Dimension Reduction for High-dimensional Small Counts with KL Divergence

Yurong Ling, Jing-Hao Xue

Abstract: Dimension reduction for high-dimensional count data with a large proportion of zeros is an important task in various applications. As a large number of dimension reduction methods rely on the proximity measure, we develop a dissimilarity measure that is well-suited for small counts based on the Kullback-Leibler divergence. We compare the proposed measure with other widely used dissimilarity measures and show that the proposed one has superior discrimination ability when applied to high-dimensional count data having an excess of zeros. Extensive empirical results, on both simulated and publicly-available real-world datasets that contain many zeros, demonstrate that the proposed dissimilarity measure can improve a wide range of dimension reduction methods.