FAM3L: Feature-Aware Multi-Modal Metric Learning for Integrative Survival Analysis of Human Cancers

Survival analysis is to estimate the survival time for an individual or a group of patients, which is a valid solution for cancer treatments. Recent studies suggested that the integrative analysis of histopathological images and genomic data can better predict the survival of cancer patients than simply using single bio-marker, for different bio-markers may provide complementary information. However, for the given multi-modal data that may contain irrelevant or redundant features, it is still challenge to design a distance metric that can simultaneously discover significant features and measure the difference of survival time among different patients. To solve this issue, we propose a Feature-Aware Multi-modal Metric Learning method (FAM3L), which not only learns the metric for distance constraints on patients' survival time, but also identifies important images and genomic features for survival analysis. Specifically, for each modality of data, we firstly design one feature-aware metric that can be decoupled into a traditional distance metric and a diagonal weight for important feature identification. Then, in order to explore the complex correlation across multiple modality data, we apply Hilbert-Schmidt Independence Criterion (HSIC) to jointly learn multiple metrics. Finally, based on the learned distance metrics, we apply the Cox proportional hazards model for prognosis prediction. We evaluate the performance of our proposed FAM3L method on three cancer cohorts derived from The Cancer Genome Atlas (TCGA), the experimental results demonstrate that our method can not only achieve superior performance for cancer prognosis, but also identify meaningful image and genomic features correlating strongly with cancer survival.