Recovery of corrupted multiple kernels for clustering
Peng Zhou, Liang Du, Lei Shi, Hanmo Wang, Yi-Dong Shen · 2015
Kernel-based methods, such as kernel k-means and kernel PCA, have been widely used in machine learning tasks. The performance of these methods critically depends on the selection of kernel func-tions; however, the challenge is that we usually do not know what kind of kernels is suitable for the given data and task in advance; this leads to re-search on multiple kernel learning, i.e. we learn a consensus kernel from multiple candidate kernels. Existing multiple kernel learning methods have dif-ficulty in dealing with noises. In this paper, we pro-pose a novel method for learning a robust yet low-rank kernel for clustering tasks. We observe that the noises of each kernel have specific structures, so we can make full use of them to clean multi-ple input kernels and then aggregate them into a robust, low-rank consensus kernel. The underly-ing optimization problem is hard to solve and we will show that it can be solved via alternating mini-mization, whose convergence is theoretically guar-anteed. Experimental results on several benchmark data sets further demonstrate the effectiveness of our method. 1