  Generating a dissimilarity matrix is typically the first step in big data
analysis. Although numerous methods exist, such as Euclidean distance,
Minkowski distance, Manhattan distance, Bray Curtis dissimilarity, Jaccard
similarity and Dice dissimilarity, it remains unclear which factors drive
dissimilarity between groups. In this paper, we introduce an approach based on
differences in moments and sparsity. We show that this method can delineate the
key factors underlying group differences. For example, in biology, mean
dissimilarity indicates differences driven by up down regulated gene
expressions, standard deviation dissimilarity reflects the heterogeneity of
response to treatment, and sparsity dissimilarity corresponds to differences
prompted by the activation silence of genes. Through extensive reanalysis of
genome, transcriptome, proteome, metabolome, immune profiling, microbiome, and
social science datasets, we demonstrate insights not captured in previous
studies. For instance, it shows that the sparsity dissimilarity is as effective
as the mean dissimilarity in predicting the alleviation effects of a COVID 19
drug, suggesting that sparsity dissimilarity is highly meaningful.
