Work

Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria

Year: 2016

Type: article

Abstract: Model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy. In the Tucker model, the minimum description length (MDL) or Bayesian information criteria have been applied to tensors via matrix unfolding, but these methods are sensitive to noise when the tensors have a multilinear low rank structure given by the Tucker model. In this study, we propose new methods for improving the MDL so it is more robust to noise. The proposed methods are justified theoretically by analyzing the “multilinear low-rank structure” of tensors. Extensive experiments including numerical simulations and a real application to image denoising are provided to illustrate the advantages of the proposed methods.

Source: IEEE Transactions on Signal Processing

DOI: 10.1109/tsp.2016.2620965

Authors: Tatsuya Yokota, Namgil Lee, Andrzej Cichocki

Institutions: Nagoya Institute of Technology, RIKEN Center for Brain Science, RIKEN, Systems Research Institute, Polish Academy of Sciences

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Model Selection for Tensor Factorization and its Applications for Big Data Analysis