Adaptive risk-aware sharable and individual subspace learning for cancer survival analysis with multi-modality data

Biomedical multi-modality data (also named multi-omics data) refer to data that span different types and derive from multiple sources in clinical practices (e.g. gene sequences, proteomics and histopathological images), which can provide comprehensive perspectives for cancers and generally improve the performance of survival models. However, the performance improvement of multi-modality survival models may be hindered by two key issues as follows: (1) how to learn and fuse modality-sharable and modality-individual representations from multi-modality data; (2) how to explore the potential risk-aware characteristics in each risk subgroup, which is beneficial to risk stratification and prognosis evaluation. Additionally, learning-based survival models generally refer to numerous hyper-parameters, which requires time-consuming parameter setting and might result in a suboptimal solution. In this paper, we propose an adaptive risk-aware sharable and individual subspace learning method for cancer survival analysis. The proposed method jointly learns sharable and individual subspaces from multi-modality data, whereas two auxiliary terms (i.e. intra-modality complementarity and inter-modality incoherence) are developed to preserve the complementary and distinctive properties of each modality. Moreover, it equips with a grouping co-expression constraint for obtaining risk-aware representation and preserving local consistency. Furthermore, an adaptive-weighted strategy is employed to efficiently estimate crucial parameters during the training stage. Experimental results on three public datasets demonstrate the superiority of our proposed model.