Functional embedding for the classification of gene expression profiles

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.