η-one-class问题和η-outlier及其LP学习算法

用SVM方法研究one-class和outlier问题．在将one-class问题理解为一种函数估计问题的基础上，作者首次定义了η-one-class和η-outlier问题的泛化错误，进而定义了线性可分性和边缘，得到了求解one-class问题的最大边缘、软边缘和v-软边缘算法．这些学习算法具有统计学习理论依据并可归结为求解线性规划问题．算法的实现采用与boosting类似的思路．实验结果表明该文的算法是有实际意义的．

η-One-Class Problems andη-Outliers with Their LP Learning Algorithms

In this paper, one-class and outlier problems are investigated by using the idea of Support Vector Machines. Based on regarding a one-class problem as the one to estimate a function, the generalization error for the one-class problem is defined for the first time. The linear separability, margin and optimal linear classifier are then defined and the regular SVM is reformulated into a framework for one-class problems. Each of the linear algorithms is motivated theoretically and they can be formulated as some linear programming problems. The proposed algorithms can be implemented by the techniques in boosting algorithms. Some synthetic and real experiments illustrate that the algorithms in this paper are practical and effective.