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The accurate diagnosis of Alzheimer's disease (AD) at different stages is essential to identify patients at high risk of dementia and plan prevention or treatment measures accordingly. In this study, we proposed a new AD staging method for the entire spectrum of AD including the AD, Mild Cognitive Impairment with and without AD conversions, and Cognitive Normal groups. Our method embedded the high dimensional multi-view features derived from neuroimaging data into a low dimensional feature space and could form a more distinctive representation than the naive concatenated features. It also updated the testing data based on the Localized Sparse Code Gradients (LSCG) to further enhance the classification. The LSCG algorithm, validated using Magnetic Resonance Imaging data from the ADNI baseline cohort, achieved significant improvements on all diagnosis groups compared to using the original sparse coding method.