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Issue No. 01 - January-February (2011 vol. 8)
ISSN: 1545-5963
pp: 246-252
Joaquim F. Pinto da Costa , University of Porto, Porto
Hugo Alonso , University of Aveiro, Aveiro
Luís Roque , ISEP, Porto
In this work, we introduce in the first part new developments in Principal Component Analysis (PCA) and in the second part a new method to select variables (genes in our application). Our focus is on problems where the values taken by each variable do not all have the same importance and where the data may be contaminated with noise and contain outliers, as is the case with microarray data. The usual PCA is not appropriate to deal with this kind of problems. In this context, we propose the use of a new correlation coefficient as an alternative to Pearson's. This leads to a so-called weighted PCA (WPCA). In order to illustrate the features of our WPCA and compare it with the usual PCA, we consider the problem of analyzing gene expression data sets. In the second part of this work, we propose a new PCA-based algorithm to iteratively select the most important genes in a microarray data set. We show that this algorithm produces better results when our WPCA is used instead of the usual PCA. Furthermore, by using Support Vector Machines, we show that it can compete with the Significance Analysis of Microarrays algorithm.
Correlation, principal component analysis, support vector machines, microarray data, gene selection.

L. Roque, H. Alonso and J. F. Pinto da Costa, "A Weighted Principal Component Analysis and Its Application to Gene Expression Data," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. , pp. 246-252, 2009.
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