Glocalization pursuit support vector machine

Graph-based methods have aroused wide interest in pattern recognition and machine learning, which capture the structural information in data into classifier design through defining a graph over the data and assuming label smoothness over the graph. Laplacian Support Vector Machine (LapSVM) is a representative of these methods and an extension of the traditional SVM by optimizing a new objective additionally appended Laplacian regularizer. The regularizer utilizes the local linear patches to approximate the data manifold structure and assumes the same label of the data on each patch. Though LapSVM has shown more effective classification performance than SVM experimentally, it in fact concerns more the locality than the globality of data manifold due to the Laplacian regularizer itself. As a result, LapSVM is relatively sensitive to the local change of the data and cannot characterize the manifold quite faithfully. In this paper, we design an alternative regularizer, termed as Glocalization Pursuit Regularizer. The new regularizer introduces a natural global structure measure to grasp the global and local manifold information as simultaneously as possible, which can be proved to make the representation of the manifold more compact than the Laplacian regularizer. We further introduce the new regularizer into SVM to develop an alternative graph-based SVM, called as Glocalization Pursuit Support Vector Machine (GPSVM). GPSVM not only inherits the advantages of both SVM and LapSVM but also uses the structural information more reasonably to guide the classifier design. The experiments both on the toy and real-world datasets demonstrate the better classification performance of our proposed GPSVM compared with SVM and LapSVM.