Towards theory of generic Principal Component Analysis

Authors:
Anatoli Torokhti;Shmuel Friedland
Affiliations:
University of South Australia, School of Mathematics and Statistics, 5095 Mawson Lakes, SA, Australia;Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, USA
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 18
Cited 3

The SVD and reduced rank signal processing

Signal Processing - Theme issue on singular value decomposition
Principal component neural networks: theory and applications

Principal component neural networks: theory and applications
Functional principal components analysis by choice of norm

Journal of Multivariate Analysis
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM

Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
A Counterexample to the Possibility of an Extension of the Eckart-Young Low-Rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition

SIAM Journal on Matrix Analysis and Applications
Constructing fixed rank optimal estimators with method of best recurrent approximations

Journal of Multivariate Analysis
Fast monte-carlo algorithms for finding low-rank approximations

Journal of the ACM (JACM)
Neural Networks in a Softcomputing Framework

Neural Networks in a Softcomputing Framework
Generalized Rank-Constrained Matrix Approximations

SIAM Journal on Matrix Analysis and Applications
Computational Methods for Modeling of Nonlinear Systems

Computational Methods for Modeling of Nonlinear Systems
Maximum likelihood array processing in spatially correlated noisefields using parameterized signals

IEEE Transactions on Signal Processing
MIMO system identification: state-space and subspace approximationsversus transfer function and instrumental variables

IEEE Transactions on Signal Processing
Statistical analysis of subspace-based estimation of reduced-ranklinear regressions

IEEE Transactions on Signal Processing
Design of two-dimensional digital filters using singular-valuedecomposition and balanced approximation method

IEEE Transactions on Signal Processing
Relative Karhunen-Loeve transform

IEEE Transactions on Signal Processing
Multislot estimation of fast-varying space-time communication channels

IEEE Transactions on Signal Processing
Reduced rank linear regression and weighted low rank approximations

IEEE Transactions on Signal Processing - Part I
Optimal transform formed by a combination of nonlinear operators: the case of data dimensionality reduction

IEEE Transactions on Signal Processing

Generic weighted filtering of stochastic signals

IEEE Transactions on Signal Processing
Data compression under constraints of causality and variable finite memory

Signal Processing
Is standard multivariate analysis sufficient in clinical and epidemiological studies?

Journal of Biomedical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we consider a technique called the generic Principal Component Analysis (PCA) which is based on an extension and rigorous justification of the standard PCA. The generic PCA is treated as the best weighted linear estimator of a given rank under the condition that the associated covariance matrix is singular. As a result, the generic PCA is constructed in terms of the pseudo-inverse matrices that imply a development of the special technique. In particular, we give a solution of the new low-rank matrix approximation problem that provides a basis for the generic PCA. Theoretical aspects of the generic PCA are carefully studied.