Enhanced Multimodal Low-Rank Embedding-Based Feature Selection Model for Multimodal Alzheimer’s Disease Diagnosis

Identification of Alzheimer’s disease (AD) with multimodal neuroimaging data has been receiving increasing attention. However, the presence of numerous redundant features and corrupted neuroimages within multimodal datasets poses significant challenges for existing methods. In this paper, we propose a feature selection method named Enhanced Multimodal Low-rank Embedding (EMLE) for multimodal AD diagnosis. Unlike previous methods utilizing convex relaxations of the $\ell _{{2},{0}}$ -norm, EMLE exploits an $\ell _{{2},\gamma }$ -norm regularized projection matrix to obtain an embedding representation and select informative features jointly for each modality. The $\ell _{{2},\gamma }$ -norm, employing an upper-bounded nonconvex Minimax Concave Penalty (MCP) function to characterize sparsity, offers a superior approximation for the $\ell _{{2},{0}}$ -norm compared to other convex relaxations. Next, a similarity graph is learned based on the self-expressiveness property to increase the robustness to corrupted data. As the approximation coefficient vectors of samples from the same class should be highly correlated, an MCP function introduced norm, i.e., matrix $\gamma $ -norm, is applied to constrain the rank of the graph. Furthermore, recognizing that diverse modalities should share an underlying structure related to AD, we establish a consensus graph for all modalities to unveil intrinsic structures across multiple modalities. Finally, we fuse the embedding representations of all modalities into the label space to incorporate supervisory information. The results of extensive experiments on the Alzheimer’s Disease Neuroimaging Initiative datasets verify the discriminability of the features selected by EMLE.