Incomplete data present serious problems when integrating large-scale brain imaging data sets from different imaging modalities. In the Alzheimer's Disease Neuroimaging Initiative (ADNI), for example, over half of the subjects lack cerebrospinal fluid (CSF) measurements; an independent half of the subjects do not have fluorodeoxyglucose positron emission tomography (FDG-PET) scans; many lack proteomics measurements. Traditionally, subjects with missing measures are discarded, resulting in a severe loss of available information. We address this problem by proposing two novel learning methods where all the samples (with at least one available data source) can be used. In the first method, we divide our samples according to the availability of data sources, and we learn shared sets of features with state-of-the-art sparse learning methods. Our second method learns a base classifier for each data source independently, based on which we represent each source using a single column of prediction scores; we then estimate the missing prediction scores, which, combined with the existing prediction scores, are used to build a multi-source fusion model. To illustrate the proposed approaches, we classify patients from the ADNI study into groups with Alzheimer's disease (AD), mild cognitive impairment (MCI) and normal controls, based on the multi-modality data. At baseline, ADNI's 780 participants (172 AD, 397 MCI, 211 Normal), have at least one of four data types: magnetic resonance imaging (MRI), FDG-PET, CSF and proteomics. These data are used to test our algorithms. Comprehensive experiments show that our proposed methods yield stable and promising results.