Clustering and metaclustering with nonnegative matrix decompositions

Abstract

Although very widely used in unsupervised data mining, most clustering methods are affected by the instability of the resulting clusters w.r.t. the initialization of the algorithm (as e.g. in k-means). Here we show that this problem can be elegantly and efficiently tackled by meta-clustering the clusters produced in several different runs of the algorithm, especially if "soft" clustering algorithms (such as Nonnegative Matrix Factorization) are used both at the object- and the meta-level. The essential difference w.r.t. other metaclustering approaches consists in the fact that our algorithm detects frequently occurring sub-clusters (rather than complete clusters) in the various runs, which allows it to outperform existing algorithms. Additionally, we show how to perform two-way meta-clustering, i.e. take both object and sample dimensions of clusters simultaneously into account, a feature which is essential e.g. for biclustering gene expression data, but has not been considered before. © Springer-Verlag Berlin Heidelberg 2005.