Microarray analysis has led to a revived interest in heatmaps, or tiled displays of permuted data arrays. Analytic software typically implements these displays by clustering rows and columns of a matrix or using linear methods such as SVD. Entries in the matrix are displayed as colored pixels, with the color map driven by values in the data (and cluster trees, if they exist, displayed at the margins).
The usefulness of these displays is a matter of faith -- an assumption, perhaps, that "the data speak for themselves." The central problem, of course, is whether the popular permutation methods produce an interpretable display for a variety of data structures. To examine this problem, we explore a number of common matrix structures -- block, Toeplitz, circulant, uniform -- to see how the widely-used methods perform. We review the performance, as well, of nonlinear mappings such as MDS. The results are not encouraging with respect to the general problem.
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