论文标题
Figlearn：使用最佳传输的过滤和图形学习
FiGLearn: Filter and Graph Learning using Optimal Transport
论文作者
论文摘要
在许多应用程序中，数据集可以被视为一组现场的观察到的信号，该信号现有在未知的基础图结构上。这些信号中的一些可以看作是通过图滤波器在图形拓扑上过滤的白噪声。因此，过滤器和图表的知识提供了有关基础数据生成过程以及数据集中出现的复杂交互的有价值信息。因此，我们引入了一个新型的图形信号处理框架，用于共同学习图形及其从信号观测值中生成过滤器。我们提出了一个新的优化问题，该问题将信号观察分布与过滤的信号分布模型之间的Wasserstein距离最小化。我们提出的方法优于合成数据的最先进的图形学习框架。然后，我们将我们的方法应用于温度异常数据集，并进一步显示该框架只有很少的信息可用来推断丢失值。
In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph filter. Hence, the knowledge of the filter and the graph provides valuable information about the underlying data generation process and the complex interactions that arise in the dataset. We hence introduce a novel graph signal processing framework for jointly learning the graph and its generating filter from signal observations. We cast a new optimisation problem that minimises the Wasserstein distance between the distribution of the signal observations and the filtered signal distribution model. Our proposed method outperforms state-of-the-art graph learning frameworks on synthetic data. We then apply our method to a temperature anomaly dataset, and further show how this framework can be used to infer missing values if only very little information is available.
