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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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    We introduce a novel graph frequency domain factor model for multivariate graph signals. This method reduces dimensionality, enhances structural understanding, and improves data analysis across various applications.

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    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.