Fig. 1

Benchmarking of scHi-C normalization and de-noising methods for cell-type clustering. a Band transformation separates scHi-C contact matrices into band-specific cell \(\times\) locus pair matrices before conducting BandNorm normalization on each band matrix per chromosome per cell. BandNorm normalizes the raw interaction counts \(Y^{cv}_r\) for locus pair r in band v and cell c into normalized count \(C^{cv}_r\). b Deep generative model, scVI-3D, for a single band matrix v with entries in the form of locus pairs r (\(r \in \mathcal {A}(v)\)) by cells c (\(c = 1, ..., N\)). The raw interaction counts \(Y^{cv}_r\) are modeled as a function of low-dimensional latent variables \(\mathbf {z}_{cv}\). Refer to the Section 5 for a detailed mathematical introduction and practical settings of the scVI-3D model. c Evaluation of the eight scHi-C normalization and de-noising methods, namely CellScale, BandScale, BandNorm, scHiCluster, scHiC Topics, Higashi, CellScale+CNN, and scVI-3D, for cell type separation across four benchmark datasets. The performances are evaluated by Adjusted Rand Index (ARI) after K-means clustering and Louvain graph clustering and by Silhouette coefficient on UMAP and t-SNE visualizations with the true cell labels. d Median ranks of the performance of the scHi-C methods across the six evaluation metrics and four data sets