From the Figure, we can observe that all three algorithms achieve the largest Fmax value on the 6-th network, and the Fmax value on each individual network has a similar rank among the eight individual networks across the different methods, i.e., the Fmax value on the 1st network ranks second according to MNet, SW, and ProMK. MNet assigns a larger weight on the 6-th network as compared to the weights for the other networks. In contrast, neither SW nor ProMK assigns the largest weight to the 6-th network. MNet, SW, and ProMK give the smallest weight to the 8-th network, though these methods do not produce the lowest Fmax for the 8-th network. The reason is that the 8-th network produces rather large smoothness loss values as compared to those of the other networks. Since λ2 is given a large value, ProMK assigns nearly equal weights to the first 7 networks. Because the smoothness loss value on the 8-th network is much larger than for the others, ProMK assigns zero weight to the 8-th network. Note that for small λ2 values, ProMK can only use one network and produces deteriorated results (see our parameter analysis in the next subsection). The Fmax values on the first three networks progressively decrease, and the weights assigned by MNet and SW to these networks also decrease. In contrast, the weights assigned by ProMK do not follow this trend. ProMK assigns larger weights to the 2nd and 3rd networks. The Fmax values on the next three (4-th, 5-th, and 6-th) networks, as well as the weights assigned by MNet, progressively increase, but the weight assigned by SW to the 4-th network is larger than those assigned to the 5-th and 6-th networks, and the weights assigned by ProMK progressively decrease. All these three methods give a smaller Fmax value to the 7-th network than to the 6-th; both MNet and SW assign a smaller weight to the 7-th network than to the 6-th, but ProMK assigns a larger weight to the 7-th network than to the 6-th. ProMK, OMG and LIG use only the smoothness loss to assign weights to the individual networks. The smaller the value of the smoothness loss for a network is, the larger the weight assigned to it is. The value of the smoothness loss of ProMK on the 3rd network is smaller than the values of the other networks, thus ProMK assigns a weight to the 3rd network that is larger than the ones assigned to other networks. However, the value of Fmax of this network is the lowest. This conflictual scenario shows that assigning a weight to a network merely based on the smoothness loss is not always reasonable. This justifies our motivation to unifying the kernel target alignment with the loss of classifier in one objective function, and also provides evidence as for why MNet works better than the other algorithms. These observations also apply to the results provided in the Additional File 1.