基于边界鉴别分析的递归维数约简算法

Recursive dimension reduction algorithm based on margin discriminant analysis

提出一种基于边界鉴别分析的递归维数约简算法.该算法把已求取边界鉴别向量正交于待求超平面法向量作为支持向量机(SVM)优化问题新的约束条件;然后对改进SVM进行递归求解,得到正交边界鉴别向量基;最后将数据样本在正交边界鉴别向量上投影实现维数约简.该算法不仅克服了现有维数约简算法难以支持小样本数据集、受数据样本分布影响等问题,而且抽取的特征向量具有更优的分类性能.仿真实验说明了算法的有效性.

A recursive dimension reduction algorithm based on marginal discriminant analysis is presented. A constraint condition that the obtained margin discriminant vectors are orthogonal to the new normal vector of classification hyperplane is added to the optimal problem of support vector machines （SVM）,and margin discriminant vectors can be recursively achieved by solving the modified SVM. The number of dimension of data can be reduced by projecting data in orthogonal margin discriminant basis. The algorithm can not only overcome some drawbacks of the most existing algorithms,such as unable to work effectively in small size sample case,easily affected by distribution of data etc,but also has better classification performance. The simulation results show the effectiveness of the proposed algorithm.