Table 9 The algorithm of our proposed method

Input: Known associations Y_train∈R^n×m, disease space kernels (\(\mathbf {K}^{d}_{SEM},\mathbf {K}^{d}_{GIP}\in \mathbf {R}^{n\times n}\)) and gene space kernels (\(\mathbf {K}^{g}_{GO},\mathbf {K}^{g}_{PPI},\mathbf {K}^{g}_{SW},\mathbf {K}^{g}_{GIP}\in \mathbf {R}^{m\times m}\)), parameters λ_d,λ_g,β and k-Nearest Neighbor for DHRLS;

Output: Predicted associations F^∗∈R^n×m;

1.Calculating disease and gene kernels, listed in Table 8;

2.Calculating disease kernel weights w_d and gene kernel weights w_g by Eq. 17 (CKA-MKL), respectively;

3.Calculating \(\mathbf {K}^{*}_{d}\) and \(\mathbf {K}^{*}_{g}\) by Eq. 14, respectively;

4.Calculating \(\mathbf {L}^{h}_{d}\) and \(\mathbf {L}^{h}_{g}\) by Eq. 21, respectively;

5.Solving Eqs. 27 and 28 (ALSA), and estimating F^∗ by Eq. 29;