Objective function based fuzzy subspace clustering

Abstract

Clustering aims at grouping data objects into classes so that the objects within a class are similar while the objects in different classes are dissimilar. Conventional clustering algorithms compute the distances between objects in the entire space of dimensions. However, as the number of dimensions increases, the data objects become sparse. Indeed any two points may become nearly equidistant. In such scenarios, clusters are often hidden in specific subspaces of the original feature space rather than in the original feature space. To overcome this difficulty a new methodology called subspace clustering has been developed. Subspace clustering finds clusters on the subsets of dimensions of a data set. However, different dimensions may be relevant to different clusters to varying degree. A refinement of subspace clustering called soft subspace clustering attempts to cluster data objects in the entire data space with continuous feature weighting. Potential target application areas of the subspace clustering algorithms are bio-informatics, text mining, and image processing, to mention just a few. In this thesis, we have proposed modifications of the following objective function based algorithms for the purpose of subspace clustering: Gustafson Kessel algorithm, Rough Fuzzy c-Means algorithm, Fuzzy Entropy clustering algorithm, and Possibilistic c-Means algorithm. The output of each algorithm comprises of a partitioning of the data set at hand along with assignment of weights to attributes specific to each cluster. Higher weight of an attribute in a cluster indicates its greater relevance to that cluster. We have proved the convergence of the algorithms presented in the thesis. We have shown through extensive experimentation that the proposed algorithms for subspace clustering either outperform the existing algorithms or produce comparable results in terms of validity measures and are effective in detecting low dimensional clusters embedded in high dimensional spaces.