Recently, robust-norm distance related principal component analysis (PCA) for feature extraction has been shown to be very effective for image analysis, which considers either minimization of reconstruction error or maximization of data variance in low-dimensional subspace. However, both of them are important for feature extraction. Furthermore, most of existing methods cannot obtain satisfactory results due to the utilization of inflexible robust norm for distance metric. To address these problems, this paper proposes a novel robust PCA formulation called Double L_2,p-norm based PCA (DLPCA) for feature extraction, in which the minimization of reconstruction error and the maximization of variance are simultaneously taken into account in a unified framework. In the reconstruction error function, we target to learn a latent subspace to bridge the relationship between the transformed features and the original features. To guarantee the objective to be insensitive to outliers, we take L_2,p-norm as the distance metric for both reconstruction error and data variance. These characteristics make our method more applicable for feature extraction. We present an effective iterative algorithm to obtain the solution of this challenging work, and conduct theoretical analysis on the convergence of the algorithm. The experimental results on several databases show the effectiveness of our model.

最近，用于特征提取的稳健范数距离相关主成分分析（PCA）已被证明对于图像分析非常有效，它考虑了重构误差的最小化或低维子空间中数据方差的最大化。但是，它们两者对于特征提取都很重要。此外，由于对距离度量使用了不灵活的鲁棒范数，大多数现有方法无法获得令人满意的结果。为了解决这些问题，本文提出了一种新的鲁棒 PCA 公式，称为 Double L _2,p-norm based PCA (DLPCA) 用于特征提取，其中在统一框架中同时考虑了重构误差的最小化和方差的最大化。在重建误差函数中，我们的目标是学习一个潜在的子空间来桥接转换后的特征和原始特征之间的关系。为了保证目标对异常值不敏感，我们取 L _2,p-norm 作为重建误差和数据方差的距离度量。这些特性使我们的方法更适用于特征提取。我们提出了一种有效的迭代算法来获得这项具有挑战性的工作的解决方案，并对算法的收敛性进行理论分析。在多个数据库上的实验结果表明了我们模型的有效性。