Covariate-adjusted heatmaps for visualizing biological data via correlation decomposition

Abstract

Motivation Heatmap is a popular visualization technique in biology and related fields. In this study, we extend heatmaps within 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 datasets effectively without dimension reduction. The benefit of the proposed covariate-adjusted heatmap 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 the variable pairs which possess the most significant differences at varying levels of correlation before and after a covariate adjustment. In addition, a z-score significance map is constructed to visualize these results. A simulation and three biological datasets are employed to illustrate the power and versatility of our proposed method. Availability and implementation GAP is available to readers and is free to non-commercial applications. The installation instructions, the user's manual, and the detailed tutorials can be found at http://gap.stat.sinica.edu.tw/Software/GAP. Supplementary informationSupplementary Dataare available at Bioinformatics online.