Joint low‐rank project embedding and optimal mean principal component analysis

Abstract

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.