Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these noti...

Multi-way data arises inmany applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is to decompose a given tensor into the p...

Title of dissertation: TENSOR COMPLETION FOR MULTIDIMENSIONAL INVERSE PROBLEMS WITH APPLICATIONS TO MAGNETIC RESONANCE RELAXOMETRY Ariel Hafftka, Doctor of Philosophy, 2016 Dissertation directed by: Professor Wojciech Czaja Department of Mathematics This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approxima...

Modern applications such as neuroscience, text mining, and large-scale social networks generate massive amounts of data with multiple aspects and high dimensionality. Tensors (i.e., multi-way arrays) provide a natural representation for such massive data. Consequently, tensor decompositions and factorizations are emerging as novel and promising tools for exploratory analysis of multidimensional...

Multidimensional signal analysis has become an important part of many processing problems. This type allows to take advantage different diversities a in order extract useful information. paper focuses on the design and development multidimensional data decomposition algorithms called Canonical Polyadic (CP) tensor decomposition, powerful tool variety real-world applications due its uniqueness e...

Abstract Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, sparsity only side effect cannot be explicitly controlled without additional regularization. In this paper, we investigated CANDECOMP/PARAFAC (NCP) with sparse regularization item using $$l_1$$ <mml:math xmlns:mml="http://w...

An iterative method for finding the largest eigenvalue of a nonnegative tensor was proposed by Ng, Qi, and Zhou in 2009. In this paper, we establish an explicit linear convergence rate of the Ng–Qi–Zhou method for essentially positive tensors. Numerical results are given to demonstrate linear convergence of the Ng–Qi–Zhou algorithm for essentially positive tensors. Copyright © 2011 John Wiley &...

It is known that if f is a multiplicative increasing function on N, then either f(n) = 0 for all n∈N or f(n) = n for some ¿0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we 1rst study the multiplicative increasing functions over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopl...

Tensor decomposition is a powerful tool for multiway data analysis. Many popular tensor decomposition approaches—such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)—conduct multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g. missing data and binary data), and (iii) noisy observations and outliers. To ad...