Multi-Objective Genetic Algorithm for Robust Clustering with Unknown Number of Clusters

Multi-Objective Genetic Algorithm for Robust Clustering with Unknown Number of Clusters

Amit Banerjee (The Pennsylvania State University, USA)
Copyright: © 2012 |Pages: 20
DOI: 10.4018/jaec.2012010101

Abstract

In this paper, a multi-objective genetic algorithm for data clustering based on the robust fuzzy least trimmed squares estimator is presented. The proposed clustering methodology addresses two critical issues in unsupervised data clustering – the ability to produce meaningful partition in noisy data, and the requirement that the number of clusters be known a priori. The multi-objective genetic algorithm-driven clustering technique optimizes the number of clusters as well as cluster assignment, and cluster prototypes. A two-parameter, mapped, fixed point coding scheme is used to represent assignment of data into the true retained set and the noisy trimmed set, and the optimal number of clusters in the retained set. A three-objective criterion is also used as the minimization functional for the multi-objective genetic algorithm. Results on well-known data sets from literature suggest that the proposed methodology is superior to conventional fuzzy clustering algorithms that assume a known value for optimal number of clusters.
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Genetic Algorithms In Robust Clustering

The clustering problem is often mapped to one of searching for an optimum partition from all possible and valid partitions such that some goodness of fit criterion is optimized. It can therefore be formally considered a particular class of NP-hard problem (Falkenauer, 1998) which has led to the development of efficient metaheuristics to provide near-optimal solutions in reasonable time. Evolutionary algorithms are a class of population-based optimization techniques that mimic the biological evolution process and include among others genetic algorithms (GA), genetic programming (GP), evolutionary strategies (ES), evolutionary programming (EP) and newer techniques such as differential evolution (DE) and memetic algorithms (MA). These methods solve the optimization problem by evolving a population of possible solutions by using a set of evolutionary operators that act on solutions based on their relative fitness. The methods differ in the way they represent potential solutions and the way the evolutionary operators are handled, which dictates their applicability to certain types of optimization problems. Selection, crossover and mutation are the most widely used evolutionary operators. The population evolves when the selection operator chooses a subset of the fittest solutions in the present generation to reproduce using recombination operators such as crossover and mutation. The evolved population on the average is fitter than the population it replaces.

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