A coarse-to-fine two-step method for semisupervised classification using quasi-linear Laplacian SVM

This paper proposes a two-step method to construct a nonlinear classifier based on semisupervised learning in a coarse-to-fine way. In the first step, a recursive density-based spatial clustering of applications with noise clustering algorithm is first introduced to find a group of density clusters, each of which contains only one kind of class labels. An SK algorithm is then applied to pairs of density clusters containing different class labels to find a set of local linear classifiers, which forms a coarse nonlinear separating boundary crossing the low-density areas by interpolating the local linear classifiers. In the second step, a Laplacian support vector machine (LapSVM) formulation based on graph construction is applied to further implicitly optimize the parameter set of the nonlinear coarse classifier. As a result, the fine-tuned nonlinear classifier is constructed in exactly the same way as a standard LapSVM, using a special data-dependent quasi-linear kernel composed of the interpolation functions and the information of the local linear classifiers obtained in the first step. Moreover, the quasi-linear kernel is used as a better similarity function for the graph construction. Numerical experiments on various real-world datasets demonstrate the effectiveness of the proposed method.