Single-cell RNA sequencing data rely heavily on dimensionality reduction methods to uncover underlying structures and patterns. Nonlinear dimensionality-reduction methods such as uniform manifold approximation and t-distributed stochastic neighbor embedding have been routinely used for this task. However, gene expression data alone often fails to capture and identify changes in cellular pathways, protein complexes, and TF-targets, which are more enlightening at the regulation level. To address this limitation, we present PVAED, a dimensionality reduction framework that integrates biological prior knowledge into a variational autoencoder (VAE) and further refines its latent embeddings with a diffusion-based denoising module. In addition, we incorporate a neighborhood-preserving loss term to ensure local similarity among cells in the reduced space. Across multiple benchmarks, PVAED achieves an average 43% improvement in low-dimensional cell representation compared to standard VAEs (evaluated across seven clustering metrics) and delivers a 34% (44%) gain in projection quality relative to classical or VAE-based approaches in terms of global (local) structure preservation. Beyond performance, PVAED offers improved interpretability through its prior-based encoder design, enabling prioritization and modeling of interpretable biological variables as hypergraphs. This framework facilitates the identification of critical regulatory factors associated with disease pathology and could also be utilized to predict potentially related genes for known pathways. Finally, we demonstrate the utility of PVAED by revealing pre-committed neuronal subpopulations in the differentiation of migrating neurons within the mammalian cerebral cortex.

The interrelation and complementary nature of multi-omics data can provide valuable insights into the intricate molecular mechanisms underlying diseases. However, challenges such as limited sample size, high data dimensionality and differences in omics modalities pose significant obstacles to fully harnessing the potential of these data. The prior knowledge such as gene regulatory network and pathway information harbors useful gene-gene interaction and gene functional module information. To effectively integrate multi-omics data and make full use of the prior knowledge, here, we propose a Multilevel-graph neural network (GNN): a hierarchically designed deep learning algorithm that sequentially leverages multi-omics data, gene regulatory networks and pathway information to extract features and enhance accuracy in predicting survival risk. Our method achieved better accuracy compared with existing methods. Furthermore, key factors nonlinearly associated with the tumor pathogenesis are prioritized by employing two interpretation algorithms (i.e. GNN-Explainer and IGscore) for neural networks, at gene and pathway level, respectively. The top genes and pathways exhibit strong associations with disease in survival analyses, many of which such as SEC61G and CYP27B1 are previously reported in the literature.

Linkage analysis serves as a way of finding locations of genes that cause genetic diseases. Linkage studies have facilitated the identification of several hundreds of human genes that can harbor mutations which by themselves lead to a disease phenotype. The fundamental problem in linkage analysis is to identify regions whose allele is shared by all or almost all affected members but by none or few unaffected members. Almost all the existing methods for linkage analysis are for families with clearly given pedigrees. Little work has been done for the case where the sampled individuals are closely related, but their pedigree is not known. This situation occurs very often when the individuals share a common ancestor at least six generations ago. Solving this case will tremendously extend the use of linkage analysis for finding genes that cause genetic diseases. In this paper, we propose a mathematical model (the shared center problem) for inferring the allele-sharing status of a given set of individuals using a database of confirmed haplotypes as reference. We show the NP-completeness of the shared center problem and present a ratio-2 polynomial-time approximation algorithm for its minimization version (called the closest shared center problem). We then convert the approximation algorithm into a heuristic algorithm for the shared center problem. Based on this heuristic, we finally design a heuristic algorithm for mutation region detection. We further implement the algorithms to obtain a software package. Our experimental data show that the software is both fast and accurate. The package is available at >;http://www.cs.cityu.edu.hk/~lwang/software/LDWP/ for noncommercial use.