An adaptive extraction of generalized eigensubspace by using exact nested orthogonal complement structure

Authors:
Tuan Duong Nguyen;Noriyuki Takahashi;Isao Yamada
Affiliations:
Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan 152-8550;Global Edge Institute, Tokyo Institute of Technology, Tokyo, Japan 152-8550;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan 152-8550
Venue:
Multidimensional Systems and Signal Processing
Year:
2013

Citing 10
Cited 1

Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Downlink beamforming for spatially distributed sources in cellular mobile communications

Signal Processing
Fast RLS-Like Algorithm for Generalized Eigendecomposition and its Applications

Journal of VLSI Signal Processing Systems
Multisurface Proximal Support Vector Machine Classification via Generalized Eigenvalues

IEEE Transactions on Pattern Analysis and Machine Intelligence
An Efficient Adaptive Minor Subspace Extraction Using Exact Nested Orthogonal Complement Structure

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Projection approximation subspace tracking

IEEE Transactions on Signal Processing
A matrix-pencil approach to blind separation of colorednonstationary signals

IEEE Transactions on Signal Processing
Robust adaptive beamforming for general-rank signal models

IEEE Transactions on Signal Processing
RLS-based adaptive algorithms for generalized eigen-decomposition

IEEE Transactions on Signal Processing
Self-organizing algorithms for generalized eigen-decomposition

IEEE Transactions on Neural Networks

A unified convergence analysis of Normalized PAST algorithms for estimating principal and minor components

Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the ith (i 驴 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.