Supervised Classification of High-Dimensional Correlated Data: Application to Genomic Data

Abstract

This work addresses the problem of supervised classification for high-dimensional and highly correlated data using correlation blocks and supervised dimension reduction. We propose a method that combines block partitioning based on interval graph modeling and an extension of principal component analysis (PCA) incorporating conditional class moment estimates in the low-dimensional projection. Block partitioning allows us to handle the high correlation of our data by grouping them into blocks where the correlation within the same block is maximized and the correlation between variables in different blocks is minimized. The extended PCA allows us to perform low-dimensional projection and clustering supervised. Applied to gene expression data from 445 individuals divided into two groups (diseased and non-diseased) and 719,656 single nucleotide polymorphisms (SNPs), this method shows good clustering and prediction performances. SNPs are a type of genetic variation that represents a difference in a single deoxyribonucleic acid (DNA) building block, namely a nucleotide. Previous research has shown that SNPs can be used to identify the correct population origin of an individual and can act in isolation or simultaneously to impact a phenotype. In this regard, the study of the contribution of genetics in infectious disease phenotypes is crucial. The classical statistical models currently used in the field of genome-wide association studies (GWAS) have shown their limitations in detecting genes of interest in the study of complex diseases such as asthma or malaria. In this study, we first investigate a linkage disequilibrium (LD) block partition method based on interval graph modeling to handle the high correlation between SNPs. Then, we use supervised approaches, in particular, the approach that extends PCA by incorporating conditional class moment estimates in the low-dimensional projection, to identify the determining SNPs in malaria episodes. Experimental results obtained on the Dielmo-Ndiop project dataset show that the linear discriminant analysis (LDA) approach has significantly high accuracy in predicting malaria episodes.