Multi-Separable Nonnegative Tucker Decomposition

Keywords: Nonnegative Tucker decomposition, NMF, separability, hyperspectral unmixing.

TL;DR: We introduce separability into nonnegative Tucker decomposition and propose a heuristic algorithm to solve the model.

Abstract: Nonnegative Tucker Decomposition (NTD) is a powerful tool for multi-way data analysis, but is NP-hard in general. Motivated by the success of separability in rendering Nonnegative Matrix Factorization (NMF) both tractable and provably robust, we introduce and study the separable Tucker decomposition, Under this assumption, we propose an efficient polynomial-time algorithm that identifies the anchor index sets via the Successive Projection Algorithm (SPA) applied to mode-wise unfoldings of the observed tensor, extracts the core tensor directly as a subtensor, and recovers each factor matrix by solving a nonnegative least-squares problem. Experiments on real-world hyperspectral imaging dataset demonstrate that the proposed method achieves accurate decompositions, comparing favorably against existing nonnegative Tucker factorization method in both solution quality and computational efficiency.

Submission Number: 146