  Identifying altered pathways that are associated with specific cancer types
can potentially bring a significant impact on cancer patient treatment.
Accurate identification of such key altered pathways information can be used to
develop novel therapeutic agents as well as to understand the molecular
mechanisms of various types of cancers better. Tri-matrix factorization is an
efficient tool to learn associations between two different entities (e.g.,
cancer types and pathways in our case) from data. To successfully apply
tri-matrix factorization methods to biomedical problems, biological prior
knowledge such as pathway databases or protein-protein interaction (PPI)
networks, should be taken into account in the factorization model. However, it
is not straightforward in the Bayesian setting even though Bayesian methods are
more appealing than point estimate methods, such as a maximum likelihood or a
maximum posterior method, in the sense that they calculate distributions over
variables 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 a
PPI network is taken into account in the factorization model through a finite
dependent 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 used
as a prognostic biomarkers for patient subgroup identification.
