Mining High-order Multimodal Brain Image Associations via Sparse Tensor Canonical Correlation Analysis

Neuroimaging techniques have shown increasing power to understand the neuropathology of brain disorders. Multimodal brain imaging data carry distinct but complementary information and thus could depict brain disorders comprehensively. To deepen our understanding, it is essential to investigate the intrinsic associations among multiple modalities. To date, the pairwise correlations between imaging data captured by different imaging modalities have been well studied, leaving formidable challenges to identify high-order associations. In this paper, we first propose a new sparse tensor canonical correlation analysis (STCCA) with feature selection to analyze the complex high-order relationships among multimodal brain imaging data. In addition, we find that methods for identifying pairwise associations and high-order associations have complementary advantages, providing a sound reason to fuse them. Therefore, we further propose an improved STCCA (STCC$A^{+}$) which integrates STCCA and sparse multiple CCA (SMCCA) to fully uncover associations among multiple imaging modalities. The proposed STCC$A^{+}$ detects equivalent association levels among multimodal imaging data compared to SMCCA. Most importantly, both STCCA and STCC$A^{+}$ yield modality-consistent imaging markers and modality-specific ones, assuring a better and meaningful feature selection capability. Finally, the identified imaging markers and their high-order correlations could form a comprehensive indication of brain disorders, showing their promise in highorder multimodal brain imaging analysis.