A Multilinear Singular Value Decomposition

On the truncated multilinear singular value decomposition

In this report, we investigate the truncated multilinear singular value decomposition (MLSVD), proposed in De Lathauwer et al. (2000). Truncating the MLSVD results in an approximation, with a prescribed multilinear rank, to a tensor. We present a new error expression for an approximate Tucker decomposition with orthogonal factor matrices. From this expression, new insights are obtained which le...

Estimates of Multilinear Singular Integral Operators and Mean Oscillation

Dimensionality reduction in higher - order signal processing and rank - ( R 1 , R 2 , . . . , RN ) reduction in multilinear algebra

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 algorith...

Reduction of broadband noise in speech signals by multilinear subspace analysis

A new noise reduction method for speech signals is proposed in this paper. The method is based upon the N-mode singular value decomposition algorithm, which exploits the multilinear subspace analysis of given speech data. Simulation results using both synthetically generated and real broadband noise components show that the enhancement quality obtained by the multilinear subspace analysis metho...

Multilinear 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 ...