The goal of this paper is to expand graph signal processing tools to deal with cases where the graph topology is not perfectly known. Assuming that the uncertainty affects only a limited number of edges, we make use of small perturbation analysis to derive closed form expressions instrumental to formulate signal processing algorithms that are resilient to imperfect knowledge of the graph topology. Then, we formulate a Bayesian approach to estimate the presence/absence of uncertain edges based only on the observed data and on the statistics of the data. Finally, we exploit our perturbation analysis to analyze clustering and semi-supervised learning algorithms. Numerical tests confirm the benefits of our perturbation-aware methods.

中文翻译：

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存在拓扑不确定性的图形信号处理

本文的目标是扩展图信号处理工具来处理图拓扑不完全已知的情况。假设不确定性只影响有限数量的边，我们利用小扰动分析来推导出闭式表达式，用于制定信号处理算法，这些算法对图拓扑的不完善知识具有弹性。然后，我们制定了一种贝叶斯方法来仅基于观察到的数据和数据的统计信息来估计不确定边缘的存在/不存在。最后，我们利用我们的扰动分析来分析聚类和半监督学习算法。数值测试证实了我们的扰动感知方法的好处。