Low-rank doubly stochastic matrix decomposition for cluster analysis

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2016-10-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
25
Series
Journal of Machine Learning Research, Volume 17
Abstract
Cluster analysis by nonnegative low-rank approximations has experienced a remarkable progress in the past decade. However, the majority of such approximation approaches are still restricted to nonnegative matrix factorization (NMF) and su er from the following two drawbacks: 1) they are unable to produce balanced partitions for large-scale manifold data which are common in real-world clustering tasks; 2) most existing NMF-type clustering methods cannot automatically determine the number of clusters. We propose a new low-rank learning method to address these two problems, which is beyond matrix factorization. Our method approximately decomposes a sparse input similarity in a normalized way and its objective can be used to learn both cluster assignments and the number of clusters. For efficient optimization, we use a relaxed formulation based on Data-Cluster-Data random walk, which is also shown to be equivalent to low-rank factorization of the doublystochastically normalized cluster incidence matrix. The probabilistic cluster assignments can thus be learned with a multiplicative majorization-minimization algorithm. Experimental results show that the new method is more accurate both in terms of clustering large-scale manifold data sets and of selecting the number of clusters.
Description
Keywords
Cluster analysis, Doubly stochastic matrix, Manifold, Multiplicative updates, Probabilistic relaxation
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Citation
Yang , Z , Corander , J & Oja , E 2016 , ' Low-rank doubly stochastic matrix decomposition for cluster analysis ' , Journal of Machine Learning Research , vol. 17 . < http://www.jmlr.org/papers/volume17/15-549/15-549.pdf >