We consider the problem of learning a graph from a given set of smooth graph signals. Our graph learning approach is formulated as a constrained quadratic program in the edge weights. We provide an implicit characterization of the optimal solution and propose a tailored ADMM algorithm to solve this problem efficiently. Several nearest neighbor and smoothness based graph learning methods are shown to be special cases of our approach. Specifically, our algorithm yields an efficient but extremely accurate approximation to b-matched graphs. We then propose a generalization of our scheme that can deal with noisy and incomplete data via joint graph learning and signal inpainting. We compare the performance of our approach with state-of-the art methods on synthetic data and on real-world data from the Austrian National Council.

中文翻译：

---

从嘈杂和不完整的数据中进行高效的图学习


我们考虑从一组给定的平滑图信号中学习图的问题。我们的图学习方法被制定为边缘权重的约束二次规划。我们提供了最优解决方案的隐式表征，并提出了一种定制的 ADMM 算法来有效地解决这个问题。几种基于最近邻和平滑度的图学习方法被证明是我们方法的特例。具体来说，我们的算法对 b 匹配图产生高效但极其准确的近似。然后，我们提出了我们的方案的概括，该方案可以通过联合图学习和信号修复来处理噪声和不完整的数据。我们将我们的方法的性能与合成数据和奥地利国民议会真实世界数据的最先进方法进行比较。