We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field — the value of the nuclear norm of a real 3-tensor depends on whether we regard it as a real 3-tensor or a complex 3-tensor with real entries. We show that every tensor has a nuclear norm attainin...

In this paper, we study nonnegative tensor data and propose an orthogonal Tucker decomposition (ONTD). We discuss some properties of ONTD develop a convex relaxation algorithm the augmented Lagrangian function to solve optimization problem. The convergence is given. employ on image sets from real world applications including face recognition, representation, hyperspectral unmixing. Numerical re...

Room reverberation is a primary cause of failure in distant speech recognition (DSR) systems. In this study, we present a multichannel spectrum enhancement method for reverberant speech recognition, which is an extension of a single-channel dereverberation algorithm based on convolutive nonnegative matrix factorization (NMF). The generalization to a multichannel scenario is shown to be a specia...

The study of the neuronal correlates of the spontaneous alternation in perception elicited by bistable visual stimuli is promising for understanding the mechanism of neural information processing and the neural basis of visual perception and perceptual decision-making. In this paper, we develop a sparse nonnegative tensor factorization-(NTF)-based method to extract features from the local field...

When an n -partite physical system is measured by observers, the joint probabilities of outcomes conditioned on observables chosen parties form a nonnegative tensor, called correlation tensor (CT). In this paper, we aim to establish some characterizations nonsignaling and Bell locality CT, respectively. By placing CTs within linear space correlation-type tensors (CTTs), prove that every CTT can...

Analysis of high dimensional data in modern applications, such as neuroscience, text mining, spectral analysis or chemometrices naturally requires tensor decomposition methods. The Tucker decompositions allow us to extract hidden factors (component matrices) with a different dimension in each mode and investigate interactions among various modes. The Alternating Least Squares (ALS) algorithms h...

Abstract. In this work we perform some mathematical analysis on a special nonnegative matrix trifactorization (NMF) and apply this NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of positive data and images in terms of tensor products of positive vectors and investigate its effectiveness in terms of the number of tensor products to be used in the approx...

Abstract Detecting and delineating hot spots in data from radiation sensors is required applications ranging monitoring large geospatial areas to imaging small objects close proximity. This paper describes a computational method for localizing potential matrices of independent Poisson where, numerical terms, spot cluster locally higher sample mean values (higher intensity) embedded lower (lower...