Bian Jintang, Zhao Dandan, Nie Feiping, Wang Rong, Li Xuelong
IEEE Trans Neural Netw Learn Syst. 2024 Mar;35(3):3601-3614. doi: 10.1109/TNNLS.2022.3194896. Epub 2024 Feb 29.
Principal component analysis (PCA) is one of the most successful unsupervised subspace learning methods and has been used in many practical applications. To deal with the outliers in real-world data, robust principal analysis models based on various measure are proposed. However, conventional PCA models can only transform features to unknown subspace for dimensionality reduction and cannot perform features' selection task. In this article, we propose a novel robust PCA (RPCA) model to mitigate the impact of outliers and conduct feature selection, simultaneously. First, we adopt σ -norm as reconstruction error (RE), which plays an important role in robust reconstruction. Second, to conduct feature selection task, we apply l -norm constraint to subspace projection. Furthermore, an efficient iterative optimization algorithm is proposed to solve the objective function with nonconvex and nonsmooth constraint. Extensive experiments conducted on several real-world datasets demonstrate the effectiveness and superiority of the proposed feature selection model.
主成分分析（PCA）是最成功的无监督子空间学习方法之一，已被应用于许多实际应用中。为了处理现实世界数据中的异常值，人们提出了基于各种度量的鲁棒主分析模型。然而，传统的PCA模型只能将特征变换到未知子空间进行降维，无法执行特征选择任务。在本文中，我们提出了一种新颖的鲁棒PCA（RPCA）模型，以减轻异常值的影响并同时进行特征选择。首先，我们采用σ范数作为重构误差（RE），它在鲁棒重构中起着重要作用。其次，为了执行特征选择任务，我们将l范数约束应用于子空间投影。此外，还提出了一种有效的迭代优化算法来求解具有非凸和非光滑约束的目标函数。在几个真实世界数据集上进行的大量实验证明了所提出的特征选择模型的有效性和优越性。
