An unsupervised approach to learn the kernel functions: from global influence to local similarity

Recently there has been a steep growth in the development of kernel-based learning algorithms. The intrinsic problem in such algorithms is the selection of the optimal kernel for the learning task of interest. In this paper, we propose an unsupervised approach to learn a linear combination of kernel functions, such that the resulting kernel best serves the objectives of the learning task. This is achieved through measuring the influence of each point on the structure of the dataset. This measure is calculated by constructing a weighted graph on which a random walk is performed. The measure of influence in the feature space is probabilistically related to the input space that yields an optimization problem to be solved. The optimization problem is formulated in two different convex settings, namely linear and semidefinite programming, dependent on the type of kernel combination considered. The contributions of this paper are twofold: first, a novel unsupervised approach to learn the kernel function, and second, a method to infer the local similarity represented by the kernel function by measuring the global influence of each point toward the structure of the dataset. The proposed approach focuses on the kernel selection which is independent of the kernel-based learning algorithm. The empirical evaluation of the proposed approach with various datasets shows the effectiveness of the algorithm in practice.