Abstract: This paper proposes a novel specific feature representation, then develops a locally linear K-nearest neighbor method called L²KNN accordingly with applications to face recognition. The specific feature representation improves upon the traditional sparse representation by adding up the nonnegative constraint, and the corresponding objective function with the group regularization is optimized to derive a novel approximate specific representation. The proposed method L²KNN shows the clustering effect of nearest neighbors (CENN). It not only can enhance the correlation between the test sample and the training samples with the same label, but also can enhance the correlation among the training samples. The L²KNN method is developed into its classifier L²KNNc (L²KNN-based classifier) in which a coefficients’ truncating method is used to improve the generalization capability of L²KNNc. The experimental results on the face data set indicate the above claim about L²KNNc

Key words: specific feature representation, locally linear K-nearest neighbor method L²KNN, clustering effect of nearest neighbors (CENN), coefficients' truncating method

摘要： 提出了一种特别的特征表示方法，并在此基础上提出了一种基于特别的特征表示方法的局部线性K最近邻算法（locally linear K-nearest neighbor method，L²KNN），并将之应用到人脸识别中。特别的特征表示方法是在传统的稀疏表示的基础上，加入了非负约束，改进了传统的稀疏表示的方法，在目标函数中增加了集群正则化项，然后优化新的目标函数得到一个新的近似的特征表示。L²KNN算法具有最近邻集群效应（clustering effect of nearest neighbors，CENN），不仅可以增强测试样本与同类的训练样本之间的相关性，而且可以增强同类训练样本之间的相关性。L²KNN算法进一步应用到L²KNNc（L²KNN-based classifier）分类器中，并提出一种系数截断的方法增加L²KNNc分类器的泛化性能，进一步提高分类器的分类性能。在人脸数据集上的实验结果证明了上述结论。

关键词: 特别的特征表示, 局部线性K最近邻算法L²KNN, 最近邻集群效应（CENN）, 系数截断方法