Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis.
This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs--a nascent but quickly growing subset of graph representation learning.

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

In the past decade, the study of networks has increased dramatically. Researchers from across the sciences—including biology and bioinformatics, computer science, economics, engineering, mathematics, physics, sociology, and statistics—are more and more involved with the collection and statistical analysis of network-indexed data. As a result, statistical methods and models are being developed in this area at a furious pace, with contributions coming from a wide spectrum of disciplines.
This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics. In addition, the examples—including extended cases studies—are drawn widely from the literature. This book should be of substantial interest both to statisticians and to anyone else working in the area of ‘network science.’
The coverage of topics in this book is broad, but unfolds in a systematic manner, moving from descriptive (or exploratory) methods, to sampling, to modeling and inference. Specific topics include network mapping, characterization of network structure, network sampling, and the modeling, inference, and prediction of networks, network processes, and network flows. This book is the first such resource to present material on all of these core topics in one place.

Real-world physical and abstract data objects are interconnected, forming gigantic, interconnected networks. By structuring these data objects and interactions between these objects into multiple types, such networks become semi-structured heterogeneous information networks. Most real-world applications that handle big data, including interconnected social media and social networks, scientific, engineering, or medical information systems, online e-commerce systems, and most database systems, can be structured into heterogeneous information networks. Therefore, effective analysis of large-scale heterogeneous information networks poses an interesting but critical challenge.
In this book, we investigate the principles and methodologies of mining heterogeneous information networks. Departing from many existing network models that view interconnected data as homogeneous graphs or networks, our semi-structured heterogeneous information network model leverages the rich semantics of typed nodes and links in a network and uncovers surprisingly rich knowledge from the network. This semi-structured heterogeneous network modeling leads to a series of new principles and powerful methodologies for mining interconnected data, including: (1) rank-based clustering and classification; (2) meta-path-based similarity search and mining; (3) relation strength-aware mining, and many other potential developments. This book introduces this new research frontier and points out some promising research directions.
Table of Contents: Introduction / Ranking-Based Clustering / Classification of Heterogeneous Information Networks / Meta-Path-Based Similarity Search / Meta-Path-Based Relationship Prediction / Relation Strength-Aware Clustering with Incomplete Attributes / User-Guided Clustering via Meta-Path Selection / Research Frontiers

The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.

This book offers researchers an understanding of the fundamental issues and a good starting point to work on this rapidly expanding field. It provides a comprehensive survey of current developments of heterogeneous information network. It also presents the newest research in applications of heterogeneous information networks to similarity search, ranking, clustering, recommendation.
This information will help researchers to understand how to analyze networked data with heterogeneous information networks. Common data mining tasks are explored, including similarity search, ranking, and recommendation. The book illustrates some prototypes which analyze networked data.
Professionals and academics working in data analytics, networks, machine learning, and data mining will find this content valuable. It is also suitable for advanced-level students in computer science who are interested in networking or pattern recognition.