针对传统局部保持投影算法对外点敏感的问题,提出了一种基于L2范数的局部保持投影算法。该算法通过采用L2范数定义目标函数并重新定义了权值矩阵,多次迭代计算投影矩阵得到局部最小值,直至达到收敛条件,进而获得最终的最优投影矩阵;通过利用最优投影矩阵将原始数据投影到最优的投影子空间,降低高维数据维度,同时能够保持原有数据特征。合成数据实验结果表明,与传统局部保持投影算法相比,所提基于L2范数的局部保持投影算法能够有效地降低数据维度,改善了算法对外点的敏感问题,提高了算法的鲁棒性。人脸识别实验结果表明,该算法能够取得较高且较为稳定的人脸识别率,人脸识别率可达80％。 A projection algorithm with locality preserving projections based on the L2 norm (LPP？？L2) is proposed to solve the problem that objective functions of traditional projection algorithms with local preservation (LPP) are based on the squared L2 norm and very sensitive to outliers. The weight matrix of the algorithm is recalculated using an iterative method and the objective function is also simplified, as a result, the optimized projection matrix is obtained. The algorithm converges to a local optimum in each iteration. The optimized projection matrix is used to project the original data into an optimal projection subspace with reduced dimension, while the characters of original data are preserved. Experimental results on synthesized data and a comparison with the LPP algorithm show that the LPP？？L2 algorithm effectively reduces the data dimension and makes the algorithm more robust to outliers, it gains higher accurate and steady classification rate in face recognition, and a recognition rate of 80% is obtained
［2］YAN Shuicheng, XU Dong, ZHANG Benyu, et al. Graph embedding and extensions: a general framework for dimensionality reduction ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40？？51.
［8］PTUCHA R, TSAGKATAKIS G, SAVAKIS A. Manifold learning for simultaneous pose and facial expression recognition ［C］∥Proceedings of the IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 2011: 3021？？3024.
［11］NIE Feiping, WANG Hua, HUANG Heng, et al. Unsupervised and semi？？supervised learning via L1？？norm graph ［C］∥Proceedings of the 2011 IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 2011: 2268？？2273,