基于非线性距离和夹角组合的最近特征空间嵌入方法

最近特征空间嵌入NFSE方法在训练过程中选取最近特征空间时采用传统的欧氏距离度量会导致类内离散度和类间离散度变化同步；测试时，最近邻规则也使用欧氏距离度量，而高维空间样本间直线距离具有趋同性。这些都会降低识别率，为解决此问题，提出了基于非线性距离和夹角组合的最近特征空间嵌入方法。在训练阶段，该方法使用非线性距离度量选取最近特征空间，使类内离散度的变化速度远小于类间离散度的变化速度，从而使转换空间中同类样本距离更小，不同类样本距离更大。在匹配阶段，使用结合夹角度量的最近邻分类器，充分利用样本相似性与样本夹角的关系，更适合高维空间中样本分类。仿真实验表明，基于非线性距离和夹角组合的最近特征空间嵌入方法的性能总体上优于对比算法。

A nearest feature space embedding method based on thecombination of nonlinear distance metric and included angle

Nearest Feature Space Embedding(NFSE) algorithm uses traditional Euclidean distance measure when choosing the nearest feature spaces in the training phase, which causes within-class scatters and between-class scatters change synchronously. The nearest neighborhoodmatching rule also uses Euclidean distance measure in the matching phase, but straight-line distances among samples in higher space are almost the same. They both can reduce the recognition rate. In order to solve this problem, this paper proposes a nearest feature space embedding method based on the combination of nonlinear distance metric and included angle (NL-IANFSE). In the training phase, NL-IANFSE brings nonlinear distance measure to make the change rate of within-class scatter much slower than that of between-class scatter so that distances of samples within same class are smaller and distances of samples belong to different classes are larger in the transformed space.In the matching phase, NL-IANFSE uses the nearest neighbor classifier that combines Euclidean distance and included anglebetween two samples，takes the relationship between similarity of samples and included angles of samples into account，and hence is more suitablefor sample classification in high-dimensional space.Experimental results show that the proposed method outperforms the other algorithms in terms of samples classification in high dimensional space.