Algorithm 1.

to minimize J in Equation (9)

Input: risk genetics (i.e. APOE) y= [y1, …, yn, …, yN]T ∊ RN,   multi-modalities ${\mathrm{X}}^{\mathrm{m}}={[{\mathrm{X}}_1^{\mathrm{m}},\dots ,{\mathrm{X}}_{\mathrm{n}}^{\mathrm{m}},\dots ,{\mathrm{X}}_{\mathrm{N}}^{\mathrm{m}}]}^{\mathrm{T}}\in {\mathrm{R}}^{\mathrm{N}\times \mathrm{d}}$,   subjects with diagnosis labels (i.e., HC, SMC, EMCI, LMCI or AD)

Output: Wi, J*

Initialization: l0 = 1, σ = 2, W0 = Z1 = 0, ρ0 = 1, I=1000

For i=1 to max_iteration I Computed the search point Zi according to Eq (16) l = li−1 while (f(Wi) + g(Wi)) > Ω(Wi, Zi), l = σl; Here Wi is computed by Eq (13) Set li ← l

End

Calculate J*