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Hierarchical convex NMF for clustering massive data

: Kersting, K.; Wahabzada, M.; Thurau, C.; Bauckhage, C.

Journal of Machine Learning Research 13 (2010), S.253-268
ISSN: 1533-7928
ISSN: 1532-4435
Asian Conference on Machine Learning (ACML) <2, 2010, Tokyo>
Zeitschriftenaufsatz, Konferenzbeitrag
Fraunhofer IAIS ()

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 non- negative 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 i s also confirmed by our extensive evaluation on DBLP publication records of 760,000 authors, 4,000,000 images harvested from the web, and 150,000,000 votes on World of Warcraft guilds.