Principal component analysis (PCA) is one of the most widely used unsupervised dimensionality reduction algorithms, but it is very sensitive to outliers because the squared ℓ2\ell _{2} -norm is used as distance metric. Recently, many scholars have devoted themselves to solving this difficulty. They learn the projection matrix from minimum reconstruction error or maximum projection variance as the starting point, which leads them to ignore a serious problem, that is, the original PCA learns the projection matrix by minimizing the reconstruction error and maximizing the projection variance simultaneously, but they only consider one of them, which imposes various limitations on the performance of model. To solve this problem, we propose a novel robust principal component analysis via joint reconstruction and projection, namely, RPCA-RP, which combines reconstruction error and projection variance to fully mine the potential information of data. Furthermore, we carefully design a discrete weight for model to implicitly distinguish between normal data and outliers, so as to easily remove outliers and improve the robustness of method. In addition, we also unexpectedly discovered that our method has anomaly detection capabilities. Subsequently, an effective iterative algorithm is explored to solve this problem and perform related theoretical analysis. Extensive experimental results on several real-world datasets and RGB large-scale dataset demonstrate the superiority of our method.

中文翻译：

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通过联合重建和投影进行鲁棒主成分分析


主成分分析（PCA）是最广泛使用的无监督降维算法之一，但它对异常值非常敏感，因为使用平方 ℓ2\ell _{2} -范数作为距离度量。近年来，许多学者致力于解决这一难题。他们以最小重建误差或最大投影方差为起点来学习投影矩阵，这导致他们忽略了一个严重的问题，即原来的PCA是通过同时最小化重建误差和最大化投影方差来学习投影矩阵的，但是他们只考虑其中之一，这对模型的性能施加了各种限制。为了解决这个问题，我们提出了一种新颖的通过联合重建和投影的鲁棒主成分分析，即RPCA-RP，它结合了重建误差和投影方差来充分挖掘数据的潜在信息。此外，我们为模型精心设计了一个离散权重，隐式区分正常数据和异常值，从而轻松去除异常值，提高方法的鲁棒性。此外，我们还意外地发现我们的方法具有异常检测能力。随后，探索了一种有效的迭代算法来解决该问题并进行了相关的理论分析。在多个真实世界数据集和 RGB 大规模数据集上的大量实验结果证明了我们方法的优越性。