A Novel Locally Multiple Kernel K-Means Based On Similarity

Most of multiple kernel clustering algorithms aim to find the optimal kernel combination and have to calculate kernel weights iteratively. For the kernel methods, the scale parameter of Gaussian kernel is usually searched in a number of candidate values of the parameter and the best is selected. In this paper, a novel multiple kernel k-means algorithm is proposed based on similarity measure. Our similarity measure meets the requirements of the clustering hypothesis, which can describe the relations between data points more reasonably by taking local and global structures into consideration. We assign to each data point a local scale parameter and combine the parameter with density factor to construct kernel matrix. According to the local distribution, the local scale parameter of Gaussian kernel is generated adaptively. The density factor is inspired by density-based algorithm. However, different from density-based algorithm, we first find neighbor data points using k nearest neighbor method and then find density-connected sets by union-find set method. Experiments show that the proposed algorithm can effectively deal with the clustering problem of datasets with complex structure or multiple scales.