Research On Supervised And Semi-Supervised Support Vector Machine

Support vector machine (SVM) that is based on Statistical Learning Theory (SLT) is a new way of Machine Learning (ML). In recently years, because of its good property on classification, regression and strong generalization ability, there has been a surge of interest in SVM. As a result, many researches on the theory, algorithm and the solution, SVM has improved a lot. And SVM become an active research area in machine learning.SVM translates the machine learning problems to optimization problems and utilizes the optimization theory to construct algorithms. The objection function of the translated SVM is not differentiable, so some fast algorithms cannot be applied on it. As a result, researchers have done a lot of work on supervised and semi-supervised which are based on smooth function. In this paper, all of the research results can be describe as follows.1. The study on Smooth Support vector machine on classification. The objective function of the unconstrained SVM model is non-smooth and non-differentiable. To overcome the difficulty, a novel smoothing method using Bezier function and rotated hyperbola function are proposed. The Newton-Armijo algorithm is adopted to train the smooth BSSVM and smooth RHSSVM models. Theory and data stimulation prove the advantages of the proposed models on training and testing accuracy and computing time. At the same time, the new algorithms reduce the memory and can efficiently handle large scale and high dimensional problems.2. The study on Smooth Support Vector Machine on regression. By using smoothing method, we give smooth Bezier Support Vector Machine on regression which is based on the s-insensitive loss function (ε-BSSVR) and Rotated Hyperbola Support Vector Machine on regression (ε-RHSSVR). For nonlinear data, we utilize the kernel function to mapping the inputting data to high dimension Hilbert space, then the programming becomes the linear problem. For high dimension data, in order to reduce the computing time, we apply the technique of Reduced Support Vector Machine. Results show that the property of ε-BSSVR and ε-RHSSVR are better than the proposed models.3. The study on Semi-Supervised Support Vector Machine. In order to improve the performance of (?)TSVM, we apply the smooth function, propose the Bezier Smooth Semi-Supervised Support Vector Machine (BSS3VM). The new method gives a good approximation to the max function, which is better than the Gaussian approximation function. Experimental results illustrate that our proposed algorithm improves (?)TSVM in terms of classification accuracy.