Related papers: An Automorphic Distance Metric and its Application…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
A key concern in network analysis is the study of social positions and roles of actors in a network. The notion of "position" refers to an equivalence class of nodes that have similar ties to other nodes, whereas a "role" is an equivalence…
We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense,…
Learning representations of sets of nodes in a graph is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph…
Since real-world objects and their interactions are often multi-modal and multi-typed, heterogeneous networks have been widely used as a more powerful, realistic, and generic superclass of traditional homogeneous networks (graphs).…
Distinguishing the automorphic equivalence of nodes in a graph plays an essential role in many scientific domains, e.g., computational biologist and social network analysis. However, existing graph neural networks (GNNs) fail to capture…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent…
Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features.…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating…
Recent work has demonstrated that vector offsets obtained by subtracting pretrained word embedding vectors can be used to predict lexical relations with surprising accuracy. Inspired by this finding, in this paper, we extend the idea to the…
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from…
The nodes in a network can be grouped into 'roles' based on similar connection patterns. This is usually achieved by defining a pairwise node similarity matrix and then clustering rows and columns of this matrix. This paper presents a new…
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…