摘要： 支持向量机是统计机器学习中的一种重要方法，被广泛地应用于模式识别、回归分析等问题。但一般支持向量机未考虑样本的总体分布，降低了支持向量机的泛化能力。针对该问题，提出一种马氏距离支持向量机学习模型，考虑总体样本的分布，并将该模型扩展到多核学习模型。通过数学方法将欧式距离核矩阵转化为马氏距离核矩阵，降低模型的实现难度。实验结果证明，该模型不仅保持了欧式距离多核学习模型的原有性质，且具有更好的分类精确度。

关键词: 马氏距离, 欧氏距离, 多核学习模型, 支持向量机, 核函数, 线性判别分析

Abstract: Support Vector Machine(SVM) is an important method in the statistical machine learning, which is widely used in the pattern recognition, regression analysis and so on. However, the general SVM does not consider the distribution of the whole sample, which influences the generalization ability. Aiming at this problem, this paper brings the SVM with the Mahalanobis distance, which considers the distribution of the whole sample and expands it to the multiple kernel model. By using the mathematics method, the paper successfully transfers the Euclidean distance kernel matrix to the Mahalanobis distance kernel matrix and makes the algorithm easily achieved. Experimental results show that the multiple kernel model based on the Mahalanobis distance gets higher classification accuracy, and the algorithm keeps the character of multiple kernel model based on the Euclidean distance.

Key words: Mahalanobis distance, Euclidean distance, multiple kernel learning model, Support Vector Machine(SVM), kernel function, Linear Discriminate Analysis(LDA)

中图分类号: 

• TP18