The Fractional Fourier Transform on Graphs: Sampling and Recovery

Signal processing on graphs expands discrete signal processing theory and techniques to signals supported on graphs. In this paper, we study the sampling and recovery of graph signals under the graph fractional Fourier transform. We show that a-bandlimited signals in the graph fractional Fourier domain can be perfectly recovered. Experimentally designed sampling strategy is used to generate optimal fractional sampling operators on graphs. We give numerical examples, and test the semi-supervised classification of online blogs and handwritten digits using fractional sampling on graphs, and compare it with GFT sampling. We find that fractional sampling on graphs can lead to better classification accuracy at an optimal fractional order.