Work

Consistent Regularized Non-Negative Tucker Decomposition for Three-Dimensional Tensor Data Representation

Year: 2025

Type: article

Abstract: Non-negative Tucker decomposition (NTD) is one of the general and prominent decomposition tools designed for high-order tensor data, with its advantages reflected in feature extraction and low-dimensional representation of data. Most NTD-based methods only apply intrinsic and different constraints to the last factor matrix that is a low-dimensional representation of the original tensor information. This processing procedure may result in the loss of the relationship between the factor matrices in all dimensions. To enhance the representation ability of NTD, we propose a consistent regularized non-negative Tucker decomposition for three-dimensional tensor data representation. Consistent regularization is symmetrically presented and mathematically expressed by intrinsic cues in multiple dimensions, that is, manifold structure and orthogonality information. The paired constraint constructed by the double parameter operator is utilized to unlock hidden semantics and maintain the consistent geometric structure of the three-dimensional tensor. Moreover, we develop the iterative updating method based on the multiplicative update rule to solve the proposed model and provide its convergence and computational complexity. The extensive numerical results of unsupervised image clustering experiments on eight real-world datasets demonstrated the feasibility and efficiency of the new method.

Source: Symmetry

DOI: 10.3390/sym17111969

Authors: Xiang Gao, Linzhang Lu

Institutions: Guizhou Normal University, Xiamen University

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China