Abstract
In this paper, we focus on the bandlimited graph signal sampling problem. To sample graph signals, we need to find small-sized subset of nodes with the minimal optimal reconstruction error. We formulate this problem as a subset selection problem, and propose an efficient Pareto Optimization for Graph Signal Sampling (POGSS) algorithm. Since the evaluation of the objective function is very time-consuming, a novel acceleration algorithm is proposed in this paper as well, which accelerates the evaluation of any solution. Theoretical analysis shows that POGSS finds the desired solution in quadratic time while guaranteeing nearly the best known approximation bound. Empirical studies on both Erdos-Renyi graphs and Gaussian graphs demonstrate that our method outperforms the state-of-the-art greedy algorithms.
Highlights
We propose the Pareto Optimization for Graph Signal Sampling (POGSS) based on POSS, and an acceleration algorithm is proposed
We consider the graph signal sampling problem, which can be formulated as a subset selection problem
An efficient procedure is proposed to accelerate the evaluation of the objective function
Summary
Traditional signal processing usually treat the data as a sequence of vectors, analyze the features in the time domain or frequency domain, and try to extract information from the features. This implies that the data rely on an Euclidean space Rn. in many real-world applications such as computer graphics [6] and machine learning [7], this assumption is not accurate enough. GSP brings the signal from the time (spatial) domain to the node domain, and allows us to use a similar tool in traditional signal processing, such as Fourier transform and wavelet analysis, to analyze the graph signals, and extract the latent information.
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