Vertex-Frequency Clustering.

We propose a novel approach for clustering the vertices of a graph. The method, Vertex-Frequency Clustering (VFC), considers the local harmonic content of one or many graph signals, forming partitions based on spectral features in the input signal. The method can be related to spectral clustering, and the length scale over which frequencies are considered is tunable. This allows one to cluster data based on intrinsic graph geometry in the context of signal dynamics. VFC is useful for unravelling active regions in a signal, collecting sets of similar observations, or detecting anomalies. We demonstrate the utility of VFC in synthetic and biological data, and show how VFC can be used to identify observations with similar feature sets and signal profiles.