It is challenging to use incomplete multimodality data for Alzheimer's Disease (AD) diagnosis. The current methods to address this challenge, such as low-rank matrix completion (i.e., imputing the missing values and unknown labels simultaneously) and multi-task learning (i.e., defining one regression task for each combination of modalities and then learning them jointly), are unable to model the complex data-to-label relationship in AD diagnosis and also ignore the heterogeneity among the modalities. In light of this, we propose a new Maximum Mean Discrepancy (MMD) based Multiple Kernel Learning (MKL) method for AD diagnosis using incomplete multimodality data. Specifically, we map all the samples from different modalities into a Reproducing Kernel Hilbert Space (RKHS), by devising a new MMD algorithm. The proposed MMD method incorporates data distribution matching, pair-wise sample matching and feature selection in an unified formulation, thus alleviating the modality heterogeneity issue and making all the samples comparable to share a common classifier in the RKHS. The resulting classifier obviously captures the nonlinear data-to-label relationship. We have tested our method using MRI and PET data from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset for AD diagnosis. The experimental results show that our method outperforms other methods.
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