Functional embedding for the classification of gene expression profiles

Abstract

Motivation: Low sample size n high-dimensional large p data with n«p are commonly encountered in genomics and statistical genetics. Ill-conditioning of the variance-covariance matrix for such data renders the traditional multivariate data analytical approaches unattractive. On the other side, functional data analysis (FDA) approaches are designed for infinite-dimensional data and therefore may have potential for the analysis of large p data. We herein propose a functional embedding (FEM) technique, which exploits the interface between multivariate and functional data, aiming at borrowing strength across the sample through FDA techniques in order to resolve the difficulties caused by the high dimension p. Results: Using pairwise dissimilarities among predictor variables, one obtains a univariate configuration of these covariates. This is interpreted as variable ordination that defines the domain of a suitable function space, thus leading to the FEM of the high-dimensional data. The embedding may then be followed by functional logistic regression for the classification of high-dimensional multivariate data as an example for downstream analysis. The resulting functional classification is evaluated on several published gene expression array datasets and a mass spectrometric data, and is shown to compare favorably with various methods that have been employed previously for the classification of these high-dimensional gene expression profiles. Availability: The implementation of FEM and Classification via Functional Embedding (CFEM) as described in this article was done with the PACE package written in Matlab. The latest version of PACE is publicly accessible at http://anson.ucdavis.edu/~mueller/data/programs.html. An example MATLAB script for FEM is available at http://www.lehigh.edu/~psw205/psw205.html. Contact: psw205@lehigh.edu; mueller@wald.ucdavis.edu © The Author 2010. Published by Oxford University Press.