Distance Metric Learning for Graph Structured Data
Nagoya Institute of Technology（名古屋工业大学）；National Institute for Material Science（国立材料科学研究所）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
38 pages, 11 figures. This is a pre-print of an article published in Machine Learning Journal. The final authenticated version is available online at: https://doi.org/10.1007/s10994-021-06009-3
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between input graphs, defining an appropriate distance metric for graphs remains a controversial issue. Hence, we propose a supervised distance metric learning method for the graph classification problem. Our method, named interpretable graph metric learning (IGML), learns discriminative metrics in a subgraph-based feature space, which has a strong graph representation capability. By introducing a sparsity-inducing penalty on the weight of each subgraph, IGML can identify a small number of important subgraphs that can provide insight into the given classification task. Because our formulation has a large number of optimization variables, an efficient algorithm that uses pruning techniques based on safe screening and working set selection methods is also proposed. An important property of IGML is that solution optimality is guaranteed because the problem is formulated as a convex problem and our pruning strategies only discard unnecessary subgraphs. Furthermore, we show that IGML is also applicable to other structured data such as itemset and sequence data, and that it can incorporate vertex-label similarity by using a transportation-based subgraph feature. We empirically evaluate the computational efficiency and classification performance of IGML on several benchmark datasets and provide some illustrative examples of how IGML identifies important subgraphs from a given graph dataset.
Graph Neural Distance Metric Learning with Graph-Bert
Florida State University（佛罗里达州立大学）；IFM Lab（IFM实验室）
图距离度量学习是许多图学习问题的基础，例如，图聚类、图分类和图匹配。现有的关于图距离度量（或图核）学习的研究工作未能保持这些度量的基本性质，例如，非负性、不可约恒等式、对称性和三角不等式。在本文中，我们将介绍一种新的图神经网络的距离度量学习方法，即GB-DISTANCE（GRAPH-BERT based Neural Distance）。基于注意力机制，GB-DISTANCE可以基于预先训练的GRAPH-BERT模型有效地学习图实例表示。与现有的监督/无监督度量不同，GB-DISTANCE可以以半监督的方式有效地学习。此外，GB-DISTANCE还可以保持上述距离度量的基本属性。在多个基准图数据集上进行了大量实验，结果表明GB-DISTANCE算法的性能优于现有的基线方法，尤其是最近提出的基于图度量的图神经网络模型，但在计算图距离方面存在明显差距。
Distance Metric Learning through Minimization of the Free Energy
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Universidade Federal Rural de Pernambuco（伯南布哥联邦农村大学）
在过去的几十年里，距离度量学习在解决机器学习和模式识别问题方面吸引了很多兴趣。在这项工作中，我们提出了一个简单的方法，从统计物理学的概念，学习最佳的距离度量给定的问题。我们制定的任务作为一个典型的统计物理问题：模式之间的距离代表的组成部分的物理系统和目标函数对应的能量。然后，我们将问题表示为复杂系统的自由能的最小化，这相当于距离度量学习。就像物理学中的许多问题一样，我们提出了一种基于Metropolis Monte Carlo的方法来找到最佳距离度量。这提供了一种自然的方式来学习距离度量，其中学习过程可以直观地看作是拉伸和旋转度量空间，直到满足某些启发式。我们提出的方法可以处理各种各样的约束，包括那些虚假的局部极小值。该方法与来自邻域分量分析（NCA）的随机最近邻的效果令人惊讶地好。人工和真实世界的数据集上的实验结果显示出明显的优越性，在一些国家的最先进的距离度量学习方法的最近邻分类。
A Dual Basis Approach for Structured Robust Euclidean Distance Geometry
Department of Statistics and Data Science University of Central Florida（统计与数据科学系 佛罗里达中央大学）；Department of Mathematics Tufts University（数学系 塔夫茨大学）；Department of Statistics and Data Science Department of Computer Science University of Central Florida（统计与数据科学系 计算机科学系 佛罗里达中央大学）
