一类快速模糊支持向量机

由H.P.Huang、C.F.Lin等人和T.Inoue,S.Abe等人提出的两类模糊支持向量机是两种类型的改进支持向量机,分别克服了过学习问题和减少了多类问题分类时存在的不可分区域。如何处理异常数据和加速训练大规模数据集是支持向量机中的急需解决的两个问题。针对这两个问题,提出了一类将两类模糊支持向量机集成的快速模糊支持向量机。训练时,根据每类数据与其类中心的距离,定义隶属函数,以加大对容易被错分样本的惩罚,利用合适的参数λ选取了每类数据中隶属度值较大的边缘数据构造模糊支持向量机,测试时,利用1-a-1和模糊支持向量机的决策函数判定未知样本的类别。含有异常数据的两类问题和机器学习数据集中手写数字识别的多类问题的实验结果,验证了提出的快速模糊支持向量机减少了训练时间同时提高了学习机的推广能力。

A Kind of Fast Fuzzy Support Vector Machines

The two kinds of Fuzzy Support Vector Machines (FSVMs) which respectively were proposed by H. P. Huang, C. F. Lin, etc. and T. Inoue, S. Abe, etc. were improved Support Vector Machines (SVMs). They respectively solved the overfitting problem and reduced the unclassifiable regions of multi-class problems. It is urgent for SVMs to deal with outliers properly and speed up training for the training set of large scale. Regarding to the requirements, a kind of fast FSVMs integrating the advantages of above FSVMs was proposed. During the training process, the membership functions were defined by the distance between the data and their class centers and assign the lager penalty values for the data which are easy to be misclassified. The selected edge data including outliers with the lager membership values were used training FSVMs. During the testing process, the classes of the unknown data were discriminated by the 1-against-1 strategy and decision functions of FSVMs. The two-class problem including outliers and the multi-class problem, such as hand-written digit recognition in the machine learning benchmark dataset, have verified the reduced training time and the improved generalization abilities of the proposed fast FSVMs.