基于2D-KPCA的拉普拉斯特征映射人脸识别*

针对拉普拉斯特征映射(LE)只能保持局部近邻信息，对新测试点无法描述的不足，提出一种基于二维核主成分分析的拉普拉斯特征映射算法(2D-KPCA LE)。与核二维主成分分析算法(K2DPCA)不同，该算法首先对训练样本空间进行二维主成分分析（2DPCA），在保留样本空间结构信息的同时通过去相关性得到低秩的投影特征矩阵；然后用核主成分分析法(KPCA)提取全局非线性特征；由于其核函数需要大量存储空间，再用拉普拉斯特征映射(LE)进行降维。在ORL和FERET人脸数据库中的仿真实验结果表明，基于2D-KPCA的拉普拉斯特征映射算法不但可以有效处理复杂的非线性特征，又可以降低算法复杂度，提高流形学习的识别率。

Face recognition with laplacian eigenmaps based on 2D-KPCA

To overcome the shortage of the new samples existing in Laplacian eigenmaps, the paper proposed face recognition with laplacian eigenmaps based on 2D-KPCA, namely, the 2D-KPCA LE algorithm. First of all, different from the kernel two-dimensional principal component analysis(K2DPCA), the 2DPCA applied to the training sample space. So the algorithm not only could retain the structural information of sample space ,but also could obtain a low-rank projection matrix by decorrelation. Then used the KPCA to extract nonlinear features. But the kernel function needed a lot of storage. The algorithm utilized laplacian eigenmaps to reduce dimensions again. Experimental results in ORL and FERET face databases show that the 2D-KPCA LE has higher recognition rate and lower the complexity of the algorithm than other manifold learning methods.