Learning local graph from multiple kernels

Abstract

Graph is a widely applied technique to characterize the relationship among data. Due to the excellent ability to handle nonlinear data and extract the useful information contained in base kernels, learning the connecting graph based on multiple kernel learning has been extensively discussed. Many existing algorithms construct the connecting graph based on the optimal kernel which is learned from base kernels. Observing these methods, we find they (1) ignore the local structure of data; (2) cannot assure that the optimal kernel is positive semi-definite; (3) cannot fully utilize the information contained in base kernels. Therefore, we introduce a novel local graph based on multiple kernel learning (LGMKL) in this paper. Specifically, LGMKL is constructed based on the optimal kernel which is automatically learned from base kernels with a nonlinear strategy and the information contained in different base kernels is also utilized in LGMKL. Then an iterative scheme with proven convergence is developed to optimize the objective function of LGMKL. Unlike most MKL-based graph learning methods, LGMKL focuses on the local structure of data. Finally, nine benchmark datasets and two synthetic datasets are adopted to test the performance of LGMKL. Extensive experiments demonstrate the superiorities of the proposed method.