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Matrix factorization-based methods become popular in dyadic data analysis, where a fundamental problem, for example, is to perform document clustering or co-clustering words and documents given a term-document matrix. Nonnegative matrix tri-factorization (NMTF) emerges as a promising tool for co-clustering, seeking a 3-factor decomposition X≈USV? with all factor matrices restricted to be nonnegative, i.e., U?0,S?0,V?0. In this paper we develop multiplicative updates for orthogonal NMTF where X≈USV? is pursued with orthogonality constraints, U?U=I, and V?V=I, exploiting true gradients on Stiefel manifolds. Experiments on various document data sets demonstrate that our method works well for document clustering and is useful in revealing polysemous words via co-clustering words and documents. 相似文献
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