Fusion of evolvable genome structure and multi-objective optimization for subspace clustering

Abstract

Subspace clustering techniques become paramount in pattern recognition for detecting local variations from high dimensional data. Several techniques exist in the recent literature for subspace clustering, majority of which optimize implicitly or explicitly a single cluster quality measure. Inspired by the success of multi-objective optimization in solving clustering problem, we developed a multi-objective based subspace clustering technique in this paper. The proposed technique simultaneously optimizes two subspace cluster quality measures, capable of capturing different cluster shapes/properties. Two existing cluster quality measures, XB-index and PBM-index, are modified to develop subspace cluster validity indices, and then those are used as optimization criteria. These cluster validity indices measure the appropriateness of generated subspace clusters in terms of intra-subspace cluster similarity and separation between subspace clusters. The proposed approach utilizes a new evolvable genome structure which stores the information about subspaces in its phenotype and genotype and evolves this genome structure with the help of different genetic operators. The developed algorithm is applied on ten standard real-life data sets and sixteen synthetic datasets for identifying different subspace clusters. The results obtained by this algorithm are compared against some state-of-the-art techniques with respect to different performance metrics. Experimentation reveals that the proposed algorithm is able to take advantages of its evolvable genomic structure and multi-objective based framework and it can be applied to any data set. In a part of the paper, the efficacy of the proposed technique is also shown for bi-clustering of gene-expression data sets.