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One of the central goals in precision health is the understanding andinterpretation of high-dimensional biological data to identify genes andmarkers associated with disease initiation, development, and outcomes. Thoughsignificant effort has been committed to harness gene expression data formultiple analyses while accounting for time-to-event modeling by includingsurvival times, many traditional analyses have focused separately onnon-negative matrix factorization (NMF) of the gene expression data matrix andsurvival regression with Cox proportional hazards model. In this work, Coxproportional hazards regression is integrated with NMF by imposing survivalconstraints. This is accomplished by jointly optimizing the Frobenius norm andpartial log likelihood for events such as death or relapse. Simulation resultson synthetic data demonstrated the superiority of the proposed method, whencompared to other algorithms, in finding survival associated gene clusters. Inaddition, using human cancer gene expression data, the proposed technique canunravel critical clusters of cancer genes. The discovered gene clusters reflectrich biological implications and can help identify survival-related biomarkers.Towards the goal of precision health and cancer treatments, the proposedalgorithm can help understand and interpret high-dimensional heterogeneousgenomics data with accurate identification of survival-associated geneclusters.

Low-Rank Reorganization via Proportional Hazards Non-negative Matrix Factorization Unveils Survival Associated Gene Clusters