  Multiple kernel learning (MKL) method is generally believed to perform better
than single kernel method. However, some empirical studies show that this is
not always true: the combination of multiple kernels may even yield an even
worse performance than using a single kernel. There are two possible reasons
for the failure: (i) most existing MKL methods assume that the optimal kernel
is a linear combination of base kernels, which may not hold true; and (ii) some
kernel weights are inappropriately assigned due to noises and carelessly
designed algorithms. In this paper, we propose a novel MKL framework by
following two intuitive assumptions: (i) each kernel is a perturbation of the
consensus kernel; and (ii) the kernel that is close to the consensus kernel
should be assigned a large weight. Impressively, the proposed method can
automatically assign an appropriate weight to each kernel without introducing
additional parameters, as existing methods do. The proposed framework is
integrated into a unified framework for graph-based clustering and
semi-supervised classification. We have conducted experiments on multiple
benchmark datasets and our empirical results verify the superiority of the
proposed framework.
