自步稀疏最优均值主成分分析

主成分分析(PCA)是一种无监督降维方法。然而现有的方法没有考虑样本的差异性，且不能联合地提取样本的重要信息，从而影响了方法的性能。针对以上问题，提出自步稀疏最优均值主成分分析方法。模型以 $ {{L}_{{2,1}}}$ 范数定义损失函数，同时用 $ {L_{{\rm{2,1}}}}$ 范数约束投影矩阵作为正则化项，且将均值作为在迭代中优化的变量，这样可一致地选择重要特征，提高方法对异常值的鲁棒性；考虑到训练样本的差异性，利用自步学习机制实现训练样本由“简单”到“复杂”的学习过程，有效地降低异常值的影响。理论分析和实验结果表明，以上方法能更有效地降低异常值对分类精度的影响，提高分类精度。

Sparse optimal mean principal component analysis based on self-paced learning

Principal component analysis (PCA) can be referred to as an unsupervised dimensionality reduction approach. However, the existing methods do not consider the difference of samples and cannot jointly extract important information of samples, thus affecting the performance of some methods. For the above problems, based on self-paced learning, we proposed a sparse optimal mean PCA algorithm. In our model, loss of function is defined by $ {L_{{\rm{2,1}}}}$ norm, the projection matrix is regularized by $ {L_{{\rm{2,1}}}}$ norm, and the mean value is taken as a variable to be optimized in the iteration. In this way, important features can be consistently selected, and the robustness of the method to outliers can be improved. Considering the difference in training samples, we utilized self-paced learning mechanism to complete the learning process of training samples from “simple” to “complex” so as to effectively reduce the influence of outliers. Theoretical analysis and the empirical study revealed that the proposed method could effectively reduce the influence of noise or outliers on the classification progress, thus improving the effect of the classification.