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This paper is concerned with the blind identification of graph filters fromgraph signals. Our aim is to determine if the graph filter generating the graphsignals is first-order lowpass without knowing the graph topology. Notice thatlowpass graph filter is a common prerequisite for applying graph signalprocessing tools for sampling, denoising, and graph learning. Our method isinspired by the Perron Frobenius theorem, which observes that for first-orderlowpass graph filter, the top eigenvector of output covariance would be theonly eigenvector with elements of the same sign. Utilizing this observation, wedevelop a simple detector that answers if a given data set is produced by afirst-order lowpass graph filter. We analyze the effects of finite-sample,graph size, observation noise, strength of lowpass filter, on the detector'sperformance. Numerical experiments on synthetic and real data support ourfindings.

Identifying First-order Lowpass Graph Signals using Perron Frobenius Theorem