Covariate-adjusted matrix visualization via correlation decomposition

Han-Ming Wu1,Yin-Jing Tien2, Meng-Ru Ho3, 4, 5, Hai-Gwo Hwu6, Wen-chang Lin5, Mi-Hua Tao5, and Chun-Houh Chen2,*


1Department of Mathematics, Tamkang University, Taipei County 25137, Taiwan, R.O.C.,
2Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, R.O.C.,
3Institute of Biomedical Informatics, National Yang-Ming University, Taipei 112, Taiwan, R.O.C.,
4Bioinformatics Program, Taiwan International Graduate Program, Academia Sinica, Taipei 115, Taiwan, R.O.C.,
5Institute of Biomedical Sciences, Academia Sinica, Taipei 115, Taiwan, R.O.C.,
6Department of Psychiatry, National Taiwan University Hospital and College of Medicine, Taipei 100, Taiwan, R.O.C.
and Department of Psychology, College of Public Health, Neurobiology and Cognitive Science Center, Taipei 100, Taiwan, R.O.C.

*to whom correspondence should be addressed.


Abstract

Motivation:
In this study, we extend the framework of matrix visualization (MV) by incorporating a covariate adjustment process through the estimation of conditional correlations. MV can explore the embedded information structure of high-dimensional large-scale data sets effectively without dimension reduction. The benefit of the proposed covariate-adjusted MV is in the exploration of conditional association structures among the subjects or variables that cannot be done with conventional MV.

Results:
For adjustment of a discrete covariate, the conditional correlation is estimated by the within and between analysis. This procedure decomposes a correlation matrix into the within- and between-component matrices. The contribution of the covariate effects can then be assessed through the relative structure of the between-component to the original correlation matrix while the within-component acts as a residual. When a covariate is of continuous nature, the conditional correlation is equivalent to the partial correlation under the assumption of a joint normal distribution. A test is then employed to identify variable pairs which possess the most significant differences at varying levels of correlation before and after a covariate adjustment. In addition, a z-score significant map is constructed to visualize these results. A simulation and three data sets are employed to illustrate the power and versatility of our proposed method.

Availability:
GAP is available to registrants and is free to non-commercial applications. The installation instructions, the User's Manual, and the detailed tutorials are available at http://gap.stat.sinica.edu.tw/Software/GAP.

Contact: cchen@stat.sinica.edu.tw

Supplementary information: Supplementary material are available at Bioinformatics online.

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Last Update: 2011/03/14, hmwu@mail.tku.edu.tw