MHeatmap: Two-Walk Laplacian Reordering and Mosaic Layout for Rectangular Matrix Visualization

MHeatmap (Mosaic Heatmap) is a visualization technique for weighted rectangular matrices that improves readability by reordering rows and columns using a Two-Walk spectral seriation approach and by scaling cell dimensions proportionally to row and column totals in a Mosaic layout. The Two-Walk method extends traditional bipartite ordering by incorporating length‑two walks, creating similarity links between rows sharing columns and columns sharing rows, and then sorting a Fiedler vector of the resulting graph Laplacian to obtain coordinated orders. The Mosaic layout partitions a unit square so that cell height and width reflect row and column totals, while color encodes the matrix entries, and the authors provide theoretical proofs and efficient sparse computation for the method, demonstrating superior performance on synthetic and real datasets.