Multi-Constraint Latent Representation Learning for Prognosis Analysis Using Multi-Modal Data

The Cox proportional hazard model has been widely applied to cancer prognosis prediction. Nowadays, multi-modal data, such as histopathological images and gene data, have advanced this field by providing histologic phenotype and genotype information. However, how to efficiently fuse and select the complementary information of high-dimensional multi-modal data remains challenging for Cox model, as it generally does not equip with feature fusion/selection mechanism. Many previous studies typically perform feature fusion/selection in the original feature space before Cox modeling. Alternatively, learning a latent shared feature space that is tailored for Cox model and simultaneously keeps sparsity is desirable. In addition, existing Cox-based models commonly pay little attention to the actual length of the observed time that may help to boost the model's performance. In this article, we propose a novel Cox-driven multi-constraint latent representation learning framework for prognosis analysis with multi-modal data. Specifically, for efficient feature fusion, a multi-modal latent space is learned via a bi-mapping approach under ranking and regression constraints. The ranking constraint utilizes the log-partial likelihood of Cox model to induce learning discriminative representations in a task-oriented manner. Meanwhile, the representations also benefit from regression constraint, which imposes the supervision of specific survival time on representation learning. To improve generalization and alleviate overfitting, we further introduce similarity and sparsity constraints to encourage extra consistency and sparseness. Extensive experiments on three datasets acquired from The Cancer Genome Atlas (TCGA) demonstrate that the proposed method is superior to state-of-the-art Cox-based models.