Orthogonal Nonnegative Tucker Decomposition

Junjun Pan; Michael K. Ng; Ye Liu; Xiongjun Zhang; Hong Yan

doi:10.1137/19m1294708

Orthogonal Nonnegative Tucker Decomposition

Junjun Pan, Michael K. Ng, Ye Liu, Xiongjun Zhang, Hong Yan

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

18 Citations (Scopus)

Abstract

In this paper, we study nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.

Original language	English
Pages (from-to)	B55-B81
Number of pages	27
Journal	SIAM Journal on Scientific Computing
Volume	43
Issue number	1
DOIs	https://doi.org/10.1137/19m1294708
Publication status	Published - Jan 2021

User-Defined Keywords

nonnegative tensor
Tucker decomposition
image processing

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10.1137/19m1294708

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abstract = "In this paper, we study nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.",

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AB - In this paper, we study nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.

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Orthogonal Nonnegative Tucker Decomposition

Abstract

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