论文标题
模态主成分分析
Modal Principal Component Analysis
论文作者
论文摘要
主成分分析（PCA）是一种广泛用于数据处理的方法，例如降低和可视化。已知标准PCA对离群值敏感，因此已经提出了各种健壮的PCA方法。已经表明，可以使用模式估计而不是平均估计来改善许多统计方法的鲁棒性，因为模式估计不受异常值的存在显着影响。因此，本研究提出了模态主成分分析（MPCA），这是基于模式估计的强大PCA方法。提出的方法通过估计投影数据点的模式来找到次要组件。作为理论贡献，概率收敛性，影响函数，有限样本分解点及其对拟议MPCA的下限。实验结果表明，所提出的方法比常规方法具有优势。
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 thus, 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 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 the conventional methods.
