Modal Principal Component Analysis
This is an incremental improvement for data processing applications requiring robustness to outliers.
The authors tackled the problem of standard PCA's sensitivity to outliers by proposing Modal PCA (MPCA), a robust method based on mode estimation, which shows advantages over conventional methods in experiments.
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.