一种基于L2,1范数的PCA维数约简算法

传统PCA存在对异常值和特征噪声敏感等问题,基于L2,1范数的PCA算法改进了这些缺点。现有的基于L2,1范数的PCA算法是通过降低矩阵的秩来实现维数约简,而秩的计算复杂。针对这一问题,提出一种新的维数约简算法。该算法提出利用迹范数代替矩阵的秩来简化L2,1-PCA的计算,提高算法效率;对于算法的求解提出了基于拉格朗日乘子的方法并将算法应用扩展Yale B人脸数据集进行图像去噪。可视化的实验结果表明所提出的算法有效。

Efficient dimension reduction algorithm via L2, 1 norm PCA

Traditional PCA is sensitive to outliers and feature noises, PCA based on L2, 1-norm can improve the problems. Whereas present L2, 1-PCA algorithms implement dimension reduction on the rank of the matrix and the rank is complex problem. In order to solve this problem, this paper proposed using trace norm instead of rank, then the calculation of L2, 1-PCA algorithm could simplify and the efficiency could improve. It also put forward an efficient augmented Lagrange multiplierALMalgorithm for the solutions. Extensive experiments on extended Yale B face data sets verify the efficiency of the proposed algorithm.