Gene expression data from microarray has very high dimensionality, resulting in extremely large sample covariance matrices. In this paper, we investigate the applicability of the block principal components analysis and a variable selection method based on principal components loadings for dimension reduction prior to performing discriminant analysis on the data. In such cases, because of high correlations among variables, the Mahalanobis distances between clusters becomes very large due to ill-conditioning. It is shown in this paper that the Mahalanobis distance is unreliable when the condition number of the covariance matrix exceeds 480,000 or the natural log of the determinant of the covariance matrix is less than −26.3.
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Lee, S.H., Singh, A.K., Gewali, L.P. (2008). Dimension reduction for performing discriminant analysis for microarrays. In: Kelemen, A., Abraham, A., Liang, Y. (eds) Computational Intelligence in Medical Informatics. Studies in Computational Intelligence, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75767-2_6
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