scHiCSRS: A Self-Representation Smoothing Method with Gaussian Mixture Model for Imputing single-cell Hi-C Data

Motivation: Single-cell Hi-C techniques make it possible to study cell-to-cell variability in genomic features. However, excess zeros are commonly seen in single-cell Hi-C (scHi-C) data, making scHi-C matrices extremely sparse and bringing extra difficulties in downstream analysis. The observed zeros are a combination of two events: structural zeros for which the loci never inter- act due to underlying biological mechanisms, and dropouts or sampling zeros where the two loci interact but are not captured due to insufficient sequencing depth. Although quality improvement approaches have been proposed as an intermediate step for analyzing scHi-C data, little has been done to address these two types of zeros. We believe that differentiating between structural zeros and dropouts would benefit downstream analysis such as clustering. Results: We propose scHiCSRS, a self-representation smoothing method that improves the data quality, and a Gaussian mixture model that identifies structural zeros among observed zeros. scHiCSRS not only takes spatial dependencies of a scHi-C 2D data structure into account but also borrows information from similar single cells. Through an extensive set of simulation studies, we demonstrate the ability of scHiCSRS for identifying structural zeros with high sensitivity and for accurate imputation of dropout values in sampling zeros. Downstream analysis for three real datasets show that data improved from scHiCSRS yield more accurate clustering of cells than simply using observed data or improved data from several comparison methods.