[论文解读] Graphs in machine learning: an introduction

Pierre Latouche, Fabrice Rossi|arXiv (Cornell University)|Jun 23, 2015

Complex Network Analysis Techniques参考文献 64被引用 9

一句话总结

本文介绍了用于无监督和有监督任务的基于图的机器学习方法，涵盖聚类、可视化及图比较。方法涉及静态图与动态图，重点在于基于模块度的社区检测、图核方法及编辑距离，应用于关系数据与演化网络。

ABSTRACT

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globally. In both contexts, supervised and un-supervised, data can be relational (augmented with one or several global graphs) as described above, or graph valued. In this latter case, each object of interest is given as a full graph (possibly completed by other characteristics). In this context, natural tasks include graph clustering (as in producing clusters of graphs rather than clusters of nodes in a single graph), graph classification, etc. 1 Real networks One of the first practical studies on graphs can be dated back to the original work of Moreno [51] in the 30s. Since then, there has been a growing interest in graph analysis associated with strong developments in the modelling and the processing of these data. Graphs are now used in many scientific fields. In Biology [54, 2, 7], for instance, metabolic networks can describe pathways of biochemical reactions [41], while in social sciences networks are used to represent relation ties between actors [66, 56, 36, 34]. Other examples include powergrids [71] and the web [75]. Recently, networks have also been considered in other areas such as geography [22] and history [59, 39]. In machine learning, networks are seen as powerful tools to model problems in order to extract information from data and for prediction purposes. This is the object of this paper. For more complete surveys, we refer to [28, 62, 49, 45]. In this section, we introduce notations and highlight properties shared by most real networks. In Section 2, we then consider methods aiming at extracting information from a unique network. We will particularly focus on clustering methods where the goal is to find clusters of vertices. Finally, in Section 3, techniques that take a series of networks into account, where each network is

研究动机与目标

• 为该领域的新研究者提供基于图的机器学习方法的全面介绍。
• 解决从静态与演化网络的图拓扑中提取知识的挑战。
• 弥合无监督图分析与涉及节点标签或图级预测的有监督学习任务之间的差距。
• 探索将关系数据（以图增强）与图值数据整合到机器学习流程中的方法。
• 强调图比较的复杂性，包括同构性与编辑距离，并阐明其在核方法中的作用。

提出的方法

• 使用邻接矩阵表示图，支持二值或加权边，以及可选的顶点/边标签。
• 应用模块度最大化与潜在位置聚类模型（LPCM）进行网络中的社区检测。
• 采用图编辑距离作为通过最小成本顶点/边操作序列比较图的度量。
• 利用基于产物图上的随机游走的图核方法，将向量空间方法推广至非向量图数据。
• 通过将节点特征与图结构相结合，在学习过程中平衡两种信息源。
• 通过考虑边与网络结构的时间演化，将方法扩展至动态图。

实验结果

研究问题

• RQ1 如何利用图拓扑在图中揭示隐藏的社区结构？
• RQ2 在必须检测并处理同构性时，有哪些有效的图比较方法？
• RQ3 在关系数据的有监督学习任务中，如何平衡节点特征与图结构？
• RQ4 精确图同构与子图同构的局限性与计算挑战是什么？
• RQ5 图核与编辑距离如何用于将标准机器学习算法推广至图结构化数据？

主要发现

• 大多数现实世界网络表现出稀疏性、一个巨大的连通分量、度分布异质性，以及最短路径按 O(log N) 缩放的小世界特性。
• 基于模块度的方法与潜在位置聚类模型在检测内部连接密集、组间连接稀疏的社区结构方面有效。
• 图编辑距离通过最小成本变换序列提供了一般性的图间差异性度量框架。
• 基于产物图上随机游走的图核方法使支持向量机（SVM）与核 k-means 等核方法可应用于图数据。
• 图同构问题在计算上仍具挑战性，目前最佳时间复杂度为 O(2^√(n log n))，而子图同构问题是 NP-完全问题。
• 关系数据与图值数据设置下，需谨慎整合节点特征与结构信息，尤其当两者冲突时。