Vertex nomination

Abstract

Vertex nomination is a subclass of recommender systems operating on attributed graphs. Attributed graphs are an attractive way to represent data from a diverse set of natural and manmade phenomena. Frequently, these data have latent attributes or class memberships that are of interest and uncovering them is of some intrinsic value. So‐called recommender systems address the ‘more like this’ problem: given a subset of the data labeled as ‘interesting’, find unlabeled examples that are ‘similarly interesting’, often with the assumption that they are from the same latent class or possess similar latent attributes. Unsurprisingly, recommender systems operating on attributed graphs have generated an interesting body of research, detailing both theoretical and practical advances for a range of applications. This advanced review examines the relevant literature, particularly focused on the importance and inclusion of edge‐ and vertex attributes, used in conjunction with the graph structure. We include example applications from human language technology, biology, and neuroscience for concreteness, although the algorithms discussed are widely applicable. WIREs Comput Stat 2014, 6:144–153. doi: 10.1002/wics.1294 This article is categorized under: Algorithms and Computational Methods > Quadratic and Nonlinear Programming

On Estimation and Inference in Latent Structure Random Graphs

“…Of course, a number of graph inference problems are comfortingly familiar and not necessarily peculiar to graphs per se: the parametric estimation of a common connection probability in an independent-edge random graph, for example, or the nonparametric estimation of a degree distribution. Other inference tasks, such as community detection, are more graph-centric, and still others, such as vertex nomination (Coppersmith, 2014, Fishkind et al, 2015 arise only in a network context. Nevertheless, even graph-specific inference tasks can frequently be resolved by appropriate Euclidean embeddings of graph data, and such Euclidean representations of graphs allow for a suite of classical statistical methods for Euclidean data, from estimation to classification to hypothesis testing (Athreya et al, 2018), to be effectively deployed in graph inference.…”

Vertex nomination via seeded graph matching

“…The classical formulation of the VN inference task can be stated as follows: given a network with latent community structure in which one of the communities is of particular interest and given a few vertices from the community of interest, the task in VN is to order the remaining vertices in the network into a nomination list, with the aim of having vertices from the community of interest concentrate at the top of the list. Thus, VN can also be thought of as a method for inferring missing vertex labels, and is related to the class/labeled instances acquisition task and collective classification methods of .…”

Vertex nomination, consistent estimation, and adversarial modification

“…In modern statistics and machine learning, graphs are a common way to take into account the complex relationships between data objects, and graphs have been used in applications across the biological (see, for example, [42,7,1,31,21,33]) and social sciences (see, for example, [35,41,20,22]). In addition to more traditional statistical inference tasks such as clustering [39,38,6,34], classification [46,11,1], and estimation [5,4,43], there has been significant work in more network-specific inference tasks such as graph matching [12,18,47], and vertex nomination [30,13,17].…”