Graph frequency-domain factor modeling

Abstract

We propose a novel factor model in the graph frequency domain for multivariate data lying on the vertices of a graph, called a multivariate graph signal. By utilizing graph filters, our model extends the frequency-domain approach of the dynamic factor model from time series to graphs, enabling a graph-aware and multiscale interpretation of factors across graph frequencies. This approach reduces the dimensionality of graph signals and improves the understanding of their structure. It also allows the use of the extracted factors for subsequent analyses, such as clustering. We describe the estimation of factors and their loadings and investigate the consistency of the factor estimator. In addition, we propose two consistent estimators for determining the number of factors. The finite sample performance of the proposed method is demonstrated through simulation studies under different graph structures, including a comparison with classical factor analysis and an exploration of how the graph structure affects the results. Furthermore, we demonstrate the effectiveness of the proposed method by applying it to G20 economic data, water quality data from the Geum River, and passenger data from the Seoul Metropolitan subway.

Contribution

We propose a graph frequency-domain factor model for dimension reduction of multivariate data residing on graphs.

Code

To be uploaded.