TY - JOUR
T1 - Alternating proximal gradient method for sparse nonnegative Tucker decomposition
AU - Xu, Yangyang
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2015/3
Y1 - 2015/3
N2 - Multi-way data arises in many applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is to decompose a given tensor into the product of a core tensor and several factor matrices with sparsity and nonnegativity constraints. An alternating proximal gradient method is applied to solve the problem. The algorithm is then modified to sparse NTD with missing values. Per-iteration cost of the algorithm is estimated scalable about the data size, and global convergence is established under fairly loose conditions. Numerical experiments on both synthetic and real world data demonstrate its superiority over a few state-of-the-art methods for (sparse) NTD from partial and/or full observations. The MATLAB code along with demos are accessible from the author’s homepage.
AB - Multi-way data arises in many applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is to decompose a given tensor into the product of a core tensor and several factor matrices with sparsity and nonnegativity constraints. An alternating proximal gradient method is applied to solve the problem. The algorithm is then modified to sparse NTD with missing values. Per-iteration cost of the algorithm is estimated scalable about the data size, and global convergence is established under fairly loose conditions. Numerical experiments on both synthetic and real world data demonstrate its superiority over a few state-of-the-art methods for (sparse) NTD from partial and/or full observations. The MATLAB code along with demos are accessible from the author’s homepage.
KW - Alternating proximal gradient method
KW - Non-convex optimization
KW - Sparse nonnegative Tucker decomposition
KW - Sparse optimization
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U2 - 10.1007/s12532-014-0074-y
DO - 10.1007/s12532-014-0074-y
M3 - Article
AN - SCOPUS:84923845547
VL - 7
SP - 39
EP - 70
JO - Mathematical Programming Computation
JF - Mathematical Programming Computation
SN - 1867-2949
IS - 1
ER -