The main drawbacks of existing methods are as follows: (1) since the sparse constraint is added during each deflation process, the selected variables are different for each time. (2) The selected variables are not highly related with response matrix thus the accuracy is low. (3) The result is not interpretable with all sparse vectors. As shown in Fig. 3, three sparse loading vectors obtained by sparse and MNPLS are plotted in Fig. 3 (a) and (b) respectively. According to Fig. 3 (a), the weighted