Smoothed Multiple Binarization -- Using PQR Tree, Smoothing, Feature Vectors and Thresholding for Matrix Reordering

摘要

Finding appropriate permutations of rows and columns of a matrix may help users to see hidden patterns in datasets. This paper presents a set of binarization-based matrix reordering algorithms able to reveal some patterns in a quantitative data set. In these algorithms, matrix binarization converts a matrix into a set of binary ones, from which the algorithms calculate desired groups of similar rows and columns. PQR trees provide a linear order of rows and columns that obey these groups as much as possible. These algorithms use mean or median filter as smoothing techniques to minimize data noise in intermediate matrix permutation steps. They also use feature vectors or thresholding for defining binarization thresholds in intermediate steps. Our experiments with synthetic matrices revealed that our algorithms are competitive with other matrix reordering algorithms in terms of quality of reordering (Moore stress) and runtime. We observed that our set of algorithms is suitable to reveal Circumplex pattern with all tested noise ratios, and other data canonical patterns with low noise ratio.