A fast feature vector approach for revealing simplex and equi-correlation data patterns in reorderable matrices

Abstract

Reorderable matrices may be used as support for tabular displays such as heatmaps. Matrix reordering algorithms provide an initial permutation of these matrices, which should help to reveal hidden patterns in the dataset in the visual structure. Some of these algorithms directly permute the data matrix, instead of its row- and column-proximity matrices. We present a data matrix reordering method ( feature vector-based sort – FVS), which reorders a data matrix aiming to reveal simplex and equi-correlation patterns. Our approach extracts feature vectors from a data matrix and uses them to calculate row and column permutations of the data matrix. We used FVS for reordering data matrices of distinct real-world scenarios, in which it revealed those patterns. Our experiments with synthetic matrices revealed that FVS is faster than other known matrix-reordering algorithms and produces results of approximately the same quality (in terms of stress function) when these patterns are hidden in the data matrix. We also present some real-world datasets reordered by our algorithm and discuss the patterns that it uncovers.

A comparative analysis of matrix reordering algorithms regarding canonical data patterns

“…The evaluation functions used distance matrices with binary proximity coefficients (Jaccard and Simple Matching). Other papers from the same research group used small variations of this process (such as using Moore Stress and Circular Correlation) to evaluate new reordering algorithms 7,17,18 applied to a subset of Wilkinson’s patterns.…”