}}(v,u)}\) for class \(\mathbf {2}\).
Theorem 5.
The global minimum of \(\max \limits _{\mathbf {C}} \mathcal {W}(\mathbf {C}, \mathbf {E_1}, \mathbf {E_2})\), i.e., \(\min \limits _{\mathbf {E_1}, \mathbf {E_2}} \max \limits _{\mathbf {C}} \mathcal {W}(\mathbf {C}, \mathbf {E_1}, \mathbf {E_2})\), is \(-\log 4\) and achieved iff \(p_{\mathbf {E_1}}(v,u) = p_{\mathbf {E_2}}(v,u)\) with \(\mathbf {C}^*(u) = \frac{1}{2}\) for class \(\mathbf {1}\) and \(\mathbf {C}^*(u) = \frac{1}{2}\) for class \(\mathbf {2}\).
The proof of Theorems 3 and 5 is omitted due to space limit. The proof methods are similar to Theorems 1 and 2.
We introduce a loss function to minimize the reconstruction error between the output and the input, and preserve the original network structure in the embedding space.
(9)
Intuitively, we want the embedding semantics of one network to be preserved when translated to another network and returned to itself, say \(\mathbf {E_1}(\mathbf {\tilde{E}_1}(\mathbf {E_2}(v^2))) \approx \mathbf {E_2}(v^2)\). A semantic preservation loss is introduced to maintain this property.
(10)
Therefore, the overall objective function of the adversarial network alignment for jointly training dual GAN models is given as follows:
We jointly train the adversarial classification model for alleviating the feature inconsistency issue and the adversarial network distribution matching model for training the unsupervised alignment without pairwise similarity computation.
3.4 Policy Gradient-Based Optimization of \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\)
Traditional network alignment methods aim at transforming or embed two networks into the same space by maximizing the similarities (or minimizing the distances) between projected or embedded nodes across networks. The node pairs with the largest similarities or smallest distances are selected as the alignment results [46, 47, 60, 106, 108, 128]. Notice that the above network alignment process include two steps: (1) optimize a trainable embedding function or transform matrix to map two networks into the same space; and (2) compute similarity scores between nodes across networks (based on a certain similarity measure) and output the most similar node pairs (i.e., hard alignment) or top-\(k\) matched nodes for each node (i.e., soft alignment). All of these methods focus on the optimization of Step 1 but Step 2 is often deterministic and non-trainable.
In this work, in order to train the network alignment task in an unsupervised way, we propose a bidirectional cycle-based adversarial learning model to translate \(G^1\) into \(\tilde{G}^2\) with \(\mathbf {M_{12}}\) and return back to \(\tilde{G}^1 \approx G^1\) with \(\mathbf {M_{21}}\), i.e., \(G^1\stackrel{\mathbf {M_{12}}}{\longrightarrow }\tilde{G}^2\stackrel{\mathbf {M_{21}}}{\longrightarrow }\tilde{G}^1 \approx G^1\). In our work, encoders \(\mathbf {E_1}\) and \(\mathbf {E_2}\) correspond to the trainable embedding function in the above Step 1, while alignmenters \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\) correspond to the non-trainable selection operation in the Step 2. We want to optimize \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\) to guarantee the quality of unsupervised learning, i.e., ensure that a node can be returned back to itself through the cycle of \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\).
The generators in the traditional GAN models generate fake images from continuous noise space and thus the standard SGD method can be used to optimize them. However, given a vertex embedding in one network, the selection process of the most relevant one among actual vertex embeddings in another network by the alignmenters is discrete and non-trainable. At each time, the alignmenter \(\mathbf {M_{21}}(u^2)\) (or \(\mathbf {M_{12}}(u^1)\)) selects the most relevant one \(\tilde{u}^1\) among actual vertex embeddings in network \(G^1\) (or \(\tilde{u}^2\) in network \(G^2\)) for the given embedding \(u^2\) in \(G^2\) (or \(u^1\) in \(G^1\)). Thus, the SGD method cannot solve this specific optimization problem in the discrete space.
Recall that Step 2 in traditional network alignment methods that compute the similarity scores and output the alignment results are often non-trainable and thus cannot be optimized, we try to utilize the policy gradient technique to optimize this step (i.e., selection of most similar vertex pairs). The RL models essentially aim at optimizing a function mapping from states to actions so as to collect as much reward as possible when the agents transition from state to state and executing an action in each state provides the agents with a reward. In our case, the states correspond to the vertex embeddings and the actions correspond to the selection of most similar vertex pairs in terms of their embeddings. The reward is to make all the translated \(\tilde{u}_i^1\) from \(u_i^2\) in \(G^2\) be the same as the actual \(u_i^1\) in \(G^1\). We thus utilize the policy gradient technique to optimize the parameters of \(\mathbf {M_{21}}\) and \(\mathbf {M_{12}}\), by maximizing the expected cumulative reward of the entire network alignment process.
Notice that \(\mathbf {M_{21}}\) and \(\mathbf {M_{12}}\) exist in only Equations (4) and (7), and we ignore irrelevant terms in the overall objective in Equation (11) and optimize \(\mathbf {M_{21}}\), when \(\mathbf {D_1}\), \(\mathbf {E_2}\), and \(\mathbf {\tilde{E}_1}\) are fixed, as follows. For convenience of presentation, let be and be , where \(u^1\) and \(u^2\) are real copies, \(\tilde{u}^1 = \mathbf {M_{21}}(u^2)\) in the training of \(\mathbf {D_1}\), \(\tilde{u}^1 = \mathbf {M_{21}}(\mathbf {M_{12}}(u^1))\) and \(\tilde{u}^2 = \mathbf {M_{12}}(\mathbf {M_{21}}(u^2))\) in the unsupervised learning loss are translated copies.
(12)
We define the environment of policy gradient as follows: (1) the state \(s_t\) at time step \(t\) for the embedding \(u_i^2\) of the copy \(v_i^2\) in network \(G^2\) of a vertex \(v_i\) is defined as the concatenation of the previously-visited embeddings \(\lbrace \tilde{u}_1^1, \ldots , \tilde{u}_{t-1}^1\rbrace\), the currently-visiting embedding \(\tilde{u}_t^1\) in network \(G^1\), and the \(u_i^2\) itself, i.e., \(s_t = \lbrace \tilde{u}_1^1, \ldots , \tilde{u}_t^1, u_i^2\rbrace\); (2) the action space \(a_t\) at step \(t\) contains two actions of \(select\) and \(skip\) to determine whether \(\tilde{u}_t^1\) in \(G^1\) will be selected for the GAN training or not, according to a logistic policy; (3) the policy model \(\pi _\theta (a_t|s_t)\) chooses an action \(a_t\) given the current state \(s_t\) at step \(t\).
We use the alignmenter \(\tilde{u}_t^1 = \mathbf {M_{21}}(u_i^2)\) as the policy model to perform the vertex matching operation; and (4) the network alignment model follows the policy to determine which action (\(select\) or \(skip\) an embedding for the alignment) at each state, and finally receives a delayed reward \(r(s_ta_t)\) at the terminal state \(T\) only when all \(N_1\) and \(N_2\) vertices in \(G^1\) and \(G^2\) are processed. We have the zero reward at other states.
We aim at maximizing the average reward for all vertices to be aligned, i.e., make all the translated \(\tilde{u}_i^1\) from \(u_i^2\) in \(G^2\) be the same as the actual \(u_i^1\) in \(G^1\). At each time, based on the current state \(u_i^2\), we follow the policy \(\pi _\theta (a_t|s_t)\) to take action \(\tilde{u}_t^1\) with the reward of \(r(s_ta_t)\). Now, we can do the gradient ascent to optimize the policy parameters of \(\mathbf {M_{21}}\) by using the REINFORCE algorithm [99]. We also use the same strategy to optimize \(\mathbf {M_{12}}\).
(15)
4 Experimental Evaluation
In this section, we perform a set of experiments to evaluate the performance of UANA on real graph datasets. All experiments were done on a Linux Server with two Intel Xeon E5-2650 v4 at 2.66 GHz, 128 GB main memory, 1 TB HDD, four NVIDIA GeForce GTX 1080 Ti (4*11 GB memory). The algorithm is implemented with TensorFlow v1.9.0 and Python v3.6.3.
Datasets. We collect five groups of real-world graph datasets from different fields, e.g., social platforms and academics, as given in Table 1.
Table 1.
Dataset
Network
\(\#\)Nodes
\(\#\)Edges
\(\#\)Matched Nodes
SNS
Myspace
10,733
22,162
267
Flickr
12,974
32,298
SNS
Last.fm
15,436
32,638
452
Flickr
12,974
32,298
Academia:
2013
13,786
51,240
10,443
DBLP17K
2014
17,363
58,024
Academia:
2013
53,249
195,383
32,377
DBLP50K
2014
54,299
197,627
Academia:
2013
100,870
701,179
67,641
DBLP100K
2014
100,876
813,804
Table 1. Statistics of the Datasets
– Social networks. Myspace [122] is a social network offering an interactive, user-submitted network of friends, where nodes specify users and edges represent the friendships between users. Last.fm [122] is a music-oriented online social network that provides a radio streaming service, where vertices represent users and edges denote their following relationships. Flickr [122] is an online social network to offer image hosting service and video hosting service, where nodes denote users and edges specify their friendships. The same users occurring in two networks are used as the ground truth for evaluation only.
– Academic networks. DBLP is a computer science bibliography website that offers an online search and retrieval service for the academic community.1 We collect three groups of DBLP datasets with highly prolific \(17K\), \(50K\), and \(100K\) authors from all research areas. We split each dataset group into two coauthor networks in different years (2013 and 2014), respectively, where nodes denote authors and edges specify their coauthorships. The same authors existing in two networks of each dataset group are used as the ground truth for evaluation.
Baseline methods. We compare our UANA algorithm with six state-of-the-art network alignment methods.
– FINAL [117] includes a family of algorithms to leverage both structure and attribute information for solving the alignment problem of two attributed networks. It formulates the problem from an optimization perspective based on the alignment consistency principle.
– iNEAT [120] integrates both network alignment and network completion into a unified learning model by jointly training two tasks and mutually enhancing each other.
– CAlign [9] jointly trains multiple tasks of network alignment, community discovery, and community alignment in an unsupervised way.
– REGAL [31] is an unsupervised network alignment framework that jointly embeds two graphs into low-dimensional space and infers the soft alignment based on the similarity computation with the assumption of topological and attribute consistency.
– Deep graph matching consensus (DGMC) [26] is a supervised graph matching procedure which aims at reaching a data-driven neighborhood consensus between matched node pairs.
– RANA [75] is a preliminary version of this manuscript that was published in the proceedings of the 2019 IEEE International Conference on Data Mining (ICDM’19). It is a supervised learning algorithm without policy gradient-based optimization.
For two supervised learning algorithms of DGMC and Reinforcement learning and Adversarial learning based Network Alignment (RANA), the 10% of ground truth is randomly selected as the training data.
Variants of our model. We evaluate three variants of UANA to show the strengths of adversarial learning and RL one by one.
– UANA is a complete version with the support of bidirectional cycle-based adversarial network distribution matching, adversarial classification, and policy gradient-based optimization.
– UANA-R is a partial version without adversarial classification. It fails to project two networks to be aligned into the same low-dimensional embedding space for alleviating the feature inconsistency issue as well as facilitating the translations of the distributions of two networks.
– UANA-C is a partial version without policy gradient-based optimization. It has to carefully choose discriminative features and similarity metrics to calculate the similarity scores between pairwise vertices across two networks to generate the alignment results. Existing works that use the Wasserstein distance to measure the distance between two discrete distributions often utilize the Cosine distance measure to compare node embeddings across networks [46, 47, 106]. In this case, by following the similar strategy, we calculate the Cosine distances between node embeddings across networks. The pairs of node embeddings with the smallest distances are selected as the alignment results. Thus, UANA-C can only optimize encoders \(\mathbf {E_1}\) and \(\mathbf {E_2}\) but not alignmenters \(\mathbf {M_{12}}\) and \(\mathbf {M_{21}}\) and it is difficult to guarantee the quality of bidirectional cycle-based adversarial network distribution matching.
Evaluation metrics. We use three measures to evaluate the quality of network alignment results generated by different methods. For each test, we perform five independent trials on each dataset group at each setting. The average performance scores of six competitor methods and three variants of our model in five trials over the same dataset groups are reported. Please refer to the cited papers for the detailed definitions of Accuracy [9, 117, 120] and F1 [112]. A larger Accuracy or F1 value indicates a better network alignment. We adopt the RMSE between the real copy \(v_i^1\) in a network \(G^1\) of a vertex \(v_i\) and the translated copy \(\tilde{v}_i^1\) by the alignment algorithms from the copy \(v_i^2\) in another network \(G^2\) of \(v_i\).
where \(v_i^1\) denotes a vertex itself and its original features. The smaller the RMSE value, the better the quality. In addition, we evaluate the execution time achieved by different network algorithms, respectively.
Parameter setting. We embed high-dimensional original features of each vertex into low-dimensional latent features. For two networks to be aligned, their encoders are jointly trained, which ensure two copies in two networks of the same vertices with inconsistent features are projected into the same embedding space for facilitating the alignment translation.
In our current implementation, all players in the dual GAN models in Equations (4) and (8) are implemented as three-layer perceptrons (input–hidden-output). The number of neurons in the hidden layer for discriminators \(\mathbf {D_k}\), encoders \(\mathbf {E_k}\) and decoders \(\mathbf {\tilde{E}_k}\), classifier \(\mathbf {C}\), and alignmenters \(\mathbf {M_{lk}}\)\((1 \le k, l \le 2, k \ne l)\) are set to \(d_1 = 20\), \(d_2 = 20\), \(d_3 = 40\), and \(d_4 = 40,\) respectively. Notice that both \(\mathbf {E_k}\) and \(\mathbf {\tilde{E}_k}\) have the same number of neurons in the hidden layer (i.e., \(d_2 = 20\)). The dimension of the embedding space is equal to 20. We solve the adversarial learning problem iteratively by first training \(\mathbf {D_1}\) and \(\mathbf {D_2}\) with fixed \(\mathbf {E_1}\), \(\mathbf {\tilde{E}_1}\), \(\mathbf {E_2}\), \(\mathbf {\tilde{E}_2}\), \(\mathbf {M_{12}}\), and \(\mathbf {M_{21}}\) using a mini-batch of size 100 and then training \(\mathbf {E_1}\), \(\mathbf {\tilde{E}_1}\), \(\mathbf {E_2}\), \(\mathbf {\tilde{E}_2}\), \(\mathbf {M_{12}}\), and \(\mathbf {M_{21}}\) with fixed \(\mathbf {D_1}\) and \(\mathbf {D_2}\) using a mini-batch of size 200. Similarly, we alternately train \(\mathbf {C}\) with \(\mathbf {E_1}\) and \(\mathbf {E_2}\) in the adversarial classification model.
4.1 Effectiveness Analysis
Figure 4 exhibits the network alignment quality by nine algorithms on the DBLP17K dataset to align its 2013 version with 2014 version. In order to verify the robustness to the noisy data, we add the noisy edges to two versions of DBLP17K with different levels of noisy data (i.e., the ratio of modified edges and attribute values to original clean ones), say 5% (i.e., 0.05), by randomly adding structure noise (i.e., edge addition and deletion) and attribute noise (i.e., attribute value modification) with the half noise level, respectively. We perform the network alignment test for all nine algorithms at different noise levels.
Fig. 4.
Fig. 4. Quality on DBLP17K 2013 vs. 2014.
It is observed from Figure 4 that among all nine methods, the generated network alignment results by our proposed UANA methods achieve the best quality in most experiments, showing the power of UANA in the presence of feature inconsistency and high-dimensional features. In most experiments, the performance by our unsupervised UANA method is comparable to our supervised RANA algorithm with the 10% of training data. A reasonable explanation is that the RANA method fails to utilize the policy gradient-based optimization approach to select the vertex pairs in two networks. The selection of discriminative features and similarity metrics may not be optimal when calculating the similarity scores between pairwise vertices across two networks.
Figures 5 and 6 present the network alignment quality on two pairs of social networks. Similar trends are observed for the network alignment comparison in these two figures: UANA achieves the largest Accuracy values (\(\gt\)0.712) and the smallest RMSE (\(\lt\)0.0101), which are better than other eight methods in most tests. Notice that even if the noise level is very high, such as 0.25 and 0.3, UANA still can achieve considerable quality improvement. It demonstrates that UANA is robust to noisy data. This advantage is very important for network alignment applications since each information network often has its unique structural and attribute features.
Fig. 5.
Fig. 5. Quality on Myspace vs. Flickr.
Fig. 6.
Fig. 6. Quality on Flickr vs. Last.fm.
In addition, we have observed from Figures 4–6 that the performance achieved by most network alignment algorithms decreases with increasing noise. This is consistent with the findings in our recent studies [74, 124, 125, 156]: Network alignment models are highly vulnerable to natural noise and adversarial attacks, i.e., small input perturbations in graph structures and node attributes can cause the model failures. In these works, we have evaluated tens of representative network alignment models. All algorithms are fairly sensitive to both random noise and adversarial attacks. In Figures 4–6, although the performance by Fast attrIbuted Network ALignment (FINAL) and Incomplete NEtwork AlignmenT (iNEAT) is relatively stable under different noise levels, their performance scores are fairly low, compared with our UANA method. Our UANA method still achieves relatively stable performance against different noise levels. The accuracy and F1 scores oscillate within the range of only 6.3% and 3.4%, demonstrating the effectiveness and robustness of UANA.
4.2 Ablation Study
Figures 4–6 also evaluate the performance of network alignment on three groups of datasets with three variants of our UANA model. We have observed that UANA averagely achieves 8.7\(\%\) Accuracy boost, 21.5\(\%\) RMSE improvement, and 6.9\(\%\) F1 growth, respectively, compared to the best network alignment results by all other algorithms. Notice that the performance of UANA-R and UANA-C is worse than that of UANA. A reasonable explanation is that UANA-R without utilizing the adversarial classification fails to project two networks to be aligned into the same low-dimensional embedding space and thus increase the difficulty of the translations of two networks with inconsistent features. On the other hand, UANA-C without considering policy gradient-based optimization relies on highly discriminative features and user-defined similarity metrics and thus may result in unstable network alignment results. These results illustrate that both adversarial classification and policy gradient-based optimization are very important in solving the network alignment problem.
4.3 Effectiveness Analysis on Flickr with Enough Ground Truth
By following the same strategy as the papers [8, 31, 70], we construct a new graph dataset with adjacency matrix \(\mathbf {A}^{\prime } = \mathbf {P} \mathbf {A} \mathbf {P}^T\), where \(\mathbf {A}\) is the adjacency matrix of the original Flickr dataset and \(\mathbf {P}\) is a randomly-generated permutation matrix. The nonzero elements in \(\mathbf {P}\) denote ground-truth vertex pairs. We add structural noise to \(\mathbf {A}^{\prime }\) by randomly adding or removing edges with a fixed probability. In addition, we add noise to attributes by flipping binary values, or choosing categorical attribute values uniformly at random from the remaining possible values with another fixed probability. Table 2 exhibits the performance of network alignment by different algorithms over Flickr and its perturbed version with enough ground truth. It is still observed that our UANA model outperforms all baseline methods in terms of three effectiveness measures and running time.
Table 2.
Measure
FINAL
CAlign
REGAL
iNEAT
DGMC
RANA
UANA
Accuracy
0.605
0.432
0.678
0.552
0.646
0.714
0.755
RMSE
0.015
0.020
0.012
0.015
0.012
0.011
0.009
F1
0.603
0.507
0.684
0.619
0.693
0.726
0.771
Table 2. Effectiveness Analysis on Flickr with Enough Ground Truth
4.4 Parameter Sensitivity
Figure 7(a) shows the impact of the number of vertex embedding dimensions in the our UANA model over the DBLP17K dataset. We have observed that the performance of both Accuracy and F1 scores (or RMSE values) initially raises (or decreases) when the number of dimension increases. Intuitively, the final embedding results with more dimensions can introduce enough information for sparse graphs, and thus help improve the quality of network alignment running on the latent representations. Later on, the performance curves keep relatively stable when the number of dimensions continuously increases. A reasonable explanation is that the additional dimensions are unnecessary for future prediction if we already have enough information for network alignment analysis. In addition, less dimensions can help improve the efficiency of both representation learning and network alignment. Thus, it is important to determine the optimal number of dimensions for the network embedding. In this experiment, the Accuracy, RMSE, and F1 scores oscillate within the range of 21.4%, 42.8%, and 12.3%, respectively.
Fig. 7.
Fig. 7. Quality vs. parameters.
The default setting of the weights of three loss functions in the overall objective in Equation (11) in our previous experiments are all fixed to 1. Figures 7(b)–(d) measure the performance effect of three loss functions with different weights for the network alignment. We vary one weighting factor, say the weight of the cycle loss from 0 to 2, and fix the settings of other two weights with 1 in each figure. It is observed that both Accuracy and F1 scores (or RMSE values) have concave (or convex) curves when we continuously increase the weight values. The Accuracy scores oscillate within the range of 22.7%, the RMSE values vary within the range of 52.8%, while the F1 scores fluctuate within the spectrum of 34.6%, respectively. This demonstrates that the optimal weighting setting for the cycle loss for unsupervised alignment, the homophily loss for maintaining the vertex homophily consistency in the embedding space, and the preservation loss for cross-network embedding translation play important roles in handling unsupervised adversarial network alignment on pairwise networks with inconsistent features.
4.5 Scalability Analysis
Complexity analysis. We use the sparse tensors of TensorFlow to implement the neural networks, which allows to perform fast computation on the sparse storage by iterating on the non-zero elements in the matrices, i.e., the edges in the graphs. In our experiments, all players in the dual GAN models in Equations (4) and (8) are implemented as three-layer perceptrons. \(D\) is the dimension of the embedding vectors. \(N_k\), \(L_k\), and \(M_k\)\((1 \le k, l \le 2, k \ne l)\) have the same definitions in Section 2. \(d_1, d_2, d_3\), and \(d_4\) have the same definitions in the parameter setting. Thus, the training cost of neural networks in \(\mathbf {E_k}\) and \(\mathbf {\tilde{E}_k}\) are \(O(L_kd_2+N_kM_kd_2+N_kd_2D)\). The training complexity of other neural networks is given as follows: \(O(N_kDd_1+N_kd_1)\) for \(\mathbf {D_k}\), \(O(N_lDd_4+N_kDd_4)\) for \(\mathbf {M_{lk}}\), and \(O(\sum _{k=1}^2 N_k(Dd_3+d_3))\) for \(\mathbf {C,}\) respectively.
Thus, the total complexity is equal to \(O(\sum _{k=1}^2 (d_1(D+1)+d_2(2D+2M_k)+d_3(D+1)+2d_4D)N_k + 2d_2L_k)\). Let \(\alpha _k = d_1(D+1)+d_2(2D+2M_k)+d_3(D+1)+2d_4D\) and \(\beta = 2d_2\), then the total cost is simplified as \(O(\sum _{k=1}^2 \alpha _k N_k+\beta L_k)\). Since other variables \(d_1, d_2, d_3, d_4, k, D, M_k\)\(\lt \lt N_k, L_k\), the computational cost is almost a linear combination of the number of vertices and the number of edges in two networks.
Tables 3 and 4 exhibit the scalability analysis results over two groups of large-scale DBLP datasets, where N/A represents that the algorithms either fail to normally terminate due to the “out of memory” issue or cannot finish the experiments in 24 hours. We use Accuracy, F1, and RMSE to evaluate the quality of network alignment results generated by different methods. A larger Accuracy or F1 value indicates a better network alignment. The smaller the RMSE value, the better the quality. We observe that UANA works well on two groups of large-scale DBLP datasets. Especially, as given in Table 4, for the largest dataset (DBLP100K), only REGAL and UANA can produce the network alignment results. However, our proposed UANA method achieve much better quality than REGAL, although UANA is slightly slower than REGAL over DBLP100K.
Table 3.
Measure
FINAL
CAlign
REGAL
iNEAT
DGMC
RANA
UANA
Accuracy
N/A
0.546
0.563
0.257
0.322
0.636
0.654
RMSE
N/A
0.008
0.010
0.010
0.011
0.008
0.009
F1
N/A
0.551
0.679
0.261
0.336
0.762
0.723
Table 3. Scalability on DBLP50K 2013 vs. 2014
Table 4.
Measure
FINAL
CAlign
REGAL
iNEAT
DGMC
RANA
UANA
Accuracy
N/A
N/A
0.654
N/A
N/A
0.774
0.783
RMSE
N/A
N/A
0.007
N/A
N/A
0.004
0.003
F1
N/A
N/A
0.627
N/A
N/A
0.740
0.749
Table 4. Scalability on DBLP100K 2013 vs. 2014
4.6 Case Study
Table 5 presents some details of the experiment results by seven network alignment algorithms on the DBLP17K dataset. We examine the network alignment results of 10 experts from 3 research areas of database, data mining, and information retrieval, respectively. The first column represents the authors on the DBLP17K 2013 dataset to be matched, and other columns denote the matched authors by seven algorithms on the DBLP17K 2013 dataset. We use the bold font to mark wrong alignment results produced by each method. Our UANA algorithm can correctly align all of 10 author pairs, while other methods produce from 2 to 4 wrong alignment results among 10 predictions. This demonstrates the strength of UANA for addressing network alignment under the environment of high-dimensional inconsistent feature space.
Table 5.
Ground truth
FINAL
CAlign
REGAL
W. Bruce Croft
W. Bruce Croft
W. Bruce Croft
W. Bruce Croft
David J. DeWitt
David J. DeWitt
David J. DeWitt
David J. Duke
Christos Faloutsos
Christos Faloutsos
Christos Faloutsos
Christos Faloutsos
Daniel A. Keim
Torben Bach Pedersen
Daniel A. Keim
Tobias Schreck
Bing Liu
Bing Liu
Bing Liu
Bing Liu
Hector Garcia-Molina
Jürg Nievergelt
Jeffrey D. Ullman
Jennifer Widom
M. Tamer Özsu
Tim Andrews
M. Tamer Özsu
Lei Chen
Michael Stonebraker
Michael Stonebraker
Michael Stonebraker
Michael Stonebraker
Wei Wang
Wei Wang
Wei Wang
Wei Wang
Chengqi Zhang
Ting Wang
Ting Wang
Chengqi Zhang
[1pt] iNEAT
DGMC
RANA
UANA
W. Bruce Croft
W. Bruce Croft
W. Bruce Croft
W. Bruce Croft
David J. DeWitt
Daniel J. Duke
David J. DeWitt
David J. DeWitt
Christos Faloutsos
Christos Faloutsos
Christos Faloutsos
Christos Faloutsos
Torben Bach Pedersen
Daniel A. Keim
Daniel A. Keim
Daniel A. Keim
Bing Liu
Bing Liu
Bing Liu
Bing Liu
Jürg Nievergelt
Andreas Paepcke
Hector Garcia-Molina
Hector Garcia-Molina
Tim Andrews
M. Tamer Özsu
M. Tamer Özsu
M. Tamer Özsu
Michael Stonebraker
Michael Stonebraker
Michael Stonebraker
Michael Stonebraker
Wei Wang
Xiang Zhang
Wei Wang
Wei Wang
Ting Wang
Chengqi Zhang
Chengqi Zhang
Chengqi Zhang
Table 5. Network Alignment Results by Seven Algorithms on DBLP17K 2013 vs. 2014
5 Related Work
GAN [29, 77] has become an active research topic in different domains, such as speech recognition, image classification, and natural language processing. The GAN model is a powerful tool to generate high-quality synthetic images without the need of multi-step Markov chains for lower computational cost, learn deep representations without extensively annotated training data, and enable machine learning to work with multi-modal outputs. Multiple GAN variations have been proposed to conduct important research problems in image, audio, video, and text data processing, such as CGAN [62], InfoGAN [7], StackGAN [111], and MaskGAN [24] for conditional adversarial nets, DCGAN [71], GAN-CLS [73], StackGAN [111], and Progressive GAN for image generation [34], DTN [87] and CoGAN [54] for image translation, GP-GAN [100] for image blending, Improved GAN [77] and CatGAN [96] for semi-supervised learning, MGAN [77] for texture synthesis, Perceptual GAN [50] for object detection, SRGAN [66] for image super-resolution, and VGAN [6] and MoCoGAN [90] for video generation.
While the standard GAN model learns a mapping from a latent space to the data distribution, inverse models such as Adversarial Autoencoders [57] and Bidirectional GAN [18] also learn a mapping from data to the latent space. This inverse mapping allows real or generated data examples to be projected back into the latent space, similar to the encoder of a variational autoencoder. The techniques have been applied to various real-world problems, including interpretable machine learning [7], semi-supervised learning [23], neural machine translation [123], 3D human motion prediction [40], cross-lingual sentence representation [28], and collaborative filtering [17].
Graph data analysis have attracted active research in the last decade [1, 5, 10, 11, 12, 30, 33, 41, 42, 52, 68, 69, 74, 75, 83, 84, 101, 102, 103, 110, 124, 125, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156]. Network alignment has received much attentions in recent years. Existing research efforts on graph matching can be classified into three broad categories: (1) Structure-based techniques, which rely only upon the topological information to match two or multiple input graphs [27, 46, 49, 56, 67, 72, 85, 106, 119, 120]. IONE [53] and PALE [60] are supervised learning models to keep major structural regularities of networks for anchor link prediction. FRUI-P [132] is an unsupervised structure-based user identification algorithm, which calculates the similarities of all the candidate identical users between two social networks based on their friend features. DeepLink [128] is a deep RL based algorithm by leveraging the duality of mapping between two networks in a semi-supervised manner. CrossMNA [13] is a cross-network embedding based supervised network alignment method by learn inter/intra-embedding vectors for each node and by computing pairwise node similarity scores across networks. (2) Attribute-based approaches, which utilize highly discriminative structure and/or attribute features for ensuring the matching effectiveness [22, 61, 64, 65, 82, 108, 118, 121, 127]. FINAL [117] leverages both structure and attribute information to solve the attributed network alignment problem. Community-based network Alignment (CAlign) [9] jointly trains multiple learning tasks of network alignment, community discovery, and community alignment in one framework for analyzing large attributed networks. FASTEN [20] is a fast Krylov subspace based network alignment algorithm to speed up and scale up the computation of Sylvester equation for the alignment of two perturbation networks. UUIL [48] solves the unsupervised user identity linkage problem by learning a projection function to minimize the Earth Mover’s distance between the distributions of users in two social networks. REpresentation learning-based Graph ALignment (REGAL) [31] is an unsupervised network alignment framework that jointly embeds two graphs into low-dimensional space and infers soft alignments by comparing node embeddings across graphs. SNNA [47] is an adversarial learning framework to solve the weakly-supervised identity alignment problem by incorporating available annotations as the learning guidance. DGMC [26] is a supervised graph matching procedure which aims at reaching a data-driven neighborhood consensus between matched node pairs. And (3) heterogeneous methods, which employ heterogeneous structural, content, spatial, and temporal features to further improve the matching performance [55, 76, 97, 104, 126, 129, 130]. SCAN-PS [113] aims at predicting social links for new users across two aligned heterogeneous social networks. MNA [37] predicts ranking scores between pairwise nodes and infers anchor links across heterogeneous social networks by considering social, spatial, temporal, and text features. COSNET [122] is an energy based model to connect multiple heterogeneous social networks by considering both local and global consistency among them. DPLink [25] is an end-to-end deep learning framework to complete the user identity linkage task for heterogeneous mobility data.
RANA [75] is a preliminary version of this manuscript that was published in the proceedings of the ICDM’19. It is a supervised learning algorithm without policy gradient-based optimization. It needs some known aligned vertices in different networks as training data and thus limits its applicability. In addition, it has to carefully choose discriminative features and similarity metrics to calculate the similarity scores between pairwise vertices across two networks to generate the alignment results.
With the burst of novel artificial intelligence techniques, RL techniques have recently been a powerful tool to answer many challenging questions in robotics [44, 45], game playing [63, 80], indoor navigation [158], power consumption management [89], machine translation [159], and so on. The RL provides a very intuitive and comprehensive solution for autonomous decision making, in which software agents ought to take actions in an environment, consisting of a set of states and a set of actions per state, so as to maximize cumulative reward or reinforcement signal [2]. The RL models essentially aim at learning and optimizing a function mapping from states to actions so as to collect as much reward as possible when the agents transition from state to state and executing an action in each state provides the agents with a reward. The RL techniques have been leveraged to solve many graph optimization problems, such as knowledge graph reasoning [92, 105], adversarial attacks on graph-structured data [16, 86], graph matching [98], medicine combination prediction [95], recommendation [43, 131], robust spammer detection [19], and graph data management [93].
6 Conclusions
We have presented a dual GAN and RL based unsupervised network alignment framework. First, we propose a bidirectional adversarial network distribution matching to perform the bidirectional cycle-based cross-network translations for matching the distributions of real and translated networks in an unsupervised way. Second, we plug a dual adversarial autoencoder module into an adversarial binary classification model to project two copies of the same vertices into the same low-dimensional embedding space. Finally, we develop an RL based optimization method to solve the vertex matching problem in the discrete space of the GAN model.
Xianqiang Bao, Ling Liu, Nong Xiao, Yang Zhou, and Qi Zhang. 2015. Policy-driven autonomic configuration management for NoSQL. In Proceedings of the 2015 IEEE International Conference on Cloud Computing. 245–252.
Andrew G. Barto, Richard S. Sutton, and Charles W. Anderson. 1983. Neuronlike adaptive elements that can solve difficult learning control problems. IEEE Transactions on Systems, Man, and Cybernetics 13, 5 (1983), 834–846.
Mohsen Bayati, Margot Gerritsen, David F. Gleich, Amin Saberi, and Ying Wang. 2009. Algorithms for large, sparse network alignment problems. In Proceedings of the 2009 9th IEEE International Conference on Data Mining. 705–710.
Mohsen Bayati, David F. Gleich, Amin Saberi, and Ying Wang. 2013. Message-passing algorithms for sparse network alignment. Transactions on Knowledge Discovery from Data 7, 1 (2013), 3:1–3:31.
Qing Chang, Jiaxiang Ren, Huaguo Zhou, Yang Zhou, and Yukun Song. 2021. Identifying wrong-way driving incidents from regular traffic videos using unsupervised trajectory-based method. To Appear in Transportation Research Record (2021).
Jiawei Chen, Janusz Konrad, and Prakash Ishwar. 2018. VGAN-based image representation learning for privacy-preserving facial expression recognition. In 2018 IEEE Conference on Computer Vision and Pattern Recognition Workshops. 1570–1579.
Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, and Pieter Abbeel. 2016. InfoGAN: Interpretable representation learning by information maximizing generative adversarial nets. In Proceedings of the 30th International Conference on Neural Information Processing Systems. 2172–2180.
Xiyuan Chen, Mark Heimann, Fatemeh Vahedian, and Danai Koutra. 2020. CONE-align: Consistent network alignment with proximity-preserving node embedding. In Proceedings of the 29th ACM International Conference on Information and Knowledge Management. 1985–1988.
Zheng Chen, Xinli Yu, Bo Song, Jianliang Gao, Xiaohua Hu, and Wei-Shih Yang. 2017. Community-based network alignment for large attributed network. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management. 587–596.
Hong Cheng, David Lo, Yang Zhou, Xiaoyin Wang, and Xifeng Yan. 2009. Identifying bug signatures using discriminative graph mining. In Proceedings of the 18th International Symposium on Software Testing and Analysis. 141–152.
Hong Cheng, Yang Zhou, Xin Huang, and Jeffrey Xu Yu. 2012. Clustering large attributed information networks: An efficient incremental computing approach. Data Mining and Knowledge Discovery 25, 3 (2012), 450–477.
Hong Cheng, Yang Zhou, and Jeffrey Xu Yu. 2011. Clustering large attributed graphs: A balance between structural and attribute similarities. ACM Transactions on Knowledge Discovery from Data 5, 2 (2011), 1–33.
Xiaokai Chu, Xinxin Fan, Di Yao, Zhihua Zhu, Jianhui Huang, and Jingping Bi. 2019. Cross-network embedding for multi-network alignment. In Proceedings of the World Wide Web Conference. 273–284.
Connor Clark and Jugal Kalita. 2014. A comparison of algorithms for the pairwise alignment of biological networks. Bioinformatics 30, 16 (2014), 2351–2359.
Donatello Conte, Pasquale Foggia, Carlo Sansone, and Mario Vento. 2004. Thirty years of graph matching in pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence 18, 3 (2004), 265–298.
Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. 2018. Adversarial attack on graph structured data. In Proceedings of the 35th International Conference on Machine Learning. 1123–1132.
Rui Ding, Guibing Guo, Xiaochun Yang, Bowei Chen, Zhirong Liu, and Xiuqiang He. 2020. BiGAN: Collaborative filtering with bidirectional generative adversarial networks. In Proceedings of the 2020 SIAM International Conference on Data Mining. 82–90.
Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell. 2017. Adversarial feature learning. In Proceedings of the 5th International Conference on Learning Representations.
Yingtong Dou, Guixiang Ma, Philip S. Yu, and Sihong Xie. 2020. Robust spammer detection by nash reinforcement learning. In Proceedings of the 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 924–933.
Boxin Du and Hanghang Tong. 2018. FASTEN: Fast Sylvester equation solver for graph mining. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 1339–1347.
Boxin Du, Si Zhang, Nan Cao, and Hanghang Tong. 2017. FIRST: Fast interactive attributed subgraph matching. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1447–1456.
Xingbo Du, Junchi Yan, and Hongyuan Zha. 2019. Joint link prediction and network alignment via cross-graph embedding. In Proceedings of the 28th International Joint Conference on Artificial Intelligence. 2251–2257.
Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Alex Lamb, Martín Arjovsky, Olivier Mastropietro, and Aaron C. Courville. 2017. Adversarially learned inference. In Proceedings of the 5th International Conference on Learning Representations.
William Fedus, Ian J. Goodfellow, and Andrew M. Dai. 2018. MaskGAN: Better text generation via filling in the ______. In Proceedings of the 2018 International Conference on Learning Representations.
Jie Feng, Mingyang Zhang, Huandong Wang, Zeyu Yang, Chao Zhang, Yong Li, and Depeng Jin. 2019. DPLink: User identity linkage via deep neural network from heterogeneous mobility data. In Proceedings of the World Wide Web Conference. 459–469.
Matthias Fey, Jan Eric Lenssen, Christopher Morris, Jonathan Masci, and Nils M. Kriege. 2020. Deep graph matching consensus. In Proceedings of the 8th International Conference on Learning Representations.
Shun Fu, Guoyin Wang, Shuyin Xia, and Li Liu. 2020. Deep multi-granularity graph embedding for user identity linkage across social networks. Knowledge-Based Systems 193, C (2020), 105301.
Zuohui Fu, Yikun Xian, Shijie Geng, Yingqiang Ge, Yuting Wang, Xin Dong, Guang Wang, and Gerard de Melo. 2020. ABSent: Cross-lingual sentence representation mapping with bidirectional GANs. In Proceedings of the 34th AAAI Conference on Artificial Intelligence, the 32nd Innovative Applications of Artificial Intelligence Conference, and the 10th AAAI Symposium on Educational Advances in Artificial Intelligence. 7756–7763.
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio. 2014. Generative adversarial nets. In Proceedings of the 27th International Conference on Neural Information Processing Systems. 2231–2239.
Mark Heimann, Haoming Shen, Tara Safavi, and Danai Koutra. 2018. REGAL: Representation learning-based graph alignment. In Proceedings of the 27th ACM International Conference on Information and Knowledge Management. 117–126.
Wei Hu, Yuzhong Qu, and Gong Cheng. 2008. Matching large ontologies: A divide-and-conquer approach. Data & Knowledge Engineering 67, 1 (2008), 140–160.
Ruoming Jin, Dong Li, Jing Gao, Zhi Liu, Li Chen, and Yang Zhou. 2021. Towards a better understanding of linear models for recommendation. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining.
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. 2017. Progressive growing of GANs for improved quality, stability, and variation. In Proceedings of the 2018 International Conference on Learning Representations.
Brian P. Kelley, Roded Sharan, Richard M. Karp, Taylor Sittler, David E. Root, Brent R. Stockwell, and Trey Ideker. 2003. Conserved pathways within bacteria and yeast as revealed by global protein network alignment. Proceedings of the National Academy of Sciences 100, 20 (2003), 11394–11399.
Brian P. Kelley, Bingbing Yuan, Fran Lewitter, Roded Sharan, Brent R. Stockwell, and Trey Ideker. 2004. PathBLAST: A tool for alignment of protein interaction networks. Nucleic Acids Research 32, Web-Server-Issue (2004), 83–88.
Xiangnan Kong, Jiawei Zhang, and Philip S. Yu. 2013. Inferring anchor links across multiple heterogeneous social networks. In Proceedings of the 22nd ACM International Conference on Information and Knowledge Management. 179–188.
Nitish Korula and Silvio Lattanzi. 2014. An efficient reconciliation algorithm for social networks. Proceedings of the VLDB Endowment 7, 5 (2014), 377–388.
Danai Koutra, Hanghang Tong, and David Lubensky. 2013. BIG-ALIGN: Fast bipartite graph alignment. In Proceedings of the 13th IEEE International Conference on Data Mining. 389–398.
Jogendra Nath Kundu, Maharshi Gor, and R. Venkatesh Babu. 2019. BiHMP-GAN: Bidirectional 3D human motion prediction GAN. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence, the 31st Innovative Applications of Artificial Intelligence Conference, and the 9th AAAI Symposium on Educational Advances in Artificial Intelligence. 8553–8560.
Kisung Lee, Ling Liu, Karsten Schwan, Calton Pu, Qi Zhang, Yang Zhou, Emre Yigitoglu, and Pingpeng Yuan. 2015. Scaling iterative graph computations with graphmap. In Proceedings of the 27th IEEE International Conference for High Performance Computing, Networking, Storage and Analysis. 57:1–57:12.
Kisung Lee, Ling Liu, Yuzhe Tang, Qi Zhang, and Yang Zhou. 2013. Efficient and customizable data partitioning framework for distributed big RDF data processing in the cloud. In Proceedings of the 2013 IEEE International Conference on Cloud Computing. 327–334.
Yu Lei, Hongbin Pei, Hanqi Yan, and Wenjie Li. 2020. Reinforcement learning based recommendation with graph convolutional q-network. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. 1757–1760.
Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. 2016. End-to-end training of deep visuomotor policies. Journal of Machine Learning Research 17, 1 (2016), 39:1–39:40.
Sergey Levine, Peter Pastor, Alex Krizhevsky, and Deirdre Quillen. 2016. Learning hand-eye coordination for robotic grasping with deep learning and large-scale data collection. International Journal of Robotics Research 37, 4–5 (2018), 421–436.
Chaozhuo Li, Senzhang Wang, Hao Wang, Yanbo Liang, Philip S. Yu, Zhoujun Li, and Wei Wang. 2019. Partially shared adversarial learning for semi-supervised multi-platform user identity linkage. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management. 249–258.
Chaozhuo Li, Senzhang Wang, Yukun Wang, Philip S. Yu, Yanbo Liang, Yun Liu, and Zhoujun Li. 2019. Adversarial learning for weakly-supervised social network alignment. In Proceedings of the 33rd AAAI Conference on Artificial Intelligence, the 31st Innovative Applications of Artificial Intelligence Conference, and the 9th AAAI Symposium on Educational Advances in Artificial Intelligence. 996–1003.
Chaozhuo Li, Senzhang Wang, Philip S. Yu, Lei Zheng, Xiaoming Zhang, Zhoujun Li, and Yanbo Liang. 2018. Distribution distance minimization for unsupervised user identity linkage. In Proceedings of the 27th ACM International Conference on Information and Knowledge Management. 447–456.
Gen Li, Li Sun, Zhongbao Zhang, Pengxin Ji, Sen Su, and Philip S. Yu. 2019. MC\({}^{\mbox{2}}\): Unsupervised multiple social network alignment. In Proceedings of the 2019 IEEE International Conference on Big Data. 1151–1156.
Jianan Li, Xiaodan Liang, Yunchao Wei, Tingfa Xu, Jiashi Feng, and Shuicheng Yan. 2017. Perceptual generative adversarial networks for small object detection. In Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition. 1951–1959.
Shengnan Li, Xin Li, Rui Ye, Mingzhong Wang, Haiping Su, and Yingzi Ou. 2018. Non-translational alignment for multi-relational networks. In Proceedings of the 27th International Joint Conference on Artificial Intelligence.4180–4186.
Ji Liu, Jizhou Huang, Yang Zhou, Xuhong Li, Shilei Ji, Haoyi Xiong, and Dejing Dou. 2021. From distributed machine learning to federated learning: A survey. arxiv:2104.14362. Retrieved from https://arxiv.org/abs/2104.14362.
Li Liu, William K. Cheung, Xin Li, and Lejian Liao. 2016. Aligning users across social networks using network embedding. In Proceedings of the 25th International Joint Conference on Artificial Intelligence. 1774–1780.
Ming-Yu Liu and Oncel Tuzel. 2016. Coupled generative adversarial networks. In Proceedings of the 30th International Conference on Neural Information Processing Systems. 469–477.
Siyuan Liu, Shuhui Wang, Feida Zhu, Jinbo Zhang, and Ramayya Krishnan. 2014. HYDRA: Large-scale social identity linkage via heterogeneous behavior modeling. In Proceedings of the 2014 ACM SIGMOD International Conference on Management of Data. 51–62.
Yangwei Liu, Hu Ding, Danyang Chen, and Jinhui Xu. 2017. Novel geometric approach for global alignment of PPI networks. In Proceedings of the 31st AAAI Conference on Artificial Intelligence31–37.
Alireza Makhzani, Jonathon Shlens, Navdeep Jaitly, and Ian J. Goodfellow. 2015. Adversarial autoencoders. In Proceedings of the 2016 International Conference on Learning Representations.
Anshu Malhotra, Luam C. Totti, Wagner Meira Jr., Ponnurangam Kumaraguru, and Virgílio A. F. Almeida. 2012. Studying user footprints in different online social networks. In Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining. 1065–1070.
Eric Malmi, Aristides Gionis, and Evimaria Terzi. 2017. Active network alignment: A matching-based approach. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management. 1687–1696.
Tong Man, Huawei Shen, Shenghua Liu, Xiaolong Jin, and Xueqi Cheng. 2016. Predict anchor links across social networks via an embedding approach. In Proceedings of the 25th International Joint Conference on Artificial Intelligence. 1823–1829.
Farzan Masrour, Pang-Ning Tan, and Abdol-Hossein Esfahanian. 2019. OPTANE: An OPtimal transport algorithm for NEtwork alignment. In Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. 448–451.
Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A. Rusu, Joel Veness, Marc G. Bellemare, Alex Graves, Martin A. Riedmiller, Andreas Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wierstra, Shane Legg, and Demis Hassabis. 2015. Human-level control through deep reinforcement learning. Nature 518, 7540 (2015), 529–533.
Xin Mu, Wei Xie, Roy Ka-Wei Lee, Feida Zhu, and Ee-Peng Lim. 2019. AD-link: An adaptive approach for user identity linkage. In Proceedings of the 2019 IEEE International Conference on Big Knowledge. 183–190.
Xin Mu, Feida Zhu, Ee-Peng Lim, Jing Xiao, Jianzong Wang, and Zhi-Hua Zhou. 2016. User identity linkage by latent user space modelling. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1775–1784.
Yudai Nagano and Yohei Kikuta. 2018. SRGAN for super-resolving low-resolution food images. In Proceedings of the Joint Workshop on Multimedia for Cooking and Eating Activities and Multimedia Assisted Dietary Management. 33–37.
Huda Nassar, Nate Veldt, Shahin Mohammadi, Ananth Grama, and David F. Gleich. 2018. Low rank spectral network alignment. In Proceedings of the 2018 World Wide Web Conference on World Wide Web. 619–628.
Kyle Kai Qin, Flora D. Salim, Yongli Ren, Wei Shao, Mark Heimann, and Danai Koutra. 2020. G-CREWE: Graph CompREssion with embedding for network alignment. In Proceedings of the 29th ACM International Conference on Information and Knowledge Management. 1255–1264.
Alec Radford, Luke Metz, and Soumith Chintala. 2016. Unsupervised representation learning with deep convolutional generative adversarial networks. In Proceedings of 2016 International Conference on Learning Representations.
Vikram Ravindra, Huda Nassar, David F. Gleich, and Ananth Grama. 2019. Rigid graph alignment. In Proceedings of the 8th International Conference on Complex Networks and Their Applications. 621–632.
Scott E. Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee. 2016. Generative adversarial text to image synthesis. In Proceedings of the 33nd International Conference on Machine Learning. 1060–1069. Retrieved from http://jmlr.org/proceedings/papers/v48/reed16.html.
Jiaxiang Ren, Zijie Zhang, Jiayin Jin, Xin Zhao, Sixing Wu, Yang Zhou, Yelong Shen, Tianshi Che, Ruoming Jin, and Dejing Dou. 2021. Integrated defense for resilient graph matching. In Proceedings of the 38th International Conference on Machine Learning. 8982–8997.
Jiaxiang Ren, Yang Zhou, Ruoming Jin, Zijie Zhang, Dejing Dou, and Pengwei Wang. 2019. Dual adversarial learning based network alignment. In Proceedings of the 19th IEEE International Conference on Data Mining. 1288–1293.
Yuxiang Ren, Charu C. Aggarwal, and Jiawei Zhang. 2019. Meta diagram based active social networks alignment. In Proceedings of the 35th IEEE International Conference on Data Engineering. 1690–1693.
Tim Salimans, Ian J. Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. 2016. Improved techniques for training GANs. In Proceedings of the 30th International Conference on Neural Information Processing Systems. 2226–2234.
Kai Shu, Suhang Wang, Jiliang Tang, Reza Zafarani, and Huan Liu. 2016. User identity linkage across online social networks: A review. SIGKDD Explorations 18, 2 (2016), 5–17.
Pavel Shvaiko and Jérôme Euzenat. 2013. Ontology matching: State of the art and future challenges. IEEE Transactions on Knowledge and Data Engineering 25, 1 (2013), 158–176.
David Silver, Aja Huang, Chris J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Vedavyas Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy P. Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. 2016. Mastering the game of Go with deep neural networks and tree search. Nature 529, 7587 (2016), 484–489.
Rohit Singh, Jinbo Xu, and Bonnie Berger. 2008. Global alignment of multiple protein interaction networks with application to functional orthology detection. Proceedings of the National Academy of Sciences 105, 35 (2008), 12763–12768.
Sen Su, Li Sun, Zhongbao Zhang, Gen Li, and Jielun Qu. 2018. MASTER: Across multiple social networks, integrate attribute and structure embedding for reconciliation. In Proceedings of the 27th International Joint Conference on Artificial Intelligence.3863–3869.
Zhiyuan Su, Ling Liu, Mingchu Li, Xinxin Fan, and Yang Zhou. 2013. ServiceTrust: Trust management in service provision networks. In Proceedings of the 10th IEEE International Conference on Services Computing. 272–279.
Zhiyuan Su, Ling Liu, Mingchu Li, Xinxin Fan, and Yang Zhou. 2015. Reliable and resilient trust management in distributed service provision networks. ACM Transactions on the Web 9, 3 (2015), 1–37.
Li Sun, Zhongbao Zhang, Pengxin Ji, Jian Wen, Sen Su, and Philip S. Yu. 2019. DNA: Dynamic social network alignment. In Proceedings of the 2019 IEEE International Conference on Big Data. 1224–1231.
Yiwei Sun, Suhang Wang, Xianfeng Tang, Tsung-Yu Hsieh, and Vasant G. Honavar. 2020. Adversarial attacks on graph neural networks via node injections: A hierarchical reinforcement learning approach. In Proceedings of the Web Conference 2020. 673–683.
Yaniv Taigman, Adam Polyak, and Lior Wolf. 2016. Unsupervised cross-domain image generation. In Proceedings of the 2017 International Conference on Learning Representations.
Shulong Tan, Ziyu Guan, Deng Cai, Xuzhen Qin, Jiajun Bu, and Chun Chen. 2014. Mapping users across networks by manifold alignment on hypergraph. In Proceedings of the 28th AAAI Conference on Artificial Intelligence.159–165.
Gerald Tesauro, Rajarshi Das, Hoi Chan, Jeffrey O. Kephart, David Levine, Freeman L. Rawson III, and Charles Lefurgy. 2007. Managing power consumption and performance of computing systems using reinforcement learning. In Proceedings of the 21st Annual Conference on Neural Information Processing Systems. 1497–1504.
Sergey Tulyakov, Ming-Yu Liu, Xiaodong Yang, and Jan Kautz. 2018. MoCoGAN: Decomposing motion and content for video generation. In Proceedings of the 2018 IEEE Conference on Computer Vision and Pattern Recognition. 1526–1535.
Guojia Wan, Shirui Pan, Chen Gong, Chuan Zhou, and Gholamreza Haffari. 2020. Reasoning like human: Hierarchical reinforcement learning for knowledge graph reasoning. In Proceedings of the 29th International Joint Conference on Artificial Intelligence. 1926–1932.
Hongzhi Wang, Zhixin Qi, Lei Zheng, Yun Feng, Junfei Ouyang, Haoqi Zhang, Xiangxi Zhang, Ziming Shen, and Shirong Liu. 2020. April: An automatic graph data management system based on reinforcement learning. In Proceedings of the 29th ACM International Conference on Information and Knowledge Management. 3465–3468.
Shaokai Wang, Xutao Li, Yunming Ye, Shanshan Feng, Raymond Y. K. Lau, Xiaohui Huang, and Xiaolin Du. 2019. Anchor link prediction across attributed networks via network embedding. Entropy 21, 3 (2019), 254.
Shanshan Wang, Pengjie Ren, Zhumin Chen, Zhaochun Ren, Jun Ma, and Maarten de Rijke. 2019. Order-free medicine combination prediction with graph convolutional reinforcement learning. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management. 1623–1632.
Yaqing Wang, Chunyan Feng, Ling Chen, Hongzhi Yin, Caili Guo, and Yunfei Chu. 2019. User identity linkage across social networks via linked heterogeneous network embedding. World Wide Web 22, 6 (2019), 2611–2632.
Yansheng Wang, Yongxin Tong, Cheng Long, Pan Xu, Ke Xu, and Weifeng Lv. 2019. Adaptive dynamic bipartite graph matching: A reinforcement learning approach. In Proceedings of the 35th IEEE International Conference on Data Engineering. 1478–1489.
Huikai Wu, Shuai Zheng, Junge Zhang, and Kaiqi Huang. 2017. GP-GAN: Towards realistic high-resolution image blending. In Proceedings of the 27th ACM International Conference on Multimedia.2487–2495.
Sixing Wu, Ying Li, Dawei Zhang, Yang Zhou, and Zhonghai Wu. 2020. Diverse and informative dialogue generation with context-specific commonsense knowledge awareness. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 5811–5820.
Sixing Wu, Ying Li, Dawei Zhang, Yang Zhou, and Zhonghai Wu. 2021. TopicKA: Generating commonsense knowledge-aware dialogue responses towards the recommended topic fact. In Proceedings of the 29th International Joint Conference on Artificial Intelligence. 3766–3772.
Sixing Wu, Minghui Wang, Dawei Zhang, Yang Zhou, Ying Li, and Zhonghai Wu. 2021. Knowledge-aware dialogue generation via hierarchical infobox accessing and infobox-dialogue interaction graph network. In Proceedings of the 30th International Joint Conference on Artificial Intelligence.
Wei Xie, Xin Mu, Roy Ka-Wei Lee, Feida Zhu, and Ee-Peng Lim. 2018. Unsupervised user identity linkage via factoid embedding. In Proceedings of the IEEE International Conference on Data Mining1338–1343.
Wenhan Xiong, Thien Hoang, and William Yang Wang. 2017. DeepPath: A reinforcement learning method for knowledge graph reasoning. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing. 564–573.
Hongteng Xu, Dixin Luo, Hongyuan Zha, and Lawrence Carin. 2019. Gromov-Wasserstein learning for graph matching and node embedding. In Proceedings of the 36th International Conference on Machine Learning. 6932–6941.
Kun Xu, Liwei Wang, Mo Yu, Yansong Feng, Yan Song, Zhiguo Wang, and Dong Yu. 2019. Cross-lingual knowledge graph alignment via graph matching neural network. In Proceedings of the 57th Conference of the Association for Computational Linguistics. 3156–3161.
Abdurrahman Yasar and Ümit V. Çatalyürek. 2018. An iterative global structure-assisted labeled network aligner. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2614–2623.
Reza Zafarani and Huan Liu. 2013. Connecting users across social media sites: A behavioral-modeling approach. In 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 41–49.
Gong Zhang, Yang Zhou, Sixing Wu, Zeru Zhang, and Dejing Dou. 2021. Cross-lingual entity alignment with adversarial kernel embedding and adversarial knowledge translation. arxiv:2104.07837. Retrieved from https://arxiv.org/abs/2104.07837.
Han Zhang, Tao Xu, and Hongsheng Li. 2017. StackGAN: Text to photo-realistic image synthesis with stacked generative adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision. 5908–5916.
Jing Zhang, Bo Chen, Xianming Wang, Hong Chen, Cuiping Li, Fengmei Jin, Guojie Song, and Yutao Zhang. 2018. MEgo2Vec: Embedding matched ego networks for user alignment across social networks. In Proceedings of the 27th ACM International Conference on Information and Knowledge Management. 327–336.
Jiawei Zhang, Xiangnan Kong, and Philip S. Yu. 2013. Predicting social links for new users across aligned heterogeneous social networks. In Proceedings of the 2013 IEEE 13th International Conference on Data Mining. 1289–1294.
Jiawei Zhang and Philip S. Yu. 2015. Integrated anchor and social link predictions across social networks. In Proceedings of the 24th International Joint Conference on Artificial Intelligence. 2125–2132.
Jiawei Zhang and Philip S. Yu. 2015. Multiple anonymized social networks alignment. In Proceedings of the 2015 IEEE International Conference on Data Mining. 599–608.
Jiawei Zhang and Philip S. Yu. 2016. PCT: Partial co-alignment of social networks. In Proceedings of the 25th International Conference on World Wide Web. 749–759.
Si Zhang and Hanghang Tong. 2016. FINAL: Fast attributed network alignment. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1345–1354.
Si Zhang and Hanghang Tong. 2019. Attributed network alignment: Problem definitions and fast solutions. IEEE Transactions on Knowledge and Data Engineering. 31, 9 (2019), 1680–1692.
Si Zhang, Hanghang Tong, Ross Maciejewski, and Tina Eliassi-Rad. 2019. Multilevel network alignment. In Proceedings of the World Wide Web Conference. 2344–2354.
Si Zhang, Hanghang Tong, Jie Tang, Jiejun Xu, and Wei Fan. 2017. iNEAT: Incomplete network alignment. In Proceedings of the 2017 IEEE International Conference on Data Mining. 1189–1194.
Si Zhang, Hanghang Tong, Jiejun Xu, Yifan Hu, and Ross Maciejewski. 2019. ORIGIN: Non-rigid network alignment. In Proceedings of the 2019 IEEE International Conference on Big Data. 998–1007.
Yutao Zhang, Jie Tang, Zhilin Yang, Jian Pei, and Philip S. Yu. 2015. COSNET: Connecting heterogeneous social networks with local and global consistency. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1485–1494.
Zhirui Zhang, Shujie Liu, Mu Li, Ming Zhou, and Enhong Chen. 2018. Bidirectional generative adversarial networks for neural machine translation. In Proceedings of the 22nd Conference on Computational Natural Language Learning. 190–199.
Zijie Zhang, Zeru Zhang, Yang Zhou, Yelong Shen, Ruoming Jin, and Dejing Dou. 2020. Adversarial attacks on deep graph matching. In Proceedings of the 34th Conference on Neural Information Processing Systems.
Xin Zhao, Zeru Zhang, Zijie Zhang, Lingfei Wu, Jiayin Jin, Yang Zhou, Ruoming Jin, Dejing Dou, and Da Yan. 2021. Expressive 1-lipschitz neural networks for robust multiple graph learning against adversarial attacks. In Proceedings of the 38th International Conference on Machine Learning. 12719–12735.
Vincent W. Zheng, Mo Sha, Yuchen Li, Hongxia Yang, Yuan Fang, Zhenjie Zhang, Kian-Lee Tan, and Kevin Chen-Chuan Chang. 2018. Heterogeneous embedding propagation for large-scale e-commerce user alignment. In Proceedings of the IEEE International Conference on Data Mining. 1434–1439.
Zexuan Zhong, Yong Cao, Mu Guo, and Zaiqing Nie. 2018. CoLink: An unsupervised framework for user identity linkage. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence, the 30th Innovative Applications of Artificial Intelligence, and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence. 5714–5721.
Fan Zhou, Lei Liu, Kunpeng Zhang, Goce Trajcevski, Jin Wu, and Ting Zhong. 2018. DeepLink: A deep learning approach for user identity linkage. In Proceedings of the 2018 IEEE Conference on Computer Communications. 1313–1321.
Fan Zhou, Zijing Wen, Goce Trajcevski, Kunpeng Zhang, Ting Zhong, and Fang Liu. 2019. Disentangled network alignment with matching explainability. In Proceedings of the 2019 IEEE Conference on Computer Communications. 1360–1368.
Jingya Zhou and Jianxi Fan. 2019. TransLink: User identity linkage across heterogeneous social networks via translating embeddings. In Proceedings of the 2019 IEEE Conference on Computer Communications. 2116–2124.
Sijin Zhou, Xinyi Dai, Haokun Chen, Weinan Zhang, Kan Ren, Ruiming Tang, Xiuqiang He, and Yong Yu. 2020. Interactive recommender system via knowledge graph-enhanced reinforcement learning. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. 179–188.
Xiaoping Zhou, Xun Liang, Xiaoyong Du, and Jichao Zhao. 2018. Structure based user identification across social networks. IEEE Transactions on Knowledge and Data Engineering 30, 6 (2018), 1178–1191.
Yang Zhou, Amnay Amimeur, Chao Jiang, Dejing Dou, Ruoming Jin, and Pengwei Wang. 2018. Density-aware local siamese autoencoder network embedding with autoencoder graph clustering. In Proceedings of the 2018 IEEE International Conference on Big Data. 1162–1167.
Yang Zhou, Hong Cheng, and Jeffrey Xu Yu. 2009. Graph clustering based on structural/attribute similarities. Proceedings of the VLDB Endowment 2, 1 (2009), 718–729.
Yang Zhou, Hong Cheng, and Jeffrey Xu Yu. 2010. Clustering large attributed graphs: An efficient incremental approach. In Proceedings of the 10th IEEE International Conference on Data Mining. 689–698.
Yang Zhou, Chao Jiang, Zijie Zhang, Dejing Dou, Ruoming Jin, and Pengwei Wang. 2019. Integrating local vertex/edge embedding via deep matrix fusion and siamese multi-label classification. In Proceedings of the 2019 IEEE International Conference on Big Data. 1018–1027.
Yang Zhou, Kisung Lee, Ling Liu, Qi Zhang, and Balaji Palanisamy. 2019. Enhancing collaborative filtering with multi-label classification. In Proceedings of the 2019 International Conference on Computational Data and Social Networks. 323–338.
Yang Zhou and Ling Liu. 2012. Clustering analysis in large graphs with rich attributes. In Data Mining: Foundations and Intelligent Paradigms: Volume 1: Clustering, Association and Classification. Dawn E. Holmes and Lakhmi C. Jain (Eds.), Springer, 7–27.
Yang Zhou and Ling Liu. 2013. Social influence based clustering of heterogeneous information networks. In Proceedings of the 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 338–346.
Yang Zhou and Ling Liu. 2014. Activity-edge centric multi-label classification for mining heterogeneous information networks. In Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York, NY, 1276–1285.
Yang Zhou and Ling Liu. 2015. Social influence based clustering and optimization over heterogeneous information networks. ACM Transactions on Knowledge Discovery from Data 10, 1 (2015), 1–53.
Yang Zhou and Ling Liu. 2019. Approximate deep network embedding for mining large-scale graphs. In Proceedings of the 2019 IEEE International Conference on Cognitive Machine Intelligence. 53–60.
Yang Zhou, Ling Liu, and David Buttler. 2015. Integrating vertex-centric clustering with edge-centric clustering for meta path graph analysis. In Proceedings of the 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1563–1572.
Yang Zhou, Ling Liu, Kisung Lee, Balaji Palanisamy, and Qi Zhang. 2020. Improving collaborative filtering with social influence over heterogeneous information networks. ACM Transactions on Internet Technology 20, 4 (2020), 36:1–36:29.
Yang Zhou, Ling Liu, Kisung Lee, Calton Pu, and Qi Zhang. 2015. Fast iterative graph computation with resource aware graph parallel abstractions. In Proceedings of the 24th ACM Symposium on High-Performance Parallel and Distributed Computing. 179–190.
Yang Zhou, Ling Liu, Kisung Lee, and Qi Zhang. 2015. GraphTwist: Fast iterative graph computation with two-tier optimizations. Proceedings of the VLDB Endowment 8, 11 (2015), 1262–1273.
Yang Zhou, Ling Liu, Chang-Shing Perng, Anca Sailer, Ignacio Silva-Lepe, and Zhiyuan Su. 2013. Ranking services by service network structure and service attributes. In Proceedings of the 20th International Conference on Web Service. 26–33.
Yang Zhou, Ling Liu, Calton Pu, Xianqiang Bao, Kisung Lee, Balaji Palanisamy, Emre Yigitoglu, and Qi Zhang. 2015. Clustering service networks with entity, attribute and link heterogeneity. In Proceedings of the 22nd International Conference on Web Service. 257–264.
Yang Zhou, Ling Liu, Sangeetha Seshadri, and Lawrence Chiu. 2016. Analyzing enterprise storage workloads with graph modeling and clustering. IEEE Journal on Selected Areas in Communications 34, 3 (2016), 551–574.
Yang Zhou, Jiaxiang Ren, Dejing Dou, Ruoming Jin, Jingyi Zheng, and Kisung Lee. 2020. Robust meta network embedding against adversarial attacks. In Proceedings of the 20th IEEE International Conference on Data Mining. 1448–1453.
Yang Zhou, Jiaxiang Ren, Ruoming Jin, Zijie Zhang, Dejing Dou, and Da Yan. 2020. Unsupervised multiple network alignment with multinominal GAN and variational inference. In Proceedings of the 2020 IEEE International Conference on Big Data. 868–877.
Yang Zhou, Jiaxiang Ren, Sixing Wu, Dejing Dou, Ruoming Jin, Zijie Zhang, and Pengwei Wang. 2019. Semi-supervised classification-based local vertex ranking via dual generative adversarial nets. In Proceedings of the 2019 IEEE International Conference on Big Data. 1267–1273.
Yang Zhou, Sangeetha Seshadri, Lawrence Chiu, and Ling Liu. 2014. GraphLens: Mining enterprise storage workloads using graph analytics. In Proceedings of the 2014 IEEE International Congress on Big Data. 1–8.
Yang Zhou, Sixing Wu, Chao Jiang, Zijie Zhang, Dejing Dou, Ruoming Jin, and Pengwei Wang. 2018. Density-adaptive local edge representation learning with generative adversarial network multi-label edge classification. In Proceedings of the 18th IEEE International Conference on Data Mining. 1464–1469.
Yang Zhou, Zeru Zhang, Sixing Wu, Victor Sheng, Xiaoying Han, Zijie Zhang, and Ruoming Jin. 2021. Robust network alignment via attack signal scaling and adversarial perturbation elimination. In Proceedings of the 30th Web Conference. 3884–3895.
Qiannan Zhu, Xiaofei Zhou, Jia Wu, Jianlong Tan, and Li Guo. 2019. Neighborhood-aware attentional representation for multilingual knowledge graphs. In Proceedings of the 28th International Joint Conference on Artificial Intelligence. 1943–1949.
Yuke Zhu, Roozbeh Mottaghi, Eric Kolve, Joseph J. Lim, Abhinav Gupta, Li Fei-Fei, and Ali Farhadi. 2017. Target-driven visual navigation in indoor scenes using deep reinforcement learning. In 2017 IEEE International Conference on Robotics and Automation. 3357–3364.
Barret Zoph and Quoc V. Le. 2016. Neural architecture search with reinforcement learning. In Proceedings of the 2017 International Conference on Learning Representations.
Yang TYan FQiao FWang JQian Y(2025)Fusing Monotonic Decision Tree Based on Related FamilyIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.348764137:2(670-684)Online publication date: 1-Feb-2025
Peng YChen XMiao DQin XGu XLu P(2024)Multi-granularity attribute similarity model for user alignment across social platforms under pre-aligned data sparsityInformation Processing and Management: an International Journal10.1016/j.ipm.2024.10386661:6Online publication date: 1-Nov-2024
CIKM '21: Proceedings of the 30th ACM International Conference on Information & Knowledge Management
Network alignment, in general, seeks to discover the hidden underlying correspondence between nodes across two (or more) networks when given their network structure. However, most existing network alignment methods have added assumptions of additional ...
CIKM '21: Proceedings of the 30th ACM International Conference on Information & Knowledge Management
Nowadays, it is common for a person to possess different identities on multiple social platforms. Social network alignment aims to match the identities that from different networks. Recently, unsupervised network alignment methods have received ...
AAMAS '18: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems
This paper proposes adversarial attacks for Reinforcement Learning (RL). These attacks are then leveraged during training to improve the robustness of RL within robust control framework. We show that this adversarial training of DRL algorithms like Deep ...
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Yang TYan FQiao FWang JQian Y(2025)Fusing Monotonic Decision Tree Based on Related FamilyIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.348764137:2(670-684)Online publication date: 1-Feb-2025
Peng YChen XMiao DQin XGu XLu P(2024)Multi-granularity attribute similarity model for user alignment across social platforms under pre-aligned data sparsityInformation Processing and Management: an International Journal10.1016/j.ipm.2024.10386661:6Online publication date: 1-Nov-2024
Duan SLong YXiao YWang RLi Q(2024)E-commerce bookstore user alignment model based on multidimensional feature joint representation and implicit behavior compensationExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.122084238:PDOnline publication date: 27-Feb-2024
Peng YChen XMiao DQin XGu XLu P(2024)Unveiling user identity across social media: a novel unsupervised gradient semantic model for accurate and efficient user alignmentComplex & Intelligent Systems10.1007/s40747-024-01626-611:1Online publication date: 12-Nov-2024
Sun LLi MYang YLi XLiu LZhang PDu H(2024)Rcoco: contrastive collective link prediction across multiplex network in Riemannian spaceInternational Journal of Machine Learning and Cybernetics10.1007/s13042-024-02118-215:9(3745-3767)Online publication date: 5-Apr-2024
Luo CWang SLi TChen HLv JYi Z(2023)RHDOFS: A Distributed Online Algorithm Towards Scalable Streaming Feature SelectionIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2023.326597434:6(1830-1847)Online publication date: 1-Jun-2023
Yang LWang XZhang JYang JXu YHou JXin KWang F(2023)HackGAN: Harmonious Cross-Network Mapping Using CycleGAN With Wasserstein–Procrustes Learning for Unsupervised Network AlignmentIEEE Transactions on Computational Social Systems10.1109/TCSS.2022.314435010:2(746-759)Online publication date: Apr-2023
Saxena SChandra J(2023)EvoAlign: A Continual Learning Framework for Aligning Evolving Networks2023 IEEE 10th International Conference on Data Science and Advanced Analytics (DSAA)10.1109/DSAA60987.2023.10302602(1-10)Online publication date: 9-Oct-2023
