Kernel Integration Using von Neumann Entropy

Kernel methods provide a computational framework to integrate heterogeneous biological data from different sources for a wide range of learning algorithms by designing a kernel for each di®erent information source and combining them in a unique kernel through simple mathematical operations. We develop here a novel technique for weighting kernels based on their von Neumann entropy. This permits to assess the kernel quality without using label information, and to integrate kernels before the beginning of the learning process. Moreover, we carry out a comparison with the unweighted kernel summation and a popular technique based on semi-definite programming on kernel integration benchmark data sets. Finally, we empirically study the variation of the performance of a support vector machine classi¯er considering pairs of kernels combined in di®erent ratios, and we show how, surprisingly, the unweighted sum of kernels seems to lead to the same performance than a more complex weighting schema.