ncku-talk2009-11-05

NCTS(South)/ NCKU Math Colloquium

DATE 2009-11-05　15:10-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. I-Ping Tu 杜億萍教授（Institute of Statistical Science, Academia Sinica, Taiwan）

TITLE An Eigenvector Variability Plot

ABSTRACT Principal components analysis is perhaps the most widely used method for exploring multivariate data. In this paper, we propose a variability plot composed of measures on the stability of each eigenvectors over samples as a data exploration tool.
We also show that this variability measure gives a good measure on the intersample variability of eigenvectors through asymptotic analysis. For distinct eigenvalues, the asymptotic behavior for this variability measure is comparable to the size of the asymptotic covariance of the eigenvector in Anderson (1963). A simulation for functional data analysis with dimension p greater than sample size n is provided. The proposed variability plot is successful to distinguish the signal components, noise components and 0 eigenvalue components. Applying this method on a gene expression data set for a gastric cancer study, many hills on the proposed variability plot are observed. When the intersample variability of eigenvectors is considered, the cutoff point on informative eigenvectors should not be on the top of the hill as suggested by the proposed variability plot.
This is a joint work with Prof. Chen, Hung and Prof. Chen, Xin.

NCTS(South)/ NCKU Math Colloquium

DATE	2009-11-05　15:10-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. I-Ping Tu 杜億萍教授（Institute of Statistical Science, Academia Sinica, Taiwan）

TITLE	An Eigenvector Variability Plot

ABSTRACT	Principal components analysis is perhaps the most widely used method for exploring multivariate data. In this paper, we propose a variability plot composed of measures on the stability of each eigenvectors over samples as a data exploration tool. We also show that this variability measure gives a good measure on the intersample variability of eigenvectors through asymptotic analysis. For distinct eigenvalues, the asymptotic behavior for this variability measure is comparable to the size of the asymptotic covariance of the eigenvector in Anderson (1963). A simulation for functional data analysis with dimension p greater than sample size n is provided. The proposed variability plot is successful to distinguish the signal components, noise components and 0 eigenvalue components. Applying this method on a gene expression data set for a gastric cancer study, many hills on the proposed variability plot are observed. When the intersample variability of eigenvectors is considered, the cutoff point on informative eigenvectors should not be on the top of the hill as suggested by the proposed variability plot. This is a joint work with Prof. Chen, Hung and Prof. Chen, Xin.