Alternating proximal gradient method for sparse nonnegative Tucker decomposition

TL;DR

This paper introduces an alternating proximal gradient method for sparse nonnegative Tucker decomposition, effectively handling missing data and demonstrating superior performance on synthetic and real datasets.

Contribution

The paper proposes a novel APG algorithm for sparse NTD with convergence guarantees and scalability, improving over existing methods especially with incomplete data.

Findings

Algorithm achieves scalable per-iteration cost

Global convergence under loose conditions

Outperforms state-of-the-art methods on real data

Abstract

Multi-way data arises in many applications such as electroencephalography (EEG) 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 (APG) 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.