Accurate　diagnosis　of　Alzheimer＇s　disease　(AD)　and　its　prodromal　stage　mild　cognitive　impairment　(MCI)　is　of　great　interest　to　patients　and　clinicians.　Recent　studies　have　demonstrated　that　multiple　neuroimaging　and　biological　measures　contain　complementary　information　for　diagnosis　and　prognosis.　Classification　methods　are　needed　to　combine　these　multiple　biomarkers　to　provide　an　accurate　diagnosis.　State-of-the-art　approaches　calculate　a　mixed　kernel　or　a　similarity　matrix　by　linearly　combining　kernels　or　similarities　from　multiple　modalities.　However,　the　complementary　information　from　multi-modal　data　are　not　necessarily　linearly　related.　In　addition,　this　linear　combination　is　also　sensitive　to　the　weights　assigned　to　each　modality.　In　this　paper,　we　present　a　multi-modality　classification　framework　to　efficiently　exploit　the　complementarity　in　the　multi-modal　data.　First,　pairwise　similarity　is　calculated　for　each　modality　individually　using　the　features　including　regional　MRI　volumes,　voxel-based　FDG-PET　signal　intensities,　CSF　biomarker　measures,　and　categorical　genetic　information.　Similarities　from　multiple　modalities　are　then　combined　in　a　nonlinear　graph　fusion　process,　which　generates　a　unified　graph　for　final　classification.　Based　on　the　unified　graphs,　we　achieved　classification　area　under　curve　(AUC)　of　receiver-operator　characteristic　of　98.1%　between　AD　subjects　and　normal　controls　(NC),　82.4%　between　MCI　subjects　and　NC　and　77.9%　in　a　three-way　classification,　which　are　significantly　better　than　those　using　single-modality　biomarkers　and　those　based　on　state-of-the-art　linear　combination　approaches.