Chongqing Key Laboratory of Image cognition, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China.
Computer Vision Institute, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China; Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, Shenzhen 518060, China.
Neural Netw. 2019 Oct;118:1-16. doi: 10.1016/j.neunet.2019.05.020. Epub 2019 Jun 8.
Principal component analysis (PCA) is a widely used tool for dimensionality reduction and feature extraction in the field of computer vision. Traditional PCA is sensitive to outliers which are common in empirical applications. Therefore, in recent years, massive efforts have been made to improve the robustness of PCA. However, many emerging PCA variants developed in the direction have some weaknesses. First, few of them pay attention to the 2D structure of error matrix. Second, to estimate data mean from sample set with outliers by averaging is usually biased. Third, if some elements of a sample are disturbed, to extract principal components (PCs) by directly projecting data with transformation matrix causes incorrect mapping of sample to its genuine location in low-dimensional feature subspace. To alleviate these problems, we present a novel robust method, called nuclear norm-based on PCA (N-PCA) to take full advantage of the structure information of error image. Meanwhile, it is developed under a novel unified framework of PCA to remedy the bias of computing data mean and the low-dimensional representation of a sample both of which are treated as unknown variables in a single model together with projection matrix. To solve N-PCA, we propose an iterative algorithm, which has a closed-form solution in each iteration. Experimental results on several open databases demonstrate the effectiveness of the proposed method.
主成分分析（PCA）是计算机视觉领域中一种广泛使用的降维和特征提取工具。传统的 PCA 对经验应用中常见的异常值很敏感。因此，近年来，人们做出了巨大的努力来提高 PCA 的鲁棒性。然而，许多新兴的 PCA 变体在发展方向上存在一些弱点。首先，它们很少关注误差矩阵的 2D 结构。其次，通过平均值从包含异常值的样本集中估计数据均值通常存在偏差。第三，如果一个样本的某些元素受到干扰，通过直接用变换矩阵投影数据来提取主成分（PC）会导致样本在低维特征子空间中的真实位置的映射不正确。为了解决这些问题，我们提出了一种新的稳健方法，称为基于核范数的 PCA（N-PCA），以充分利用误差图像的结构信息。同时，它是在 PCA 的一个新的统一框架下开发的，以纠正计算数据均值和样本的低维表示的偏差，这两个偏差都被视为单个模型中的未知变量，以及投影矩阵。为了解决 N-PCA 问题，我们提出了一种迭代算法，在每次迭代中都有一个闭式解。在几个公开数据库上的实验结果证明了所提出方法的有效性。
