Averaging of kernel functions
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In kernel-based machines, the integration of several kernels to build more flexible learning methods is a promising avenue for research. In particular, in Multiple Kernel Learning a compound kernel is build by learning a kernel that is the weighted mean of several sources. We show in this paper that the only feasible average for kernel learning is precisely the arithmetic average. We also show that three familiar means (the geometric, inverse root mean square and harmonic means) for positive real values actually generate valid kernels.
CitationBelanche, Ll.; Tosi, A. Averaging of kernel functions. A: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. "ESANN 2012: the 20th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium from 25 to 27 April 2012: proceedings". 2012, p. 363-368.