Abstract
Single-cell multi-omics clustering requires integrated representations that preserve shared biological states and modality-specific signals. Graph-based generative methods often couple clustering and reconstruction through a common latent pathway and a single neighborhood graph. We propose SP-LSNTA-GeDGC, which combines task-oriented shared–private (SP) routing and Latent Spectral Neighborhood–Transport Alignment (LSNTA) within a graph-embedded deep generative clustering (GeDGC) framework. Modality-specific residuals support reconstruction, while clustering uses the shared representation without introducing an independent private posterior. LSNTA integrates shared-latent spectral learning, feature-gated mutual nearest neighbors and unbalanced optimal transport to refine graph sample centers and cross-modal relations. The refined centers also serve as reconstruction targets during joint training. Consensus neighborhoods and averaged pairwise transport extend the framework to more than two inputs. Across five bimodal benchmarks, five-run comparisons on identical processed inputs yield a mean clustering accuracy (ACC) increase of 3.08 percentage points over GeDGC. Holm-adjusted paired t tests support ACC and adjusted Rand index (ARI) improvements on Pbmc10k, while gains on other datasets remain descriptive. Metric means decrease on the transcripts, epitopes and accessibility sequencing (TEA-seq) dataset, whereas the compatible four-input dyngen simulation shows small gains. Component ablations reveal dataset-dependent effects without establishing an additional SP–LSNTA interaction. These findings support conditional clustering benefits under known-K evaluation, while broader multimodal generalization and computational scalability remain open challenges.