DDoS attack detection in smart grid network using reconstructive machine learning models

Proposed class specific reconstruction based method for classification

The presented approach for DDoS attack detection based on reconstructive models consists of two primary stages. Firstly, we train a global domain-specific reconstructive model using the entire dataset in an unsupervised manner. In the second stage, we train class-specific reconstructive models by utilizing the global representation as an initial starting point. This methodology enables the encoding of both domain-specific and class-level data characteristics. Let $\mathbf{T}={\left\{{\mathbf{X}}_n\right\}}_{n=1}^c\in {\mathbb{R}}^{d\times N}$ be the training data for c attack classes having N samples: $N={\sum }_{n=1}^c{s}_n$ in total, where s_n represents the count of training samples within the attack class denoted by index n which is defined as ${\mathbf{X}}_n={\left\{{\mathbf{x}}_n^i\right\}}_{i=1}^{s_n}\in {\mathbb{R}}^{d\times s_n}$ (where ${\mathbf{x}}_n^i\in {\mathbb{R}}^d$ is a d-dimensional feature vector. While the value of s_n may vary among different training classes, the dimension of ${\mathbf{x}}_n^i$ will remain consistent.Consider Y as the set of class labels, denoted as ${y_n}_{n=1}^c$, corresponding to the training classes within T. Our task of DDoS attack detection aims to predict the label y_t for the test sample x_t using the training dataset T.

Training stage: During the training stage, we initiate the weights of a multi-layer neural network, forming a global domain-specific reconstructive model, using the autoencoder training. This model comprises h hidden layers and its parameters are acquired through an unsupervised manner utilizing all the available samples in T. We represent the global reconstructive model as L_G, composed of its constituent parts ${\mathbf{W}}_G^1,\dots ,{\mathbf{W}}_G^{h+1}$. Each ${\mathbf{W}}_G^i$ corresponds to the parameter matrix of layer i, obtained using auto-encoding training techniques. This global reconstructive model serves as an initial framework, upon which we build class-specific reconstructive models in our subsequent stages.

As L_G encapsulates domain-specific representation, acquired through its training to reconstruct samples from that domain, we can employ it to build distinct reconstructive models for all the c training classes separately. That is, rather than starting with random initialization for the hidden layer weights, we preferred to employ the weights contained within L_G as the initial settings for our class-specific models. As a result, we establish a total of c reconstructive models, each tailored to one of the c classes, denoted as Ljj = 1^c. Each class-specific model is explicitly defined as ${\mathbf{L}}_j={\mathbf{W}}_j^1,\dots ,{\mathbf{W}}_j^{h+1}$.

Testing stage: During the testing stage, we reconstruct a given test sample ${\mathbf{x}}_t^i$ by applying each class-specific model from the set Ljj = 1^c. The reconstructed sample obtained by the model Lj is represented as $\hat{\mathbf{x}}{tj}^i$ and can be defined as: (1)${\displaystyle {\hat{\mathbf{x}}}_{tj}^i=f\left({\mathbf{x}}_{tj}^i,{\mathbf{L}}_j\right)={\mathbf{W}}_j^{h+1}g\left({\mathbf{W}}_j^h,\dots ,g\left({\mathbf{W}}_j^1{\mathbf{x}}_t^i\right)\right)}$ where the reconstruction function is denoted as f, and g represents the activation function used by the layers. To quantify the reconstruction error for a given sample xtⁱ, we compute the distance (e.g., Euclidean) between sample xtⁱ and sample ${\hat{\mathbf{x}}}^{i}tj$, which is expressed as $e^i\left(j\right)=|{\mathbf{x}}_t^i-{\hat{\mathbf{x}}}^{i}tj{|}_2$. Subsequently, the estimated label $l_t^i$ for ${\mathbf{x}}_t^i$ is determined by identifying the class associated with the minimum reconstruction error. (2)${\displaystyle l_t^i=\underset{j}{argmin}{\mathbf{e}}^i\left(j\right).}$

The entire process of the two stages discussed is outlined in Algorithm 1 .

 
_______________________ 
Algorithm 1 Proposed Reconstructive Model Based Attack Classification Al- 
gorithm_____________________________________________________________________________________________ 
Require: : 
  Training Dataset T containing c sets of attack samples Xs  = {xim}sm 
i=1  ∈ 
 Rd×sm grouped into c categories 
  Labels of classes denoted by Y = {ym}cm=1 
    Test sample xit ∈ Rd 
    Hidden layers h 
Ensure: : The predicted label yt for xt. 
Ensure: : Predicted Label yt for xt. 
  Training Phase: 
  Train Global Reconstructive Model LG = {W1G,...,Wh+1 
G   } using the entire 
   T and h hidden layers. 
  for j = 1 : c do 
      Train individual reconstructive models Lj  =  {W1j,...Wh+1 
j    } for each 
   class. 
  Testing Phase: 
  for j = 1 : c do 
      Reconstruct Test Sample: ˆ xitj = f(xit;Lj) {Reconstruction (??)} 
    Compute Reconstruction Error: ei(j) = ∥xit − ˆ xitj∥2 
    Predicted Label: lit ≜ arg min 
     j       ei(j)______________________________________________________    

Different classes of autoencoders used for learning representations

An autoencoder is a neural network architecture trained via a back-propagation algorithm, wherein the input values are set equivalent to the target values, which blend into the input samples themselves. An autoencoder comprises two essential components: an encoder denoted as h(⋅), responsible for mapping an input data point x_i ∈ ℝ^d as a latent expression h(xi) ∈ ℝ^dh, further a decoder, referred to as g(⋅), tasked with reconstructing the input data x_i from this latent representation, ensuring that g(h(x_i)) ≈ x_i. The measure of this reconstruction is estimated using a predefined loss function l(x_i, g(h(x_i))), which quantifies the dissimilarity between the original data and its reconstructed part. The primary purpose is to minimize this loss function to adapt and optimize the parameters of the autoencoder. Various forms of loss functions are available, including but not confined to squared error loss or the Kullback–Leibler ($\mathcal{KL}$) divergence. In the field of machine learning literature, various types of autoencoders have previously been introduced (Rifai et al., 2011; Baldi & Hornik, 1989; Vincent et al., 2008; Williams & Hinton, 1986; Lee et al., 2009; Kavukcuoglu et al., 2009). In this article, we explore three types of autoencoders for our algorithm. These include the deep autoencoder, extreme learning machine autoencoder, and the marginalized denoising autoencoder. The encoders are explained briefly in the next sections.

UNB ISCX Intrusion Detection Evaluation 2012 dataset

One of the datasets available publicly we incorporated for experimental analysis is the UNB ISCX Intrusion Detection Evaluation 2012 dataset (Ali & Li, 2019) referred to as IDE2012. We utilized two testbeds within this dataset. The first one is the testbed of 11th June, named IDE2012/11, and the second is the 16th June testbed referred to as IDE2012/16 as documented in UNB (2012). IDE2012/11 testbed contains 204 features each for 325,757 samples. IDE2012/16 testbed contains a total sample of nearly 464,989 and contains 204 features each. Labels provided for each sample are unrated, acceptable, safe, and unsafe. We further discretized these labels as unsafe (1), and safe (0) for simplification. Some of the significant attributes of each data packet are event generator, ndpi risk, Payload byte first, source and destination port, event priority and ndpi detected protocol, etc. 15% of this dataset (10,000 packets) demonstrated signs of DDoS attack infection. This observed infection rate serves to emphasize the prevalence and impact of DDoS attacks within the dataset. Part of this data set is shown in Table 2.

To assess the adaptability of our model among varying portions of data, we selected 10,000 samples randomly of every dataset. Additionally, extending beyond the traditional two classes 0 for safe and 1 for unsafe, our evaluation encompasses four-class classification settings. Designated labels are 0 for safe, 1 for unsafe, 2 for acceptable, and 3 for unrated. A breakdown of these dataset divisions along with names are shown in Table 3.

UNSW-NB15 dataset

One of the publicly available intrusion detection data set used in our experiments is UNSW-NB15 (UNSW, 2015) dataset. Australian university named The University of New South Wales (UNSW), created the data set utilizing the IXIA perfect-storm tool and offers extensive network data of 700,001 samples with 49 features each, captured under a controlled environment. To push the limits of the proposed method, we further partitioned the UNSW-NB15 dataset into four distinct subsets are shown in Table 4.

A few features of the UNSW-NB15 dataset are attack category, source IP, transaction protocol, record start time, destination IP, source jitters (mSec), duration, etc. For experimentation, we transformed non-numerical features into discrete features. We further discretized the provided label and assigned “attack” a value of 0 and “non-attack” a value of 1.

Impact of number of neurons over accuracy

We have evaluated the accuracy of the proposed technique by integrating varying numbers of Neurons to construct the ultimate classifier. The datasets used for experimentations are D1 to D9. Precisely, we changed the amount of Neurons to be combined, between 2 to 10. Furthermore, we randomly selected the number of layers for each Neuron from the set L_m = [1, 3, 5, 7, 9, 11]. Subsequently, these Multi-layer Stacked Denoising Autoencoders (MSDAs) are fused using the Reconstructive-based scheme for classification, resulting in the creation of our final classifier.

The accuracy results presented in Figs. 6, 7, 8 show the variation in performance by varying numbers of MSDAs for each dataset. Eventually, the accuracy improved with the increment of MSDAs.Evidently, as the number of MSDAs increases, the accuracy improves across all datasets and starts saturating at approximately six MSDAs. This trend underscores the effectiveness of the proposed fusion approach.