Semi-supervised deep matrix factorization model for clustering multi-omics data

Multi-omics data are inherently high-dimensional, sparse, and noisy, posing significant challenges for clustering and integration. Conventional clustering and linear dimensionality reduction methods often fail to handle noise effectively or provide interpretability, while standard non-negative matrix factorization approaches are too shallow to capture non-linear patterns. Multi-view non-negative matrix factorization enables integration of complementary views, but it remains primarily unsupervised and seldom leverages available label information.

We propose SSD-MO, a Semi-Supervised Deep Non-Negative Matrix Factorization model for Multi-Omics Data, designed to address these challenges by leveraging both labelled and unlabelled samples for enhanced data integration and clustering performance. SSD-MO combines semi-supervised learning with a multi-layer deep factorization framework, preserving local geometric structure and incorporating orthogonal and diversity constraints. Its effectiveness was validated on six multi-omics datasets from The Cancer Genome Atlas, using evaluation metrics such as clustering accuracy, normalized mutual information, and F-scores.

SSD-MO significantly improved clustering accuracy, achieving an increase in F-score by 9%-24% compared to unsupervised baselines and 7%-20% over semi-supervised benchmarks. Precision (64%-73%) and Recall (70%-88%) values further demonstrated its robust performance across datasets.

This method provides a robust framework for multi-omics data integration and holds promise for applications in genomics and precision medicine.