Alternative Representations for Artificial Immune Systems

Artificial Immune Systems (AIS) have been proposed to solve binary classification problems; distinguishing between instances of self and of non-self. For any classification system such as AIS, the choice of classifier representation used impacts substantially on the kind of classification problem that can be handled. Despite this, most classication systems such as AIS make use of only one representation, frequently without explicit consideration of its suitability to the classification problem of interest. As many AIS make use of binary encoding, AIS are thus frequently being applied to boolean functions. One other notable field of classification system research is also applied extensively to boolean functions, namely Learning Classifier Systems (LCS). Here we consider boolean functions and the suitability of different representations for their classification. We compare a simple representation proposed for use in AIS, Hammingdistance based matching, with a traditional representation from Learning Classifier Systems (LCS), binary classifiers with wildcards. These different representations realise different shapes in a high-dimensional instance space; hyperspheres (AIS) and hyperplanes (LCS). In fact, hyperplanes are a more general case of the kind of classifiers implemented for use with the r-chunks matching rule in AIS (Balthrop et al., 2002). We consider the different characteristics of these representations, analysing how their size (number of instances covered) and instance space size (number of distinct classifiers) varies differently with both problem size (instance string length) and classifier size (hyperplane dimension or hypersphere radius). As well as these differences, we consider how hyperspheres and hyperplanes differ in the way in which they generalise. These differences are likely to mean that the traditional hypersphere-based AIS representation is of limited applicability. For example, it is likely that many boolean functions cannot be well covered by sets of general hypersphere classifiers, unless specificity of matching is used to arbitrate between multiple classifiers matching a single instance. Similarly, differences in the generalisation mechanisms of the two representations mean that increasing the dimensionality of a problem, through increasing the number of its attributes, will have different consequences according to which representation is used. As well as the usefulness per se of analysing differences between classifier representations, implementing a suite of alternatives may enable a classification system to learn to use the most appropriate one when faced with a particular classification problem (Marshall and Kovacs, 2006), or even to evolve new representations. While the maintenance of detectors using different representations has already been proposed for AIS, this has been achieved by random permutations on bit order of the detector strings (Hofmeyr and Forrest, 2000). Our results show, that as the number and size of classifiers is different when using hyperplane or hypersphere representations (Marshall and Kovacs, 2006), a simple permutation on the detector string is insufficient to map between the different representations. The different representations have different informational content, and hence offer genuine differences to each other. We thus propose going beyond simple permutation in maintaining diversity of representations in an AIS.