Nonnegative tensor factorization is an extension of nonnegative matrix factorization(NMF) to a multilinear case, where nonnegative constraints are imposed on the PARAFAC/Tucker model. In this paper, to identify speaker from a noisy environment, we propose a new method based on PARAFAC model called constrained Nonnegative Tensor Factorization (cNTF). Speech signal is encoded as a general higher ...

In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenv...

Learning fruitful representation from data is one of fundamental problems in machine learning and pattern recognition. Various methods have been developed, including factor analysis, principal component analysis (PCA), independent component analysis (ICA), manifold learning, and so on. Among those, nonnegative matrix factorization (NMF) has recently drawn extensive attention, since promising re...

T here has been a recent surge of interest in matrix and tensor factorization (decomposition), which provides meaningful latent (hidden) components or features with physical or physiological meaning and interpretation. Nonnegative matrix factorization (NMF) and its extension to three-dimensional (3-D) nonnegative tensor factorization (NTF) attempt to recover hidden nonnegative common structures...

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor A such that the tensor complementarity problem (q,A): finding x ∈ R such that x ≥ 0,q+Axm−1 ≥ 0, and x⊤(q+Axm−1) = 0, has a solution for each vector q ∈ Rn. Several subclasses of Q-tensors are given: P-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative ten...

Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and represent...

We consider the problem of nonnegative tensor factorization. Our aim is to derive an efficient algorithm that is also suitable for parallel implementation. We adopt the alternating optimization (AO) framework and solve each matrix nonnegative least-squares problem via a Nesterov-type algorithm for strongly convex problems. We describe two parallel implementations of the algorithm, with and with...

We introduce M -tensors. This concept extends the concept ofM -matrices. We denote Z-tensors as the tensors with nonpositive off-diagonal entries. We show that M -tensors must be Ztensors and the maximal diagonal entry must be nonnegative. The diagonal elements of a symmetric M -tensor must be nonnegative. A symmetric M -tensor is copositive. Based on the spectral theory of nonnegative tensors,...