Practical graph signal sampling with log-linear size scaling

Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set can help minimize the effect of noise in the input signal. While many existing sampling set selection methods are computationally intensive because they require an eigendecomposition, existing eigendecompostion-free methods are still much slower than random sampling algorithms for large graphs. In this paper, we propose a sampling algorithm that can achieve speeds similar to random sampling, while reaching accuracy similar to existing eigendecomposition-free methods for a broad range of graph types. Keywords—Graph, signal, sampling, D-optimal, volume, coherence.