Combinatorial Kernel Matrix Model Selection Using Feature Distances

Constructing an optimal combinatorial kernel matrix is crucial in kernel methods. We propose a criterion for this model selection problem in the feature space. Differing from the previously popular kernel target alignments criterion, which is subject to limiting the combinatorial matrix that projects the inputs into two additive inverse features, the proposed criterion overcomes the limitation and measures the goodness of a combinatorial kernel matrix based on the feature distances. We first introduce the kernel target alignment and discuss its limitation for combinatorial kernel matrix. Then we present the feature-distances based combinatorial kernel matrix evaluating criterion formally. Finally, we analyze the properties of the proposed criterion and examine its performance on simulated data base. Both theoretical analysis and experimental results demonstrate that the proposed combinatorial kernel matrix evaluating criterion is sound and effective, and lays the foundation for further research of combinatorial kernel methods.