Cooperative problem decomposition in Pareto competitive classifier models of coevolution
EuroGP'08 Proceedings of the 11th European conference on Genetic programming
Classification as clustering: A pareto cooperative-competitive gp approach
Evolutionary Computation
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A novel approach to the classification of large and unbalanced multi-class data sets is presented where the widely acknowledged issues of scalability, solution transparency, and problem decomposition are addressed simultaneously within the context of the Genetic Programming (GP) paradigm. A cooperative coevolutionary training environment that employs multi-objective evaluation provides the basis for problem decomposition and reduced solution complexity. Scalability is achieved through a Pareto competitive coevolutionary framework, allowing the system to be readily applied to large data sets without recourse to hardware-specific speedups. A key departure from the canonical GP approach to classification involves expressing the output of GP in terms of a non-binary, local membership function (Gaussian), where it is no longer necessary for an expression to represent an entire class. Decomposition is then achieved through reformulating the classification problem as one of cluster consistency, where individuals learn to associate subsets of training exemplars with each cluster. Classification problems are now solved by several specialist classifiers as opposed to a single 'super' individual. Finally, although multi-objective methods have been reported previously for GP classification domains, we explicitly formulate the objectives for cooperative behavior. Without this the user is left to choose a single individual as the overall solution from a front of solutions. This work is able to utilize the entire front of solutions without recourse to heuristics for selecting one individual over another or duplicating behaviors between different classifiers. Extensive benchmarking is performed against related frameworks for classification including Genetic Programming, Neural Networks, and deterministic methods. In contrast to classifiers evolved using competitive coevolution alone, we demonstrate the ability of the proposed coevolutionary model to provide a non-overlapping decomposition or association between learners and exemplars, while returning statistically significant improvements in classifier performance. In the case of the Neural Network methods, benchmarking is conducted against the more challenging second order neural learning algorithm of conjugate gradient optimization (previous comparisons limit Neural Network training to first order methods). The ensuing comparison indicated that most data sets benefit from the proposed algorithm, which remains competitive even against the well-established deterministic algorithms, such as C4.5.