Efficient Quantification of Profile Matching Risk in Social Networks Using Belief Propagation

Abstract

Many individuals share their opinions (e.g., on political issues) or sensitive information about them (e.g., health status) on the internet in an anonymous way to protect their privacy. However, anonymous data sharing has been becoming more challenging in today’s interconnected digital world, especially for individuals that have both anonymous and identified online activities. The most prominent example of such data sharing platforms today are online social networks (OSNs). Many individuals have multiple profiles in different OSNs, including anonymous and identified ones (depending on the nature of the OSN). Here, the privacy threat is profile matching: if an attacker links anonymous profiles of individuals to their real identities, it can obtain privacy-sensitive information which may have serious consequences, such as discrimination or blackmailing. Therefore, it is very important to quantify and show to the OSN users the extent of this privacy risk. Existing attempts to model profile matching in OSNs are inadequate and computationally inefficient for real-time risk quantification. Thus, in this work, we develop algorithms to efficiently model and quantify profile matching attacks in OSNs as a step towards real-time privacy risk quantification. For this, we model the profile matching problem using a graph and develop a belief propagation (BP)-based algorithm to solve this problem in a significantly more efficient and accurate way compared to the state-of-the-art. We evaluate the proposed framework on three real-life datasets (including data from four different social networks) and show how users’ profiles in different OSNs can be matched efficiently and with high probability. We show that the proposed model generation has linear complexity in terms of number of user pairs, which is significantly more efficient than the state-of-the-art (which has cubic complexity). Furthermore, it provides comparable accuracy, precision, and recall compared to state-of-the-art. Thanks to the algorithms that are developed in this work, individuals will be more conscious when sharing data on online platforms. We anticipate that this work will also drive the technology so that new privacy-centered products can be offered by the OSNs.

Appendices

Appendix

A Scalability of the BP-Based Algorithm

We study the effect of the OSNs’ size to precision and recall of the proposed algorithm. In Sect. 5.4, we provided the results when the number of users in OSN T is fixed. Here, we provide the results of the other two scenarios. In Fig. 7, for each dataset, we show the precision/recall values of the BP-based algorithm when the number of users in the target OSN (OSN T) increases while the number of auxiliary users (i.e., users in OSN A) is fixed. We set the number of users in OSN A as 1000 and increase the number of users in OSN T from 100 to 1000 in steps of 100.

In Fig. 8, for each dataset, we show the precision/recall values of the BP-based algorithm when the number of users in both OSNs (i.e., OSN A and T) increases from 100 to 1000 in steps of 100. In both scenarios, we observe that the precision/recall values of the proposed algorithm only slightly decrease with the increase of the number of users in the target OSN, or the increase of the number of users in both OSNs, which shows the scalability of our proposed algorithm.

Fig. 7.

The effect of target OSN’s (OSN T) size to precision/recall when the size of auxiliary OSN (OSN A) is 1000 in $\mathrm {D1}$, $\mathrm {D2}$, and $\mathrm {D3}$.

Fig. 8.

The effect of auxiliary and target OSNs’ (OSN A and T) size to precision/recall in $\mathrm {D1}$, $\mathrm {D2}$, and $\mathrm {D3}$.

To further check the effect of the auxiliary OSN’s size to precision and recall of the BP-based algorithm, we quantify the precision/recall values obtained by the proposed algorithm for larger scales in $\mathrm {D3}$. We fix the number of users in the target OSN (i.e., OSN T) to 1000 while the number of users in the auxiliary OSN (i.e., OSN A) increases from 1000 to 8000 in steps of 1000 (in Fig. 4 the number of users in OSN T was fixed to 100 while the number of users in OSN A was increasing from 100 to 1000). We show the results for $\mathrm {D3}$ in Fig. 9. The precision/recall values slightly decrease with the increase of the number of users in OSN A, confirming the scalability of the proposed algorithm. Note that, in $\mathrm {D3}$, we only use the graph connectivity attribute for profile matching. We expect that the decrease in precision/recall values will be smaller when both the graphical structure and other attributes of the users are used to generate the model.

Fig. 9.

The effect of auxiliary OSN’s (OSN A) size to precision/recall when the size of target OSN (OSN T) is 1000 in $\mathrm {D3}$.