New Routes from Minimal Approximation Error to Principal Components

Authors:
Abhilash Alexander Miranda;Yann-Aël Borgne;Gianluca Bontempi
Affiliations:
Machine Learning Group, Département d'Informatique, Université Libre de Bruxelles, Brussels, Belgium 1050;Machine Learning Group, Département d'Informatique, Université Libre de Bruxelles, Brussels, Belgium 1050;Machine Learning Group, Département d'Informatique, Université Libre de Bruxelles, Brussels, Belgium 1050
Venue:
Neural Processing Letters
Year:
2008

Citing 8
Cited 7

Applied multivariate statistical analysis

Applied multivariate statistical analysis
Introduction to statistical pattern recognition (2nd ed.)

Introduction to statistical pattern recognition (2nd ed.)
Principal component neural networks: theory and applications

Principal component neural networks: theory and applications
Pattern Recognition and Neural Networks

Pattern Recognition and Neural Networks
Pattern Classification (2nd Edition)

Pattern Classification (2nd Edition)
Pattern Recognition and Machine Learning (Information Science and Statistics)

Pattern Recognition and Machine Learning (Information Science and Statistics)
Application of the Karhunen-Loève Expansion to Feature Selection and Ordering

IEEE Transactions on Computers
Mine detection using scattering parameters

IEEE Transactions on Neural Networks

An exploratory study to design a novel hand movement identification system

Computers in Biology and Medicine
Scene image clustering based on boosting and GMM

Proceedings of the Second Symposium on Information and Communication Technology
An optimal design of the extrapolated impulse response filter with analytical solutions

Signal Processing
Block dependency feature based classification scheme for uncalibrated image steganalysis

ICDEM'10 Proceedings of the Second international conference on Data Engineering and Management
Document categorization based on minimum loss of reconstruction information

MICAI'12 Proceedings of the 11th Mexican international conference on Advances in Computational Intelligence - Volume Part II
Minimizer of the Reconstruction Error for multi-class document categorization

Expert Systems with Applications: An International Journal
Cloud based intelligent system for delivering health care as a service

Computer Methods and Programs in Biomedicine

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce two new methods of deriving the classical PCA in the framework of minimizing the mean square error upon performing a lower-dimensional approximation of the data. These methods are based on two forms of the mean square error function. One of the novelties of the presented methods is that the commonly employed process of subtraction of the mean of the data becomes part of the solution of the optimization problem and not a pre-analysis heuristic. We also derive the optimal basis and the minimum error of approximation in this framework and demonstrate the elegance of our solution in comparison with a recent solution in the framework.