基于加权马氏距离的模糊多核支持向量机

Fuzzy Multiple Kernel Support Vector Machine Based on Weighted Mahalanobis Distance

模糊支持向量机通过引入模糊隶属度有效区分不同样本的重要程度,降低了传统支持向量机对噪声数据的敏感性。针对基于欧氏距离设计的隶属度函数忽略了样本的总体分布,且未考虑样本特征重要性的区分,提出了一种基于加权马氏距离的模糊支持向量机方法。首先应用Relief-F算法计算样本特征权重,然后基于该权重计算样本距其类中心的加权马氏距离,最后根据该距离值度量样本隶属度。在此基础上,考虑到核函数及其核参数难以确定,将模糊支持向量机与多核学习方法相结合,提出基于加权马氏距离的模糊多核支持向量机,采用加权求和形式构建多核,并遵循中心核对齐原则确定每个核的权重。该方法不仅降低了弱相关特征对分类效果的影响,而且使数据表达更加全面准确。实验结果表明,基于加权马氏距离的模糊支持向量机的分类精度高于基于欧氏距离和基于马氏距离的模糊支持向量机,且基于加权马氏距离的模糊多核支持向量机的分类性能较单核模型更优。

Fuzzy support vector machine(FSVM)effectively distinguishes the importance of different samples by introducing fuzzy memberships,which reduces the sensitivity of traditional support vector machines to noise data.The membership function designed based on Euclidean distance ignores the overall distribution of samples and does not consider the different importance of sample features.A fuzzy support vector machine method based on weighted Mahalanobis distance is proposed.This method first applies the Relief-F algorithm to estimate the weight of each feature.Then it utilizes the weight for calculating the weighted Mahalanobis distance between the sample and the center of its class.Finally,the fuzzy membership of the sample is calculated based on weighted Mahalanobis distance.Furthermore,considering the difficulty of determining the kernel function and its parameters,a fuzzy multi-kernel support vector machine(FMKSVM)based on weighted Mahalanobis distance is put forward,which combines FSVM with multiple kernel learning methods.The multi-kernel is constructed in the form of weighted sum,and the weight of each kernel is calculated according to the central kernel alignment method(CKA).The proposed method not only reduces the influence of weakly relevant features on classification results,but also enables a more adequate and accurate representation of the data.Experimental results show that,FSVM based on weighted Mahalanobis distance has higher classification accuracy than FSVM based on Euclidean distance and Mahalanobis distance,and the classification performance of FMKSVM based on weighted Mahalanobis distance is superior to that of the single-kernel model.