Principal Component Analysis in the Graph Frequency Domain
Methodology
2024-10-14 v1
Abstract
We propose a novel principal component analysis in the graph frequency domain for dimension reduction of multivariate data residing on graphs. The proposed method not only effectively reduces the dimensionality of multivariate graph signals, but also provides a closed-form reconstruction of the original data. In addition, we investigate several propositions related to principal components and the reconstruction errors, and introduce a graph spectral envelope that aids in identifying common graph frequencies in multivariate graph signals. We demonstrate the validity of the proposed method through a simulation study and further analyze the boarding and alighting patterns of Seoul Metropolitan Subway passengers using the proposed method.
Keywords
Cite
@article{arxiv.2410.08422,
title = {Principal Component Analysis in the Graph Frequency Domain},
author = {Kyusoon Kim and Hee-Seok Oh},
journal= {arXiv preprint arXiv:2410.08422},
year = {2024}
}