[BK07] A combined approach using wavelets and PCA methods

Conférence Internationale avec comité de lecture : CARME'07, Correspondence Analysis and Related Methods, Rotterdam, January 2007,
Résumé: The Principal Components Analysis (PCA) method is the most known and used method of data analysis. It synthesis data in creating small numbers of new variables called principal components (PC). The presence of noise in dataset may influence negatively adequate choice of number of components to determinate and consequently, it may affect the result of the PCA. We propose in this work the use the wavelet thresholding as a new efficient way of denoising, and a generalization of wavelet denoising compound with the method of univariat denoising of the PCA. Indeed, in the first step we use a wavelet decomposition for every column of X ( where X is the initial data set matrix). So we obtain coefficient which are perfectly localisated in the plane (time-scale). Then, theses coefficients will be thresholded, and we reconstitute the denoising matrix with these new coefficients and we apply the PCA method to the obtained matrix . The procedure is validated on several real cases.


@inproceedings {
title="{A combined approach using wavelets and PCA methods}",
author=" S. Benammou and Z. Kacem ",
booktitle="{CARME'07, Correspondence Analysis and Related Methods, Rotterdam}",