χ2-BidLSTM: A Feature Driven Intrusion Detection System Based on χ2 Statistical Model and Bidirectional LSTM

. 2022 Mar 4;22(5):2018. doi: 10.3390/s22052018

Algorithm 1.

χ^{2}

-BidLSTM implementation process

▹ Obtain the $χ^{2}$ test scores for each feature using $χ^{2}$ statistical model

▹ Rank(sort) the features in descending order based on their $χ^{2}$ test scores

1:
$a r r$ ← {}
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for i ← 1 to n do
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$t e s t_s c o r e \leftarrow c h i . s q a u r e d (D [i], L)$ ▹ Compute the $χ^{2}$ score between features in the dataset D and class labels L
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append (i, $t e s t_s c o r e$ ) to $a r r$
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end for
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rank the features of $a r r$ ▹ Sort the features in a descending order based on their $χ^{2}$ test scores
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store the feature scores of $a r r$ to $S E L E C T E D$
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return $S E L E C T E D$

▹ Find the features with the highest test value $(v_m a x)$ from the ranked features

▹ Obtain the best feature subset for training using forward search
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$S E L E C T E D$ ← {}
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$v_m a x$ ←−1
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$S u b F$ ← index of D
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while $S u b F$ != NULL do
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$i n d e x \leftarrow N U L L$
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for i ← 0 to $S u b F$ length do
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$t e m p f e a t u r e_l i s t \leftarrow (S E L E C T E D \cup S u b F [i])$
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$t e m p v \leftarrow v (t e m p f e a t u r e_l i s t)$
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if $t e m p v > v_m a x$ then
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index ← i
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end if
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end for
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if index == NULL then
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break
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else
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append $S u b F [i n d e x]$ to $S E L E C T E D$
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Remove $S u b F [i n d e x]$ from $S u b F$
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end if
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end while
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return $S E L E C T E D$ as optimal set

▹ Model training interface with a K-fold cross-validation using the optimal set
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for f = 1 to k do
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[ ]Training_set = New_List[ $| V |$ ]
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[ ]Testing_set = New_List[ $| V |$ ] ▹ Construct the training set
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for m = 1 to k do
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if m == f then
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continue
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end if
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for v = 1 to $| V |$ do
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Train[v] + fold[v][m]
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end for
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end for ▹ Construct the testing set
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for v = 1 to $| V |$ do
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Test[v] + fold[v][m]
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end for ▹ Fit BidLSTM model for training and testing
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model = BidLSTM()
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BidLSTM.Fit(Train) ▹ Train model with K-1 folds
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Evaluate model perfomance with remaining Kth folds
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scores = cross_val_scores()
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Return scores ▹ Return the classification accuracy and validation scores
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end for
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Test model with an unseen test dataset
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Return test scores