Principal component analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. A number of variants of PCA have been proposed to improve the robustness of the algorithm. However, the existing methods either cannot select the useful features consistently or is still sensitive to outliers. In order to reveal the intrinsic manifold structure and preserve the global structure of data, it is needed to learn more efficient optimal projection matrix for sample sets with outliers. To this end, the authors propose a novel PCA, named low-rank project embedding and optimal mean principal component analysis (abbreviated as LRPE-OMPCA), which can learn the optimal mean and the optimal projection matrix and preserve the global geometric information and discriminative structure captured by the self-representation coefficient weight matrix into the low-dimensional embedding subspace. Thus, not only can the proposed method further reduce the influence of outliers but also can discard the useless features, which effectively improve the robustness of the method. An effective iterative algorithm to solve the LRPE-OMPCA is designed. Experimental results on several image databases illustrate the robustness and effectiveness of the proposed method.

中文翻译：

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联合低等级项目嵌入和最优平均主成分分析

主成分分析（PCA）是使用最广泛的无监督降维方法。已经提出了PCA的许多变体，以提高算法的鲁棒性。但是，现有方法要么无法一致地选择有用的功能，要么仍然对异常值敏感。为了揭示固有的流形结构并保留数据的整体结构，需要为离群值的样本集学习更有效的最优投影矩阵。为此，作者提出了一种新颖的PCA，称为低秩项目嵌入和最佳平均主成分分析（缩写为LRPE-OMPCA），它可以学习最优均值和最优投影矩阵，并将自表示系数权重矩阵捕获的全局几何信息和判别结构保存到低维嵌入子空间中。因此，提出的方法不仅可以进一步减少离群值的影响，而且可以丢弃无用的特征，从而有效地提高了方法的鲁棒性。设计了一种有效的迭代算法来求解LRPE-OMPCA。在几个图像数据库上的实验结果说明了该方法的鲁棒性和有效性。设计了一种有效的迭代算法来求解LRPE-OMPCA。在几个图像数据库上的实验结果说明了该方法的鲁棒性和有效性。设计了一种有效的迭代算法来求解LRPE-OMPCA。在几个图像数据库上的实验结果说明了该方法的鲁棒性和有效性。