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Heterogeneous gene network estimation for single-cell transcriptomic data via a joint regularized deep neural network

Estimation of intracellular gene networks has been a critical component of single-cell transcriptomic data analysis, which can provide crucial insights into the complex interplay between genes, facilitating the discovery of the biological basis of human life at single-cell resolution. Despite notable achievements, existing methodologies often falter in their practicality, primarily due to their narrow focus on simplistic linear relationships and inadequate handling of cellular heterogeneity. To bridge these gaps, we propose a joint regularized deep neural network method incorporating Mahalanobis distance-based K-means clustering (JRDNN-KM) to estimate multiple networks for various cell subgroups simultaneously, accounting for both unknown cellular heterogeneity and zero inflation, and, more importantly, complex nonlinear relationships among genes. We introduce an innovative selection layer for network construction, along with hidden layers that include both shared and subgroup-specific neurons, to capture common patterns and subgroup-specific variations across networks. Applied to real single-cell transcriptomic data from multiple tissues and species, JRDNN-KM demonstrates higher accuracy and biological interpretability in network estimation, and more accurately identifies cell subgroups compared to current state-of-the-art methods.Building on network construction, we further find hub genes with important biological implications and modules with statistical enrichment of biological processes.