Gode: graph Fourier transform based outlier detection using empirical Bayesian thresholding

This paper proposes a novel outlier detection method that uses Graph Fourier Transform (GFT) coupled with empirical Bayes thresholding, named Ebayesthresh. While traditional outlier detection techniques are primarily designed for Euclidean data, this study focuses on non-Euclidean data, specifically graph signals. By utilizing the GFT, a given signal is transformed into the frequency domain, allowing for spectral analysis. According to the Lebesgue decomposition theorem and Wold’s theorem, when a graph signal satisfies the stationarity condition, its frequency domain exhibits a mixture of sparse signals and noise. Bayesian modeling is used to estimate the sparsity in the frequency domain, which enables the identification of outliers. Experimental datasets are utilized to compare the performance of the proposed method with existing approaches. Furthermore, the usefulness of the proposed method is demonstrated through real-world data analysis using earthquake data from 2010 to 2014.