In recent years, with the rapid popularization of intelligent terminals and sensors, massive data have been accumulated rapidly, and the processing technology of big data has attracted more and more attention. Among them, large information data with functional characteristics such as physiological data, growth curve data, temperature data, etc. are also attracting significant attention. In fact, these data are discrete samples of continuous functions, and these data are usually known as functional data.
The main problem in functional data analysis is dimensionality reduction, and one of the common ways to reduce dimension is to take only a few principal components by performing functional principal component analysis (PCA) on given functional data. The conventional functional principal component analysis method uses the L2-norm, which has the advantage of being computationally convenient, but it is not efficient for data with outliers because the L2-norm is highly affected by outliers. It can be expected that the PCA method using the L1-norm instead of the L2-norm will have better robustness. Without considering the computational complexity when using the L1-norm, high computational cost of functional data analysis cannot be avoided.
Paek Hyon I, a researcher at the Faculty of Applied Mathematics, proposed a method for improving robustness by using L1-norm instead of L2-norm in the functional principal component analysis for functional data with vertical outliers, and constructed an efficient computational algorithm to reduce computational complexity.
This algorithm can achieve more efficient functional principal components with high robustness from data contaminated by vertical outliers while reducing the computational complexity of functional principal component analysis.
It was demonstrated through modeling studies that this method is more robust to outliers than L2-norm functional principal component analysis.
You can find details in his paper “L1-norm Principal Component Analysis Method for Functional Data with Vertical Outliers” in “Proceedings of KUTIC-2025”.