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For the last decade, it has been shown that neuroimaging can be a potential tool for the diagnosis of Alzheimer's Disease (AD) and its prodromal stage, Mild Cognitive Impairment (MCI), and also fusion of different modalities can further provide the complementary information to enhance diagnostic accuracy. Here, we focus on the problems of both feature representation and fusion of multimodal information from Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). To our best knowledge, the previous methods in the literature mostly used hand-crafted features such as cortical thickness, gray matter densities from MRI, or voxel intensities from PET, and then combined these multimodal features by simply concatenating into a long vector or transforming into a higher-dimensional kernel space. In this paper, we propose a novel method for a high-level latent and shared feature representation …