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Graph reduction method using localization operator and its application to pyramid transform

This paper proposes a graph reduction method by using the localization operator for signals defined on graphs. In the previous work, we proposed a method for sensor position selection considering signal localizations in graph vertex and spectral domains. This paper extends the selection method to graph reduction. It selects downsampled nodes according to the graph cut-off frequencies so that the downsampled signal preserves the much information for predicting the values on removed nodes. Furthermore, it also considers the localization in the graph vertex domain. We design the multiscale analysis with the graph reduction and apply it to graph signal denoising.