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Non-negative Tri-factor tensor decomposition with applications

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Abstract

Non-negative matrix factorization (NMF) mainly focuses on the hidden pattern discovery behind a series of vectors for two-way data. Here, we propose a tensor decomposition model Tri-ONTD to analyze three-way data. The model aims to discover the common characteristics of a series of matrices and at the same time identify the peculiarity of each matrix, thus enabling the discovery of the cluster structure in the data. In particular, the Tri-ONTD model performs adaptive dimension reduction for tensors as it integrates the subspace identification (i.e., the low-dimensional representation with a common basis for a set of matrices) and the clustering process into a single process. The Tri-ONTD model can also be regarded as an extension of the Tri-factor NMF model. We present the detailed optimization algorithm and also provide the convergence proof. Experimental results on real-world datasets demonstrate the effectiveness of our proposed method in author clustering, image clustering, and image reconstruction. In addition, the results of our proposed model have sparse and localized structures.

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Zhang, ZY., Li, T. & Ding, C. Non-negative Tri-factor tensor decomposition with applications. Knowl Inf Syst 34, 243–265 (2013). https://doi.org/10.1007/s10115-011-0460-y

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