A convex semi-nonnegative matrix factorisation approach to fuzzy c-means clustering

Abstract

We propose an alternative approach to fuzzy c-means clustering which eliminates the weighting exponent parameter of conventional algorithms. It is based on a particular convex factorisation of data matrix. The proposed method is invariant under certain linear transformations of the data including principal component analysis. We tested its accuracy using both synthetic data and real datasets, and compared it to that provided by the usual fuzzy c-means algorithm. We were able to ascertain that our proposal can be a credible yet easier alternative to this approach to fuzzy clustering. Moreover, it showed no noticeable sensitivity to the initial guess of the partition matrix.