Dimensionality reduction in higher - order signal processing and rank - ( R 1 , R 2 , . . . , RN ) reduction in multilinear algebra
نویسندگان
چکیده
In this paper we review a multilinear generalization of the singular value decomposition and the best rank-(R1, R2, . . . , RN) approximation of higher-order tensors. We show that they are important tools for dimensionality reduction in higher-order signal processing. We discuss applications in independent component analysis, simultaneous matrix diagonalization and subspace variants of algorithms based on higher-order statistics. © 2004 Elsevier Inc. All rights reserved.
منابع مشابه
Low-Rank Signal Processing: Design, Algorithms for Dimensionality Reduction and Applications
We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed to introduce the reader to the fundamentals of reduced-rank signal processing and to describe how dimensionality reduction is performed on an observed discr...
متن کاملA Monte Carlo-Based Search Strategy for Dimensionality Reduction in Performance Tuning Parameters
Redundant and irrelevant features in high dimensional data increase the complexity in underlying mathematical models. It is necessary to conduct pre-processing steps that search for the most relevant features in order to reduce the dimensionality of the data. This study made use of a meta-heuristic search approach which uses lightweight random simulations to balance between the exploitation of ...
متن کاملMultilinear Subspace Analysis of Image Ensembles
Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing ensembles of images resulting from the interaction of any number of underlying factors. We present a dimensionality reduction algorithm that enables subspace analysis within the multilinear framework. This N -mode orthogonal iteration algorithm is based on a tensor decomposition known ...
متن کاملImpact of linear dimensionality reduction methods on the performance of anomaly detection algorithms in hyperspectral images
Anomaly Detection (AD) has recently become an important application of hyperspectral images analysis. The goal of these algorithms is to find the objects in the image scene which are anomalous in comparison to their surrounding background. One way to improve the performance and runtime of these algorithms is to use Dimensionality Reduction (DR) techniques. This paper evaluates the effect of thr...
متن کاملOn the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors
In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely, the approximation of a given higher-order tensor, in an optimal leastsquares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value decomposition (SVD); however, this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004