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 information: Supplementary Data are available at Bioinformatics online.

BACKGROUND: The hierarchical clustering tree (HCT) with a dendrogram 1 and the singular value decomposition (SVD) with a dimension-reduced representative map 2 are popular methods for two-way sorting the gene-by-array matrix map employed in gene expression profiling. While HCT dendrograms tend to optimize local coherent clustering patterns, SVD leading eigenvectors usually identify better global grouping and transitional structures. RESULTS: This study proposes a flipping mechanism for a conventional agglomerative HCT using a rank-two ellipse (R2E, an improved SVD algorithm for sorting purpose) seriation by Chen 3 as an external reference. While HCTs always produce permutations with good local behaviour, the rank-two ellipse seriation gives the best global grouping patterns and smooth transitional trends. The resulting algorithm automatically integrates the desirable properties of each method so that users have access to a clustering and visualization environment for gene expression profiles that preserves coherent local clusters and identifies global grouping trends. CONCLUSION: We demonstrate, through four examples, that the proposed method not only possesses better numerical and statistical properties, it also provides more meaningful biomedical insights than other sorting algorithms. We suggest that sorted proximity matrices for genes and arrays, in addition to the gene-by-array expression matrix, can greatly aid in the search for comprehensive understanding of gene expression structures. Software for the proposed methods can be obtained at http://gap.stat.sinica.edu.tw/Software/GAP.