Semi-supervised classification with Laplacian multiple kernel learning

Nonlinear Semi-Supervised Metric Learning Via Multiple Kernels and Local Topology

Changing the metric on the data may change the data distribution, hence a good distance metric can promote the performance of learning algorithm. In this paper, we address the semi-supervised distance metric learning (ML) problem to obtain the best nonlinear metric for the data. First, we describe the nonlinear metric by the multiple kernel representation. By this approach, we project the data into a high dimensional space, where the data can be well represented by linear ML. Then, we reformulate the linear ML by a minimization problem on the positive definite matrix group. Finally, we develop a two-step algorithm for solving this model and design an intrinsic steepest descent algorithm to learn the positive definite metric matrix. Experimental results validate that our proposed method is effective and outperforms several state-of-the-art ML methods.

Laplacian Embedded Infinite Kernel Model for Semi-Supervised Classification

Promoted by its convexity and low time complexity, Laplacian embedded support vector regression (LapESVR) model based on manifold regularization (MR) has assumed an important role in semi-supervised classification. Conventionally, the LapESVR model is based on a single kernel function that is intrinsically capable of describing one feature mapping relation only. However, when the data to be processed is from a complex dataset where multiple features of the data are required to be treated, the classification performance using the LapESVR based on a single kernel substantially degrade, indicating that the classification requirement in this case is beyond the capability of the LapESVR. In addition, the processing data is often subject to the impact of abnormal data samples; therefore, in practice assigning a fixed value that is related to the average distance of the processing data as the parameter value of kernel function of the LapESVR is by no means optimal. To solve the problems as mentioned regarding the LapESVR, this paper proposes a Laplacian embedded infinite kernel regression (LapEIKR) model. The proposed model combines the multiple kernels linearly to improve its ability of characterization of the processing data, typical in semi-supervised classification of complex datasets, with multiple features. Further, the parameter setting of the multiple kernels of the LapEIKR model is turned into an optimization problem by formulating a corresponding minimum objective function and an iterative algorithm, and then the values of the settings are facilitated to be obtained by a formulated calculation, assuming the optimal values with respect to the designed objective function. Comparative experiments on the UCI datasets, benchmark datasets and Caltech256 datasets show that the proposed LapEIKR model is improving in terms of adaptivity and efficiency.