  Given multi-platform genome data with prior knowledge of functional gene
sets, how can we extract interpretable latent relationships between patients
and genes? More specifically, how can we devise a tensor factorization method
which produces an interpretable gene factor matrix based on gene set
information while maintaining the decomposition quality and speed? We propose
GIFT, a Guided and Interpretable Factorization for Tensors. GIFT provides
interpretable factor matrices by encoding prior knowledge as a regularization
term in its objective function. Experiment results demonstrate that GIFT
produces interpretable factorizations with high scalability and accuracy, while
other methods lack interpretability. We apply GIFT to the PanCan12 dataset, and
GIFT reveals significant relations between cancers, gene sets, and genes, such
as influential gene sets for specific cancer (e.g., interferon-gamma response
gene set for ovarian cancer) or relations between cancers and genes (e.g., BRCA
cancer - APOA1 gene and OV, UCEC cancers - BST2 gene).
