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where n is computed for output unit n using Formula 137 Hence, after the input from each input-output pair in the training data set is fed to the ANN which produces the actual output, the connection weights to the output units are rst adjusted according to Formulas 135 and 137, followed by the adjustment of the connection weights to the units in the hidden layer preceding to the output layer according to Formulas 135 and 1310 If there is another hidden layer, the connection weights to that hidden layer can be adjusted in the same manner using Formulas 135 and 1310 This process gives the following back-propagation learning algorithm which adjusts the connection weights in a back-propagation manner from the output layer to the hidden layer if the ANN has one hidden layer [1]: Step 1 Step 2 Step 3 Step 4 Step 5 Present i p to the ANN, obtain o p Adjust the connection weights to the output layer using Formulas 135 and 137 Adjust the connection weights to the hidden layer using Formulas 135 and 1310 Repeat Steps 1 3 for all p Repeat Steps 1 4 until there is no signi cant change of the connection weights or the error of the actual output from the target output is below a pre-set threshold
132 THE ANN APPLICATION TO CYBER ATTACK DETECTION
The Windows performance objects data described in 7 is used to test the ANN application to cyber attack detection through signature recognition Table 131 collects the mean shift attack characteristics in Table 81, the distribution change attack characteristics in Table 91, the autocorrelation change attack characteristics in Table 101, and the wavelet change attack characteristics in Table 111 For each attack characteristic in Table 131, two feedforward ANNs are developed for the combinations of the attack with the text editing norm and the web browsing norm, respectively Each ANN has one input that takes the value of the data variable involved in the attack characteristic The ANN has one hidden layer of 20 units, and one output layer of one unit whose target value is close to 1 for attack and 0 for normal use The sigmoid activation function is used for each unit of the ANN For the combination of the attack and the text editing norm, the attack data from Run 1 of the data collection and the rst 300 observations of the text editing data from Run 2 of the data collection are used to train the ANN to learn attack signature patterns and normal use patterns Only the attack signature patterns are needed to recognize attacks for cyber attack detection However, the normal use data is necessary in training the ANN because the ANN needs the contrast of the attack data and the normal use data to learn attack signature patterns that are distinguishable from normal use patterns Statistica Neural Networks [2] is the software used to build the ANN The back-propagation learning algorithm with the time-varying learning rate, case-presentation order shuf ing and additive noise for robust generalization is used to train the ANN A threshold is selected by the software during the training to classify the output value of the ANN into attack or normal use If the output value is greater than the threshold, the output is classi ed as attack; otherwise, the output is classi ed as normal use The threshold is selected by the software to minimize the classi cation error when comparing the actual outputs with the target outputs of the training data The trained ANN is tested on the testing data that includes the remaining 300 observations of the text editing data from Run 2 of the data collection and the mixed attack and norm data from Run 2 of the data collection Each data observation in the testing data set is classi ed by the ANN as attack or normal use
Table 131 A list of attack characteristics used to build and test cyber attack detection models Attacks Apache ARP Distributed WML WDaL+ DUS A DUR WPH+ DUS Fork FTP Hardware Remote Rootkit Security Software Vulnerability WDL A+