Arbitrary shape clustering via NMF factorization

Organizing data into clusters is a key task for data mining problems. In this paper we address the problem of arbitrarily shaped clustering of points belonging to a linear space. A model based on the Euclidean distance is assumed to define the similarity among the points. An algorithm, based on the symmetric nonnegative matrix factorization (NMF) of the similarity matrix, is proposed. The main contribution of our approach consists in the merging technique of the clusters which exploits information already contained in the matrix obtained by NMF. Extensive experimentation shows that the proposed algorithm is effective and robust also for noisy data.