Hierarchical Convex NMF for Clustering Massive Data

We present an extension of convex-hull non-negative matrix factorization (CH-NMF) which was recently proposed as a large scale variant of convex non-negative matrix factorization or Archetypal Analysis. CH-NMF factorizes a non-negative data matrix V into two nonnegative matrix factors V WH such that the columns of W are convex combinations of certain data points so that they are readily interpretable to data analysts. There is, however, no free lunch: imposing convexity constraints on W typically prevents adaptation to intrinsic, low dimensional structures in the data. Alas, in cases where the data is distributed in a non-convex manner or consists of mixtures of lower dimensional convex distributions, the cluster representatives obtained from CH-NMF will be less meaningful. In this paper, we present a hierarchical CH-NMF that automatically adapts to internal structures of a dataset, hence it yields meaningful and interpretable clusters for non-convex datasets. This is also confirmed ...

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Kristian Kersting, Mirwaes Wahabzada, Christian Thurau, Christian Bauckhage
• Keywords: Convex Non-negative Matrix, Convex-hull Non-negative Matrix, JMLR 2010, Non-Negative Matrix Factorization