机器学习中的图：介绍
Graphs in machine learning: an introduction
摘要：
图形通常用于描述感兴趣的对象之间的交互。因为它们是基于一个简单的形式主义，它们被用于从计算机科学到历史科学的许多科学领域。本文介绍了几种基于图的学习方法。这包括无监督和监督方法。无监督学习算法通常旨在可视化潜在空间中的图形和/或聚类节点。两者都专注于从图拓扑中提取知识。虽然大多数现有的技术仅适用于静态图，其中边不随时间演变，但最近的发展表明，它们可以扩展到处理不断变化的网络。在有监督的上下文中，通常旨在使用图和节点特征（当它们可用时）来推断附加到节点的标签或数值。平衡这两个信息来源可能具有挑战性，特别是因为它们可能在本地或全球范围内存在分歧。在这两种情况下，监督和无监督，数据可以是关系（用一个或多个全局图增强），如上所述，或图值。在后一种情况下，每个感兴趣的对象都是一个完整的图（可能由其他特征完成）。在这种情况下，自然任务包括图聚类（如产生图的集群而不是单个图中的节点集群），图分类等。1真实网络图的第一个实际研究可以追溯到Moreno [51]在30年代的原始工作。从那时起，人们对图形分析的兴趣越来越大，这与建模和处理这些数据的强劲发展有关。图表现在被用于许多科学领域。例如，在生物学[54，2，7]中，代谢网络可以描述生化反应的途径[41]，而在社会科学中，网络用于表示参与者之间的关系[66，56，36，34]。其他例子包括电网[71]和网络[75]。最近，网络也被认为是在其他领域，如地理[22]和历史[59，39]。在机器学习中，网络被视为建模问题的强大工具，以便从数据中提取信息并用于预测目的。这就是本文的研究对象。关于更完整的调查，我们参考[28，62，49，45]。在本节中，我们将介绍一些符号，并重点介绍大多数真实网络所共有的属性。在第2节中，我们考虑了从唯一网络中提取信息的方法。我们将特别关注聚类方法，其目标是找到顶点的聚类。最后，在第3节中，将考虑一系列网络的技术，其中每个网络都是
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
