Recent　studies　have　demonstrated　that　biomarkers　from　multiple　modalities　contain　complementary　information　for　the　diagnosis　of　Alzheimer’s　disease　(AD)　and　its　prodromal　stage　mild　cognitive　impairment　(MCI).　In　order　to　fuse　data　from　multiple　modalities,　most　previous　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　propose　a　nonlinear　graph　fusion　method　to　efficiently　exploit　the　complementarity　in　the　multi-modal　data　for　the　classification　of　AD.　Specifically,　a　graph　is　first　constructed　for　each　modality　individually.　Afterwards,　a　single　unified　graph　is　obtained　via　a　nonlinear　combination　of　the　graphs　in　an　iterative　cross　diffusion　process.　Using　the　unified　graphs,　we　achieved　classification　accuracies　of　91.8%　between　AD　subjects　and　normal　controls　(NC),　79.5%　between　MCI　subjects　and　NC　and　60.2%　in　a　three-way　classification,　which　are　competitive　with　state-of-the-art　results.　©　Springer　International　Publishing　Switzerland　2015.