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Identifying altered pathways that are associated with specific cancer typescan potentially bring a significant impact on cancer patient treatment.Accurate identification of such key altered pathways information can be used todevelop novel therapeutic agents as well as to understand the molecularmechanisms of various types of cancers better. Tri-matrix factorization is anefficient tool to learn associations between two different entities (e.g.,cancer types and pathways in our case) from data. To successfully applytri-matrix factorization methods to biomedical problems, biological priorknowledge such as pathway databases or protein-protein interaction (PPI)networks, should be taken into account in the factorization model. However, itis not straightforward in the Bayesian setting even though Bayesian methods aremore appealing than point estimate methods, such as a maximum likelihood or amaximum posterior method, in the sense that they calculate distributions overvariables and are robust against overfitting. We propose a Bayesian(semi-)nonnegative matrix factorization model for human cancer genomic data,where the biological prior knowledge represented by a pathway database and aPPI network is taken into account in the factorization model through a finitedependent Beta-Bernoulli prior. We tested our method on The Cancer Genome Atlas(TCGA) dataset and found that the pathways identified by our method can be usedas a prognostic biomarkers for patient subgroup identification.

Bayesian Semi-nonnegative Tri-matrix Factorization to Identify Pathways Associated with Cancer Types