Semi-supervised low rank kernel learning algorithm via extreme learning machine

Semi-supervised kernel learning methods have been received much more attention in the past few years. Traditional semi-supervised non-parametric kernel learning (NPKL) methods usually formulate the learning task as a semi-definite programming (SDP) problem, which is very time consuming. Although some fast semi-supervised NPKL methods have been proposed recently, they usually scale very poorly. Furthermore, many semi-supervised NPKL methods are developed based on the manifold assumption. But, such an assumption might be invalid when handling some high-dimensional and sparse data, which has severely negative effect on the performance of learning algorithms. In this paper, we propose a more efficient semi-supervised NPKL method, which can effectively learn a low-rank kernel matrix from must-link and cannot-link constraints. Specially, by virtue of the nonlinear embedding functions based on extreme learning machine (ELM), the proposed method has the ability of coping with data points that do not have a clear manifold structure in a low dimensional space. The proposed method is formulated as a trace ratio optimization problem, which is combined with dimensionality reduction in ELM feature space and aims to find optimal low-rank kernel matrices. The proposed optimization problem can be solved much more efficiently than SDP solvers. Extensive experiments have validated the superior performance of the proposed method compared to state-of-the-art semi-supervised kernel learning methods.