# Alternating proximal gradient method for sparse nonnegative Tucker decomposition

arXiv: https://arxiv.org/abs/1302.2559 · HTML: https://mlsanity.com/paper/1302.2559/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2013.

## Built on by (most cited first, 11 of 11)

- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals](https://mlsanity.com/paper/2110.14434/) (2021)
- [Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion](https://mlsanity.com/paper/2305.07976/) (2023)
- [FCNCP: A Coupled Nonnegative CANDECOMP/PARAFAC Decomposition Based on Federated Learning](https://mlsanity.com/paper/2404.11890/) (2024)
- [Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem](https://mlsanity.com/paper/2111.12399/) (2021)
- [2D+3D facial expression recognition via embedded tensor manifold regularization](https://mlsanity.com/paper/2201.12506/) (2022)
- [Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation](https://mlsanity.com/paper/2211.03934/) (2022)
- [Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation](https://mlsanity.com/paper/2302.05119/) (2023)
- [A General Continuous-Time Formulation of Stochastic ADMM and Its Variants](https://mlsanity.com/paper/2404.14358/) (2024)
- [LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion](https://mlsanity.com/paper/2508.03755/) (2025)
- [An Inertial Block Proximal Linearized Method with Adaptive Momentum for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2608.05502/) (2026)

## Abstract (arXiv)

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.