Alpha-divergence-based nonnegative tensor factorization (NTF) is applied to blind multispectral image (MSI) decomposition. The matrix of spectral profiles and the matrix of spatial distributions of the materials resident in the image are identified from the factors in Tucker3 and PARAFAC models. NTF preserves local structure in the MSI that is lost as a result of vectorization of the image when...

We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, but doubles the computation.

Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmo...

In order to overcome the limitation of traditional nonnegative factorization algorithms, the paper presents a generalized discriminant orthogonal non-negative tensor factorization algorithm. At first, the algorithm takes the orthogonal constraint into account to ensure the nonnegativity of the low-dimensional features. Furthermore, the discriminant constraint is imposed on low-dimensional weigh...

We introduce an efficient algorithm for computing a low-rank nonnegative CANDECOMP/PARAFAC (NNCP) decomposition. In text mining, signal processing, and computer vision among other areas, imposing nonnegativity constraints to low-rank factors has been shown an effective technique providing physically meaningful interpretation. A principled methodology for computing NNCP is alternating nonnegativ...

There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as ge...

In this paper, we prove that a compact quasi-Einstein manifold $(M^n,\,g,\,u)$ of dimension $n\geq 4$ with boundary $\partial M,$ nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, the standard hemisphere $\Bbb {S}^n_+,$ or $g=dt^{2}+\psi ^{2}(t)g_{L}$ $u=u(t),$ where $g_{L}$ Einstein Ricci curvature. A similar classification result obtained by assum...

This paper investigates the problem of speaker recognition in noisy conditions. A new approach called nonnegative tensor principal component analysis (NTPCA) with sparse constraint is proposed for speech feature extraction. We encode speech as a general higher-order tensor in order to extract discriminative features in spectrotemporal domain. Firstly, speech signals are represented by cochlear ...

αand β-divergence based nonnegative tensor factorization (NTF) is combined with nonlinear band expansion (NBE) for blind decomposition of the magnetic resonance image (MRI) of the brain. Concentrations and 3D tensor of spatial distributions of brain substances are identified from the Tucker3 model of the 3D MRI tensor. NBE enables to account for the presence of more brain substances than number...