What is Symmetry Based Distance

Identification of cancer subtypes is the central goal in the cancer gene expression data analysis. Modified symmetry-based clustering is an unsupervised learning technique for detecting symmetrical convex or non-convex shaped clusters. To enable fast automatic clustering of cancer tissues (samples), in this chapter, the authors propose a rough set based hybrid approach for modified symmetry-based clustering algorithm. A natural basis for analyzing gene expression data using the symmetry-based algorithm is to group together genes with similar symmetrical patterns of microarray expressions. Rough-set theory helps in faster convergence and initial automatic optimal classification, thereby solving the problem of unknown knowledge of number of clusters in gene expression measurement data. For rough-set-theoretic decision rule generation, each cluster is classified using heuristically searched optimal reducts to overcome overlapping cluster problem. The rough modified symmetry-based clustering algorithm is compared with another newly implemented rough-improved symmetry-based clustering algorithm and existing K-Means algorithm over five benchmark cancer gene expression data sets, to demonstrate its superiority in terms of validity. The statistical analyses are also performed to establish the significance of this rough modified symmetry-based clustering approach.