Linked PARAFAC/CP Tensor Decomposition and Its Fast Implementation for Multi-block Tensor Analysis
نویسندگان
چکیده
In this paper we propose a new flexible group tensor analysis model called the linked CP tensor decomposition (LCPTD). The LCPTD method can decompose given multiple tensors into common factor matrices, individual factor matrices, and core tensors, simultaneously. We applied the Hierarchical Alternating Least Squares (HALS) algorithm to the LCPTD model; besides we impose additional constraints to obtain sparse and nonnegative factors. Furthermore, we conducted some experiments of this model to demonstrate its advantages over existing models.
منابع مشابه
Consensus-based In-Network Computation of the PARAFAC Decomposition
Higher-order tensor analysis is a multi-disciplinary tool widely used in numerous application areas involving data analysis such as psychometrics, chemometrics, and signal processing, just to mention a few. The parallel factor (PARAFAC) decomposition, also known by the acronym CP (standing for “CANDECOMP/PARAFAC” or yet “canonical polyadic”) is the most popular tensor decomposition. Its widespr...
متن کاملTensor modeling and signal processing for wireless communication systems. (Modélisation et traitement tensoriel du signal pour les systèmes de communication sans-fil)
In several signal processing applications for wireless communications, the received signal is multidimensional in nature and may exhibit a multilinear algebraic structure. In this context, the PARAFAC tensor decomposition has been the subject of several works in the past six years. However, generalized tensor decompositions are necessary for covering a wider class of wireless communication syst...
متن کاملInfTucker: t-Process based Infinite Tensor Decomposition
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...
متن کاملCramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition
This paper presents a Cramér-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a random Gaussian i.i.d. tensor). A novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor o...
متن کاملLow Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC
The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an N-D tensor of size I1 × · · · × IN with rank R, the algorithm is computationally demanding due to construction of large approximate Hessian of size (RT × RT ) and its inversion where T = n...
متن کامل