Research On Integrated Clustering Based On Nonnegative Matrix Decomposition

We address the problem of combining multiple partitions (or clusterings) into a single consolidated partition (or clustering). Our approach for this problem is based on nonnegative matrix factorization (NMF), which decomposes the input cluster assignment matrix into two matrices H and W. Starting from a straight-forward application of standard NMF, we reasonably extend the general approach of NMF into two directions:CNA (Cluster-wise weighted NMF-based Aggregation) and INA (Instance-wise weighted NMF-based Aggregation). CNA incorporates cluster weights by considering the difference of local cluster reliability in partitions, while INA incorporates instance weights further considering both instance and cluster reliability. For both CNA and INA, we develop an efficient optimization algorithm for estimating parameters by repeating1) updating H and W fixing weights and2) updating weights fixing H and W, alternately. The first update exactly follows the well-established algorithm of the standard NMF while the second update is derived from an analytic solution of our problem formulation. Thus our algorithm is time-efficient, comparing to usual NMF-based approaches for ensemble clustering. We empirically evaluated the performance of our three proposed approaches using various benchmark datasets, comparing with six existing methods for ensemble clustering. Experimental results indicate that our method outperformed all other compared methods, being statistically significant, under various experimental settings.