Robust PCA and classification in biosciences.
BACKGROUND
Principal components analysis (PCA) is a very popular dimension reduction technique that is widely used as a first step in the analysis of high-dimensional microarray data. However, the classical approach that is based on the mean and the sample covariance matrix of the data is very sensitive to outliers. Also, classification methods based on this covariance matrix do not give good results in the presence of outlying measurements.


RESULTS
First, we propose a robust PCA (ROBPCA) method for high-dimensional data. It combines projection-pursuit ideas with robust estimation of low-dimensional data. We also propose a diagnostic plot to display and classify the outliers. This ROBPCA method is applied to several bio-chemical datasets. In one example, we also apply a robust discriminant method on the scores obtained with ROBPCA. We show that this combination of robust methods leads to better classifications than classical PCA and quadratic discriminant analysis.


BACKGROUND
All the programs are part of the Matlab Toolbox for Robust Calibration, available at http://www.wis.kuleuven.ac.be/stat/robust.html.
Hubert
Mia
M
Department of Mathematics, Katholieke Universiteit Leuven, W. De Croylaan 54, B-3001 Leuven, Belgium. Mia.Hubert@wis.kuleuven.ac.be
Engelen
Sanne
S
D000465:Algorithms; D000818:Animals; D001690:Biological Science Disciplines / Q000379:methods; D003198:Computer Simulation; D020869:Gene Expression Profiling / Q000379:methods*; D051379:Mice; D008957:Models, Genetic; D015233:Models, Statistical; D009369:Neoplasms / Q000145:classification* / Q000235:genetics*; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D025341:Principal Component Analysis / Q000379:methods*; D051381:Rats; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012984:Software