Support Vector Machines (SVMs) are popular tools for data mining tasks such as classification, regression, and density estimation. However, original SVM (C-SVM) only considers local information of data points on or over the margin. Therefore, C-SVM loses robustness. To solve this problem, one approach is to translate (i.e., to move without rotation or change of shape) the hyperplane according to the distribution of the entire data. But existing work can only be applied for 1-D case. In this paper, we propose a simple and efficient method called General Scaled SVM (GS-SVM) to extend the existing approach to multi-dimensional case. Our method translates the hyperplane according to the distribution of data projected on the normal vector of the hyperplane. Compared with C-SVM, GS-SVM has better performance on several data sets.
In this paper, to resolve unclassifiable regions in the support vector machines, we propose fuzzy support vector machines (FSVMs). Using the decision function obtained by training the SVM, for each class, we define a truncated polyhedral pyramidal membership function. Since, for the data in the classifiable regions, the classification results are the same, the generalization ability of the FSVM is the same as or better than that of the SVM. To further improve the generalization ability, we introduce the Bayes theory, assuming that the class distributions are normal, to optimize the bias term of the optimal hyperplane. We evaluate our methods for four benchmark data sets and demonstrate the superiority of the FSVM and Bayes FSVM over the SVM. A new large margin classifier, named Maxi-Min Margin Machine (M4) is proposed in this paper. This new classifier is constructed based on both a "local: and a "global" view of data, while the most popular large margin classifier, Support Vector Machine (SVM) and the recently-proposed important model, Minimax Probability Machine (MPM) consider data only either locally or globally. This new model is theoretically important in the sense that SVM and MPM can both be considered as its special case. Furthermore, the optimization of M4 can be cast as a sequential conic programming problem, which can be solved efficiently. We describe the M4 model definition, provide a clear geometrical interpretation, present theoretical justifications, propose efficient solving methods, and perform a series of evaluations on both synthetic data sets and real world benchmark data sets. Its comparison with SVM and MPM also demonstrates the advantages of our new model. This paper describes a new large margin classifier, named SVM LDA. This classifier can be viewed as an extension of support vector machine (SVM) by incorporating some global information about the data. The SVM LDA classifier can be also seen as a generalization of linear discriminant analysis (LDA) by incorporating the idea of (local) margin maximization into standard LDA formulation. We show that existing SVM software can be used to solve the SVM LDA formulation. We also present empirical comparisons of the proposed algorithm with SVM and LDA using both synthetic and real world benchmark data. This paper proposes a new large margin classifier--the structured large margin machine (SLMM)--that is sensitive to the structure of the data distribution. The SLMM approach incorporates the merits of "structured" learning models, such as radial basis function networks and Gaussian mixture models, with the advantages of "unstructured" large margin learning schemes, such as support vector machines and maxi-min margin machines. We derive the SLMM model from the concepts of "structured degree" and "homospace", based on an analysis of existing structured and unstructured learning models. Then, by using Ward's agglomerative hierarchical clustering on input data (or data mappings in the kernel space) to extract the underlying data structure, we formulate SLMM training as a sequential second order cone programming. Many promising features of the SLMM approach are illustrated, including its accuracy, scalability, extensibility, and noise tolerance. We also demonstrate the theoretical importance of the SLMM model by showing that it generalizes existing approaches, such as SVMs and M4s, provides novel insight into learning models, and lays a foundation for conceiving other "structured" classifiers. Support Vector Machine (SVM) is one of the most popular classifiers in pattern recognition, which aims to find a hyperplane that can separate two classes of samples with the maximal margin. As a result, traditional SVM usually more focuses on the scatter between classes, but neglects the different data distributions within classes which are also vital for an optimal classifier in different real-world problems. Recently, using as much structure information hidden in a given dataset as possible to help improve the generalization ability of a classifier has yielded a class of effective large margin classifiers, typically as Structured Large Margin Machine (SLMM). SLMM is generally derived by optimizing a corresponding objective function using SOCP, and thus in contrast to SVM developed from optimizing a QP problem, it, though more effective in classification performance, has the following shortcomings: 1) large time complexity; 2) lack of sparsity of solution, and 3) poor scalability to the size of the dataset. In this paper, still following the above line of the research, we develop a novel algorithm, termed as Structural Support Vector Machine (SSVM), by directly embedding the structural information into the SVM objective function rather than using as the constraints into SLMM, in this way, we achieve: 1) to overcome the above three shortcomings; 2) empirically better than or comparable generalization to SLMM, and 3) theoretically and empirically better generalization than SVM.