A non-negative tensor factorization approach to feature extraction for image analysis

In this paper, a decomposition method is proposed for Separable Non-negative Tensor Factorization (SNTF), which yields a structure similar to the PARATUCK2 model for the decomposition of non-negative tensors. Among many different possibilities for performing tensor factorization, we develop a specific procedure for SNTF with an aim to decompose multi-way dataset expressed in the form of a tensor into low-rank components that extract dominant features in the data. The SNTF method is evaluated using real image data and the results show that the proposed SNTF is superior to other NTF methods in terms of error performance and computational efficiency.

I. Introduction

A dataset is called non-negative if only non-negative values are allowed in the data expression. Examples of non-negative data include images and power spectra of signals. Often, the non-negative data can be expressed as a non-negative matrix , which may have a lower rank than would be indicated by its dimensions. The Non-negative Matrix Factorization (NMF), finds a compact representation of as , where and are non-negative matrices with smaller dimensions.