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19 Artificial Immune Models
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Dendritic injection models the dendritic cells, which function in the natural immune system has only recently been understood The DWB-model has proven to be robust to noise, adaptive and scalable in learning antigen structures
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Adapted Arti cial Immune Network
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One of the drawbacks in the model of Timmis [845] is the di culty to keep the network size within certain boundaries through all the iterations This drawback makes the model unstable The model presented in [909] adapts the model in [845] with a few changes in the implementation Some of these changes are that the training set is used as the antigen set in the model with a set of randomly initiated antibodies The model in [845] randomly assigns the patterns in the training set to the antigen set and antibody set A further change to the model is in the initialization of the network a nity threshold (NAT) In [845] the NAT was calculated as an average distance between all the patterns in the antigen set In the adapted model, only the average distance between the n k lowest distances in the antigen set was calculated, where n is the size of the antigen set and k some constant The stimulation level of an antibody in the adapted model is de ned as the a nity between the antibody and the set of antigens The model in [845] considered the degree of stimulation of the antibody and the degree of suppression of the antibody by other antibodies The adapted model in [909] improves on the model in [845] in that the maximum network size is limited to the number of training patterns in the training set and stable clusters are formed with a minimal number of control parameters
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The aiNet model developed by De Castro and Von Zuben [184, 187] implements some of the principles found in the immune network theory A typical network in the model consists of nodes (the B-Cells or antibodies) which are connected by edges to form node pairs A weight value (connection strength) is assigned to each edge, to indicate the similarity between two nodes Thus, the network that is formed during training is presented by an edge-weighted graph Algorithm 198 summarizes aiNet aiNet uses clonal selection [97] to adapt the network of antibodies, B, to training patterns, DT Thus, the data in the training set is seen as antigens During training the model builds a network of memory cells to determine any clusters in the data The model uses Euclidean distance as a metric of a nity (or dissimilarity), d (zp , yj ), between a training pattern, zp , and an antibody, yj , in the network A higher value of d (zp , yj ) implies a higher degree of dissimilarity between an antibody and an antigen training pattern Clonal selection is applied to nh of the antibodies with the highest a nity (dissimilarity) to a speci c antigen The number of clones, nc , for each antibody, yj , is
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194 Network Theory Models
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Algorithm 198 aiNet Learning Algorithm Determine the antigen patterns as training set DT ; while stopping condition not true do for each antigen pattern, zp DT do for each antibody, yj B do Calculate the antigen a nity fa (zp , yj ); end Select nh of the highest a nity antibodies as set H; for each yj H do Create nc clones of yj ; Mutate the nc created clones and add to set H ; end for each yj H do Calculate the antigen a nity, fa (zp , yj ); end Select nh % of the highest a nity antibodies as set M; for each yj M do if fa (zp , yj ) > amax then Remove yj from M; end end for each yj1 M do for each yj2 M do Calculate the network a nity fa (yj1 , yj2 ); if fa (yj1 , yj2 ) < s then Mark yj1 and yj2 as elimination from M; end end end Remove all elimination antibodies from M; B = B M; end for each yj1 B do for each yj2 B do Calculate the network a nity, fa (yj1 , yj2 ); if fa (yj1 , yj1 ) < s then Mark yj1 and yj2 as elimination from B; end end end Remove all elimination antibodies from B; Replace nl % of the lowest a nity antibodies in B with randomly generated antibodies; end
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