Immunology as a Metaphor for Computational ... - Napier University

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Chapter 6. A Self-Organising SDM — SOSDM 1736.7.3 Making the System Truly DynamicIn order for SOSDM to operate in a truly unsupervised manner in a non-stationaryenvironment, SOSDM should be able to create and delete antibodies in response tothe data it is exposed to, as generally the number of antibodies required will not beknown a priori. [Fritzke, 1994] notes that a purely incremental approach to generatinga network or model is unsatisfactory in a dynamic environment, as the centres (or antibodiesin the SOSDM case) must be able to adapt to changing data, and that therefore,a model must also contain a mechanism for removing anibodies when appropriate.Possible ways of achieving this are now considered.6.7.3.1 Adding AntibodiesThe incremental algorithms proposed by Fritzke (e.g. [Fritzke, 1994, Fritzke, 1995]handles addition of nodes by simply adding new units after presentation of every λ inputsignals. This is unsatisfactory for SOSDM as we wish the number of antibodies tocorrelate with the number of clusters, hence using such an addition mechanism wouldwork only if combined with an efficient method of removing antibodies. Furthermore,the choice of λ is also difficult.The method used in COSDM, (chapter 5), was to add antibodies whenever theglobal fitness of the system had stagnated. This approach seems reasonable forCOSDM where the fitness measure of the system has a direct influence on the evolutionof the co-evolving populations of potential antibodies; in SOSDM on the otherhand, the global fitness or recall accuracy of the system is incidental — it does nothave any direct influence on the movement of antibodies during the self-organisationof the system. Therefore, this method appears somewhat of a ’cheat’ and again incurshigh overheads in having to calculate recall accuracy at every iteration.Therefore, a mechanism is suggested in which stagnation of the system is detectednot in respect to recall accuracy but in terms of movement of antibodies — if no movementof any antibody has happened over a fixed number of generations s (the stagnationthreshold) then an antibody is added. The new antibody is generated in a randomposition with its counters initialised to zeros.
Chapter 6. A Self-Organising SDM — SOSDM 1746.7.3.2 Deletion[Fritzke, 1997a] suggests a method of deleting ’dead units’ when trying to track nonstationarydistributions using the GNG algorithm that involves a local utility measure.In the typical GNG application, it is possible to compute how much the error for somegiven input signal ξ would increase if the winning unit s 1 were not present, and thesignal instead had to be mapped to the runner-up unit, s 2 . The increase in error is2 . This allows the total utility of each unit to bethen2simply ξ w m s2 ξ w m m s1 mcalculated by summing the utilities over all input signals, and then a unit is removedwhenever its utility falls below some predefined threshold. However, this method doesnot transfer well to SOSDM; in the pure GNG algorithm, error is easily calculated as2 , but in SOSDM, although the winning antibodies are determined based onξ w m s2 mthe correlation between the address of the antibody and the data to be stored, the errorin the recall accuracy depends also on the counters stored at the physical address. Secondly,the recall error can only be calculated once all data has been stored, and hencethere is an extremely high overhead in calculating such a utility measure, especially ina very large database. For these reasons, the use of a utility function was rejected as amethod of deleting nodes.The following method of deleting antibodies is suggested :- the sum of the bindingaffinities of the antibody with all its binding antigens, R is compared to the total bindingaffinity the antibody would exhibit if it had bound to all available antigens; if theratio of these quantities is less than some predefined percentage d (the deletion threshold),then the antibody is deleted. However, as in the COSDM model, an antibody isallowed to exist for at least n epochs after creation in order to give it an opportunityto survive. Furthermore, a caveat is applied that if an antibody uniquely recognises atleast one antigen, then it is allowed to remain.6.7.3.3 ResultsA series of experiments was performed in which SODSM was used to try and clusterthe half-schema, quarter-schema and eighth-schema data used throughout this thesis.Each dataset contained 200 antigens, and in each experiment SOSDM was initialisedwith 2 antibodies. The stagnation threshold s is set to 10 iterations, and the deletion
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AbstractThe biological immune syste
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DeclarationI declare that this thes
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Table of Contents1 Introduction 11.
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Chapter 4Applying an Immune System
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Page 220 and 221: Bibliography 205[Farmer et al., 198
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Page 224 and 225: Bibliography 209[Kohonen, 1982b] Ko
Page 226 and 227: Bibliography 211[Potter and De Jong
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