Orthogonal Nonnegative Tucker Decomposition

TL;DR

This paper introduces Orthogonal Nonnegative Tucker Decomposition (ONTD), a new method for analyzing nonnegative tensor data, with a convex relaxation algorithm and proven convergence, demonstrated on real-world image datasets.

Contribution

The paper proposes ONTD, a novel orthogonal nonnegative tensor decomposition method, along with a convex relaxation algorithm and convergence analysis, applied to real-world image data.

Findings

Effective in face recognition tasks

Improves image representation quality

Demonstrates convergence of the proposed algorithm

Abstract

In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.