Density-induced And Adaptive Support Vector Machine

Support vector machine(SVM), depending on the optimization method, has beena powerful tool for machine learning. It is based on the structural risk minimizationprinciple and has been widely used in classical statistics, information retrieval, economicwarning etc. When we use SVM to deal with classification problems, it is a hot topic thathow to reduce computational time and improve classification accuracy. This is also ourresearch content.The main content in this paper can be summarized as follows:1. Least squares density-induced margin support vector machine(LS-DMSVM). Whileconstructing optimal problem, DMSVM has considerated the distribution of samples andassigns every point a relative density, which makes DMSVM have good performance innumerical experiments. In this paper, we discuss a least squares version for DMSVM.We attempt to solve a set of linear equations, instead of quadratic programming forDMSVM's, which reduces computational time and gives good classification accuracy.2. Adaptive support vector machine with homogeneous decision function. In ouralgorithm, the distribution of samples also has been taken into consideration. We view theparameters afecting the margin as variables, so that the margin of bounding hyperplanesis as large as possible. Moreover, we introduce a pair of parameters ν+and ν to controlbounds of the fractions of support vectors and margin errors. So the parameters havea better theoretical interpretation than the penalty factor C in the standard SVM. Wealso show that our algorithm can deal with imbalanced data efectively. Experiments onseveral artificial and machine learning datasets indicate the proposed algorithm has goodclassification accuracy.