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We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…

Advanced graph neural networks have shown great potentials in graph classification tasks recently. Different from node classification where node embeddings aggregated from local neighbors can be directly used to learn node labels, graph…

Network embedding is an important step in many different computations based on graph data. However, existing approaches are limited to small or middle size graphs with fewer than a million edges. In practice, web or social network graphs…

Most existing graph visualization methods based on dimension reduction are limited to relatively small graphs due to performance issues. In this work, we propose a novel dimension reduction method for graph visualization, called…

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…

Unsupervised text embedding methods, such as Skip-gram and Paragraph Vector, have been attracting increasing attention due to their simplicity, scalability, and effectiveness. However, comparing to sophisticated deep learning architectures…

Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…

A collaborative network is a social network that is comprised of experts who cooperate with each other to fulfill a special goal. Analyzing this network yields meaningful information about the expertise of these experts and their subject…

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

This paper investigates the problem of network embedding, which aims at learning low-dimensional vector representation of nodes in networks. Most existing network embedding methods rely solely on the network structure, i.e., the linkage…

Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…

Network embedding has proved extremely useful in a variety of network analysis tasks such as node classification, link prediction, and network visualization. Almost all the existing network embedding methods learn to map the node IDs to…

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…

A graph embedding is an emerging approach that can represent a graph structure with a fixed-length low-dimensional vector. node2vec is a well-known algorithm to obtain such a graph embedding by sampling neighboring nodes on a given graph…