Graph Frequency-Domain Factor Modeling

Area of Science:

• Graph signal processing
• Multivariate statistics
• Network analysis

Background:

• Traditional factor models struggle with graph-structured data.
• Extending time series frequency-domain models to graphs is challenging.
• A need exists for dimensionality reduction techniques that leverage graph topology.

Purpose of the Study:

• To propose a novel factor model in the graph frequency domain for multivariate graph signals.
• To enable a graph-aware and multiscale interpretation of factors across graph frequencies.
• To reduce the dimensionality of graph signals for improved structural understanding and subsequent analyses.

Main Methods:

• Utilizing graph filters to extend dynamic factor models to the graph frequency domain.
• Developing latent modeling for dimensionality reduction of graph signals.
• Proposing consistent estimators for factor estimation and determining the number of factors.

Main Results:

• The proposed model achieves lower reconstruction errors compared to classical factor analysis.
• The model successfully incorporates graph structure into the analysis.
• Simulation studies across various graph structures demonstrate finite sample performance.

Conclusions:

• The novel factor model provides an effective approach for analyzing multivariate graph signals.
• The method enhances understanding of data structure by leveraging graph topology.
• The model's effectiveness is demonstrated on real-world datasets including economic, environmental, and transportation data.