Social Networks with Rich Edge Semantics introduces a new mechanism for representing social networks in which pairwise relationships can be drawn from a range of realistic possibilities, including different types of relationships, different strengths in the directions of a pair, positive and negative relationships, and relationships whose intensities change with time. For each possibility, the book shows how to model the social network using spectral embedding. It also shows how to compose the techniques so that multiple edge semantics can be modeled together, and the modeling techniques are then applied to a range of datasets. Features Introduces the reader to difficulties with current social network analysis, and the need for richer representations of relationships among nodes, including accounting for intensity, direction, type, positive/negative, and changing intensities over time Presents a novel mechanism to allow social networks with qualitatively different kinds of relationships to be described and analyzed Includes extensions to the important technique of spectral embedding, shows that they are mathematically well motivated and proves that their results are appropriate Shows how to exploit embeddings to understand structures within social networks, including subgroups, positional significance, link or edge prediction, consistency of role in different contexts, and net flow of properties through a node Illustrates the use of the approach for real-world problems for online social networks, criminal and drug smuggling networks, and networks where the nodes are themselves groups Suitable for researchers and students in social network research, data science, statistical learning, and related areas, this book will help to provide a deeper understanding of real-world social networks.

Social Networks with Rich Edge Semantics introduces a new mechanism for representing social networks in which pairwise relationships can be drawn from a range of realistic possibilities, including different types of relationships, different strengths in the directions of a pair, positive and negative relationships, and relationships whose intensities change with time. For each possibility, the book shows how to model the social network using spectral embedding. It also shows how to compose the techniques so that multiple edge semantics can be modeled together, and the modeling techniques are then applied to a range of datasets. Features Introduces the reader to difficulties with current social network analysis, and the need for richer representations of relationships among nodes, including accounting for intensity, direction, type, positive/negative, and changing intensities over time Presents a novel mechanism to allow social networks with qualitatively different kinds of relationships to be described and analyzed Includes extensions to the important technique of spectral embedding, shows that they are mathematically well motivated and proves that their results are appropriate Shows how to exploit embeddings to understand structures within social networks, including subgroups, positional significance, link or edge prediction, consistency of role in different contexts, and net flow of properties through a node Illustrates the use of the approach for real-world problems for online social networks, criminal and drug smuggling networks, and networks where the nodes are themselves groups Suitable for researchers and students in social network research, data science, statistical learning, and related areas, this book will help to provide a deeper understanding of real-world social networks.

This book treats the subject of global optimization with minimal restrictions on the behavior on the objective functions. In particular, optimal conditions were developed for a class of noncontinuous functions characterized by their having level sets that are robust. The integration-based approach contrasts with existing approaches which require some degree of convexity or differentiability of the objective function. Some computational results on a personal computer are presented.