Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.

中文翻译：

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模态主成分分析

主成分分析 (PCA) 是一种广泛用于数据处理的方法，例如降维和可视化。众所周知，标准 PCA 对异常值很敏感，并且已经提出了各种稳健的 PCA 方法。已经表明，使用模式估计而不是均值估计可以提高许多统计方法的鲁棒性，因为模式估计不受异常值存在的显着影响。因此，本研究提出了模态主成分分析 (MPCA)，这是一种基于模态估计的稳健 PCA 方法。所提出的方法通过估计投影数据点的众数来找到次要分量。作为理论贡献，推导出了概率收敛特性、影响函数、有限样本分解点及其所提出的 MPCA 的下限。