GIFT: Guided and Interpretable Factorization for Tensors - An Application to Large-Scale Multi-platform Cancer Analysis

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).