  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.
