A. Ionescu Tulcea, C. Ionescu Tulcea's Topics in the Theory of Lifting. PDF

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Journal of the American Statistical Association, 457, 77-87. , TAMAYO, P. et al. (1999): Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science, 286, 531-537. HWARINEN, A,, KARHUNEN, J . and OJA, E. (2001): Independent Component Analysis, Wiley, New York. , RINGNER, M. et al. (2001): Classification and Diagnostic Prediction of Cancers Using Gene Expression Profiling and Artificial Neural Networks. Nature Medicine, 7, 673-679. , NARASIMHAN, B.

As shown in Table 3, none of the three methods is successful in accurately predict the class membership. 042). It is worth noting that these minimum values are referred to approximately the same number of selected genes. 333 Table 3. Leukemia data set: cross-validated misclassification rates for different values of m ( k = 7 for ICA and k = 5 for SVD). 5 Conclusions and open issues As the preliminary results on these real data sets show, the proposed strategy seems to represent a useful tool to detect subsets of relevant genes for supervised cell classification based on microarray data.

The proposed solution consists of building classification rules on genes selected by looking at the tails of the distributions of gene projections along suitable directions. Since gene expression profiles are typically non-gaussian, it seems relevant to catch not only the linear (second-order) aspects of the data structure but also the non-linear (higher-order) ones. For this reason, our proposal focuses on searching the less statistically dependent projections. These directions are obtained by independent component analysis (Hyvarinen et al.

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Topics in the Theory of Lifting. by A. Ionescu Tulcea, C. Ionescu Tulcea

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