Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization

Yanfeng Sun, Junbin Gao, Xia Hong, Bamdev Mishra, Baocai Yin

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Original languageEnglish
Article number7182334
Pages (from-to)476-489
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume38
Issue number3
Early online dateAug 2015
DOIs
Publication statusPublished - 01 Mar 2016

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