基于类内散度的粗糙one-class支持向量机

Rough Set One-class Support Vector Machine Based on Within-class Scatter

粗糙one-class支持向量机(ROC-SVM)在粗糙集理论基础上通过构建粗糙上超平面和下超平面来处理过拟合问题,但是在寻找最优分类超平面的过程中,忽略了训练样本类内结构这一非常重要的先验知识。因此,提出了一种基于类内散度的粗糙one-class支持向量机(WSROC-SVM),该方法通过最小化训练样本类内散度来优化训练样本类内结构,一方面使训练样本在高维特征空间中与坐标原点的间隔尽可能大,另一方面使得训练样本在粗糙上超平面尽可能紧密。在合成数据集和UCI数据集上的实验结果表明,较原始算法,该方法有着更高的识别率和更好的泛化性能,在解决实际分类问题上更具优越性。

Classical rough one-class support vector machine（ROC-SVM） constructs rough upper margin and rough lo- wer margin to deal with the over-fitting problem on rough set theory. However, in the process of searching for the opti- mal classification hyper-plane, ROC-SVM ignores the inner-class structure of the training data which is a very important prior knowledge. Thus, a rough set one-class support vector machine based on within-class scatter（WSROC-SVM） was proposed. This algorithm optimizes the inner-class structure of the training data by minimizing the within-class scatter of the training data. It not only precipitates margin between the origin and the training data in a higher dimensional space as large as possible, but also makes the training data close around the rough upper margin as tight as possible. Experimental results carried out on one synthetic dataset and the UCI dataset indicate that the proposed method improves the accuracy as well as the generalization of the result. And it is more advantageous in solving practical classification problems.