Locally adaptive multiple kernel clustering

Conventional multiple kernel learning aims to construct a global combination of multiple kernels in input space. For a data set which has varying local distributions in input space, using a uniform combination of multiple kernels may not always work well. In this paper, we proposed a localized multiple kernel learning method for clustering. Instead of using a uniform combinational kernel over the whole input space, our method associates to each cluster a localized kernel. We assign to each cluster a weight vector for feature selection and combine each weight vector with a Gaussian kernel to form a unique kernel for the corresponding cluster. By optimizing the weight vector and the width parameter of Gaussian kernel jointly for each cluster, each kernel can be localized to match the data distribution of its corresponding cluster. A locally adaptive strategy based on the kernel k-means clustering is used to optimize the kernel for each cluster. We experimentally compared our methods to the kernel k-means clustering, averaged multiple kernel clustering, self-tuning spectral clustering and Variable Bandwidth Mean Shift algorithm. Experimental results demonstrate the effectiveness of our method.