Abstract:  Nearest feature space embedding (NFSE) method uses traditional Euclidean distance measure to select the nearest feature spaces, which causes within-class scatters and between-class scatters changing synchronously and cannot reflect the distribution of samples in the higher dimensional space accurately. Traversing all the classes when selecting the nearest feature space classes of every sample makes the training time long. To solve above problems, this paper proposes the nearest feature space embedding method based on nonlinear distance metric (NDNFSE), by using nonlinear distance formula to select the nearest feature spaces and using the nearest neighbor classifier combined with Euclidean distance and included angle between two samples to improve the recognition rate. NDNFSE only selects the nearest feature spaces within the nearest classes of every sample to save the training time. According to the experimental results, NDNFSE outperforms comparison algorithms for classification as a whole, with much shorter training time than that of NFSE.

Key words: face recognition, nonlinear distance, included angle, nearest feature space embedding, nearest classes

摘要： 最近邻特征空间嵌入（nearest feature space embedding，NFSE）方法选取最近邻特征空间时使用欧氏距离度量，导致样本的类内离散度和类间离散度同步变化，无法准确反映样本在高维空间的分布；选取每个样本最近邻特征空间都要遍历所有类，导致训练时间长。针对以上问题，提出非线性距离的最近邻特征空间嵌入改进方法（nearest feature space embedding method based on nonlinear distance metric，NDNFSE），引入非线性距离公式选取最近邻特征空间，并使用结合夹角度量的最近邻分类器，提高了识别率；仅在样本的近邻类中选取最近邻特征空间，有效减少了训练时间。实验表明，NDNFSE的训练时间明显低于NFSE，识别率总体高于各对比算法。

关键词: 人脸识别, 非线性距离, 夹角, 最近邻特征空间嵌入, 近邻类