Topology constrained nonnegative matrix factorization for time varying omic expression.

Deciphering disease-specific progression from low sample size, high-dimensional omic profiles remains challenging. Traditional biomarker discovery methods are costly and limited, while Nonnegative Matrix Factorization (NMF), though popular, suffers from instability and lack of biologically relevant solutions. This study aims to overcome these limitations by introducing a more robust framework. This article proposes TopConNMF, a topology-constrained extension of NMF which incorporates structural constraints, ensures stability, accuracy, and faster performance while maintaining biological interpretability. The method was evaluated on two publicly available time-varying omic datasets with established ground truths and compared against other state-of-the-art approaches. The TopConNMF consistently demonstrated stable performance across both the datasets, delivering superior accuracy and biologically relevant factorization compared to conventional NMF and other benchmark methods. The exhaustive evaluation confirmed its robustness in capturing disease-specific profiles and its efficiency in handling complex, high-dimensional data. Thus, TopConNMF provides a deeper understanding of complex biological systems by producing stable and interpretable factorization. Its broad applicability across multiple disease manifestations highlights its potential as a valuable tool for advancing omic data analysis and biomarker discovery. Clinical Impact: TopConNMF enables reliable biomarker discovery from limited omic data, supporting early diagnosis, patient stratification, and personalized treatment, thereby bridging computational findings with clinical applications.