Alternating proximal gradient method for sparse nonnegative Tucker decomposition

Yangyang Xu

Optimization and Control mathscidoc:1912.43146

Mathematical Programming Computation, 7, (1), 39-70, 2015
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
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  title={Alternating proximal gradient method for sparse nonnegative Tucker decomposition},
  author={Yangyang Xu},
  booktitle={Mathematical Programming Computation},
Yangyang Xu. Alternating proximal gradient method for sparse nonnegative Tucker decomposition. 2015. Vol. 7. In Mathematical Programming Computation. pp.39-70.
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