Abstract: 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.

Key words: Support vector machine, Centered kernel alignment, Weighted Mahalanobis distance, Multiple kernel learning, Membership function