Graph Neural Networks: Foundations, Frontiers, and Applications

Download Graph Neural Networks: Foundations, Frontiers, and Applications PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 9811660549
Total Pages : 701 pages
Book Rating : 4.8/5 (116 download)

DOWNLOAD NOW!


Book Synopsis Graph Neural Networks: Foundations, Frontiers, and Applications by : Lingfei Wu

Download or read book Graph Neural Networks: Foundations, Frontiers, and Applications written by Lingfei Wu and published by Springer Nature. This book was released on 2022-01-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep Learning models are at the core of artificial intelligence research today. It is well known that deep learning techniques are disruptive for Euclidean data, such as images or sequence data, and not immediately applicable to graph-structured data such as text. This gap has driven a wave of research for deep learning on graphs, including graph representation learning, graph generation, and graph classification. The new neural network architectures on graph-structured data (graph neural networks, GNNs in short) have performed remarkably on these tasks, demonstrated by applications in social networks, bioinformatics, and medical informatics. Despite these successes, GNNs still face many challenges ranging from the foundational methodologies to the theoretical understandings of the power of the graph representation learning. This book provides a comprehensive introduction of GNNs. It first discusses the goals of graph representation learning and then reviews the history, current developments, and future directions of GNNs. The second part presents and reviews fundamental methods and theories concerning GNNs while the third part describes various frontiers that are built on the GNNs. The book concludes with an overview of recent developments in a number of applications using GNNs. This book is suitable for a wide audience including undergraduate and graduate students, postdoctoral researchers, professors and lecturers, as well as industrial and government practitioners who are new to this area or who already have some basic background but want to learn more about advanced and promising techniques and applications.

Introduction to Graph Neural Networks

Download Introduction to Graph Neural Networks PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3031015878
Total Pages : 109 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!


Book Synopsis Introduction to Graph Neural Networks by : Zhiyuan Zhiyuan Liu

Download or read book Introduction to Graph Neural Networks written by Zhiyuan Zhiyuan Liu and published by Springer Nature. This book was released on 2022-05-31 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs are useful data structures in complex real-life applications such as modeling physical systems, learning molecular fingerprints, controlling traffic networks, and recommending friends in social networks. However, these tasks require dealing with non-Euclidean graph data that contains rich relational information between elements and cannot be well handled by traditional deep learning models (e.g., convolutional neural networks (CNNs) or recurrent neural networks (RNNs)). Nodes in graphs usually contain useful feature information that cannot be well addressed in most unsupervised representation learning methods (e.g., network embedding methods). Graph neural networks (GNNs) are proposed to combine the feature information and the graph structure to learn better representations on graphs via feature propagation and aggregation. Due to its convincing performance and high interpretability, GNN has recently become a widely applied graph analysis tool. This book provides a comprehensive introduction to the basic concepts, models, and applications of graph neural networks. It starts with the introduction of the vanilla GNN model. Then several variants of the vanilla model are introduced such as graph convolutional networks, graph recurrent networks, graph attention networks, graph residual networks, and several general frameworks. Variants for different graph types and advanced training methods are also included. As for the applications of GNNs, the book categorizes them into structural, non-structural, and other scenarios, and then it introduces several typical models on solving these tasks. Finally, the closing chapters provide GNN open resources and the outlook of several future directions.

Graph Representation Learning

Download Graph Representation Learning PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3031015886
Total Pages : 141 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!


Book Synopsis Graph Representation Learning by : William L. William L. Hamilton

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Wavelet Tour of Signal Processing

Download A Wavelet Tour of Signal Processing PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 0080520839
Total Pages : 663 pages
Book Rating : 4.0/5 (85 download)

DOWNLOAD NOW!


Book Synopsis A Wavelet Tour of Signal Processing by : Stephane Mallat

Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat and published by Elsevier. This book was released on 1999-09-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition - Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Deep Learning on Graphs

Download Deep Learning on Graphs PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 1108831745
Total Pages : 339 pages
Book Rating : 4.1/5 (88 download)

DOWNLOAD NOW!


Book Synopsis Deep Learning on Graphs by : Yao Ma

Download or read book Deep Learning on Graphs written by Yao Ma and published by Cambridge University Press. This book was released on 2021-09-23 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive text on foundations and techniques of graph neural networks with applications in NLP, data mining, vision and healthcare.

Social Internet of Things

Download Social Internet of Things PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319946595
Total Pages : 221 pages
Book Rating : 4.3/5 (199 download)

DOWNLOAD NOW!


Book Synopsis Social Internet of Things by : Alessandro Soro

Download or read book Social Internet of Things written by Alessandro Soro and published by Springer. This book was released on 2018-07-20 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to stimulate research on the topic of the Social Internet of Things, and explore how Internet of Things architectures, tools, and services can be conceptualized and developed so as to reveal, amplify and inspire the capacities of people, including the socialization or collaborations that happen through or around smart objects and smart environments. From new ways of negotiating privacy, to the consequences of increased automation, the Internet of Things poses new challenges and opens up new questions that often go beyond the technology itself, and rather focus on how the technology will become embedded in our future communities, families, practices, and environment, and how these will change in turn.

Neural Network Fundamentals with Graphs, Algorithms, and Applications

Download Neural Network Fundamentals with Graphs, Algorithms, and Applications PDF Online Free

Author :
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!


Book Synopsis Neural Network Fundamentals with Graphs, Algorithms, and Applications by : Nirmal K. Bose

Download or read book Neural Network Fundamentals with Graphs, Algorithms, and Applications written by Nirmal K. Bose and published by McGraw-Hill Companies. This book was released on 1996 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Deep Learning Techniques and Optimization Strategies in Big Data Analytics

Download Deep Learning Techniques and Optimization Strategies in Big Data Analytics PDF Online Free

Author :
Publisher : IGI Global
ISBN 13 : 1799811948
Total Pages : 355 pages
Book Rating : 4.7/5 (998 download)

DOWNLOAD NOW!


Book Synopsis Deep Learning Techniques and Optimization Strategies in Big Data Analytics by : Thomas, J. Joshua

Download or read book Deep Learning Techniques and Optimization Strategies in Big Data Analytics written by Thomas, J. Joshua and published by IGI Global. This book was released on 2019-11-29 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many approaches have sprouted from artificial intelligence (AI) and produced major breakthroughs in the computer science and engineering industries. Deep learning is a method that is transforming the world of data and analytics. Optimization of this new approach is still unclear, however, and there’s a need for research on the various applications and techniques of deep learning in the field of computing. Deep Learning Techniques and Optimization Strategies in Big Data Analytics is a collection of innovative research on the methods and applications of deep learning strategies in the fields of computer science and information systems. While highlighting topics including data integration, computational modeling, and scheduling systems, this book is ideally designed for engineers, IT specialists, data analysts, data scientists, engineers, researchers, academicians, and students seeking current research on deep learning methods and its application in the digital industry.

Concepts and Techniques of Graph Neural Networks

Download Concepts and Techniques of Graph Neural Networks PDF Online Free

Author :
Publisher : IGI Global
ISBN 13 : 1668469057
Total Pages : 267 pages
Book Rating : 4.6/5 (684 download)

DOWNLOAD NOW!


Book Synopsis Concepts and Techniques of Graph Neural Networks by : Kumar, Vinod

Download or read book Concepts and Techniques of Graph Neural Networks written by Kumar, Vinod and published by IGI Global. This book was released on 2023-05-22 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advancements in graph neural networks have expanded their capacities and expressive power. Furthermore, practical applications have begun to emerge in a variety of fields including recommendation systems, fake news detection, traffic prediction, molecular structure in chemistry, antibacterial discovery physics simulations, and more. As a result, a boom of research at the juncture of graph theory and deep learning has revolutionized many areas of research. However, while graph neural networks have drawn a lot of attention, they still face many challenges when it comes to applying them to other domains, from a conceptual understanding of methodologies to scalability and interpretability in a real system. Concepts and Techniques of Graph Neural Networks provides a stepwise discussion, an exhaustive literature review, detailed analysis and discussion, rigorous experimentation results, and application-oriented approaches that are demonstrated with respect to applications of graph neural networks. The book also develops the understanding of concepts and techniques of graph neural networks and establishes the familiarity of different real applications in various domains for graph neural networks. Covering key topics such as graph data, social networks, deep learning, and graph clustering, this premier reference source is ideal for industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

TensorFlow Machine Learning Projects

Download TensorFlow Machine Learning Projects PDF Online Free

Author :
Publisher : Packt Publishing Ltd
ISBN 13 : 1789132401
Total Pages : 311 pages
Book Rating : 4.7/5 (891 download)

DOWNLOAD NOW!


Book Synopsis TensorFlow Machine Learning Projects by : Ankit Jain

Download or read book TensorFlow Machine Learning Projects written by Ankit Jain and published by Packt Publishing Ltd. This book was released on 2018-11-30 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implement TensorFlow's offerings such as TensorBoard, TensorFlow.js, TensorFlow Probability, and TensorFlow Lite to build smart automation projects Key FeaturesUse machine learning and deep learning principles to build real-world projectsGet to grips with TensorFlow's impressive range of module offeringsImplement projects on GANs, reinforcement learning, and capsule networkBook Description TensorFlow has transformed the way machine learning is perceived. TensorFlow Machine Learning Projects teaches you how to exploit the benefits—simplicity, efficiency, and flexibility—of using TensorFlow in various real-world projects. With the help of this book, you’ll not only learn how to build advanced projects using different datasets but also be able to tackle common challenges using a range of libraries from the TensorFlow ecosystem. To start with, you’ll get to grips with using TensorFlow for machine learning projects; you’ll explore a wide range of projects using TensorForest and TensorBoard for detecting exoplanets, TensorFlow.js for sentiment analysis, and TensorFlow Lite for digit classification. As you make your way through the book, you’ll build projects in various real-world domains, incorporating natural language processing (NLP), the Gaussian process, autoencoders, recommender systems, and Bayesian neural networks, along with trending areas such as Generative Adversarial Networks (GANs), capsule networks, and reinforcement learning. You’ll learn how to use the TensorFlow on Spark API and GPU-accelerated computing with TensorFlow to detect objects, followed by how to train and develop a recurrent neural network (RNN) model to generate book scripts. By the end of this book, you’ll have gained the required expertise to build full-fledged machine learning projects at work. What you will learnUnderstand the TensorFlow ecosystem using various datasets and techniquesCreate recommendation systems for quality product recommendationsBuild projects using CNNs, NLP, and Bayesian neural networksPlay Pac-Man using deep reinforcement learningDeploy scalable TensorFlow-based machine learning systemsGenerate your own book script using RNNsWho this book is for TensorFlow Machine Learning Projects is for you if you are a data analyst, data scientist, machine learning professional, or deep learning enthusiast with basic knowledge of TensorFlow. This book is also for you if you want to build end-to-end projects in the machine learning domain using supervised, unsupervised, and reinforcement learning techniques

Neural Networks and Deep Learning

Download Neural Networks and Deep Learning PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319944630
Total Pages : 512 pages
Book Rating : 4.3/5 (199 download)

DOWNLOAD NOW!


Book Synopsis Neural Networks and Deep Learning by : Charu C. Aggarwal

Download or read book Neural Networks and Deep Learning written by Charu C. Aggarwal and published by Springer. This book was released on 2018-08-25 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly important for understanding important concepts, so that one can understand the important design concepts of neural architectures in different applications. Why do neural networks work? When do they work better than off-the-shelf machine-learning models? When is depth useful? Why is training neural networks so hard? What are the pitfalls? The book is also rich in discussing different applications in order to give the practitioner a flavor of how neural architectures are designed for different types of problems. Applications associated with many different areas like recommender systems, machine translation, image captioning, image classification, reinforcement-learning based gaming, and text analytics are covered. The chapters of this book span three categories: The basics of neural networks: Many traditional machine learning models can be understood as special cases of neural networks. An emphasis is placed in the first two chapters on understanding the relationship between traditional machine learning and neural networks. Support vector machines, linear/logistic regression, singular value decomposition, matrix factorization, and recommender systems are shown to be special cases of neural networks. These methods are studied together with recent feature engineering methods like word2vec. Fundamentals of neural networks: A detailed discussion of training and regularization is provided in Chapters 3 and 4. Chapters 5 and 6 present radial-basis function (RBF) networks and restricted Boltzmann machines. Advanced topics in neural networks: Chapters 7 and 8 discuss recurrent neural networks and convolutional neural networks. Several advanced topics like deep reinforcement learning, neural Turing machines, Kohonen self-organizing maps, and generative adversarial networks are introduced in Chapters 9 and 10. The book is written for graduate students, researchers, and practitioners. Numerous exercises are available along with a solution manual to aid in classroom teaching. Where possible, an application-centric view is highlighted in order to provide an understanding of the practical uses of each class of techniques.

Backpropagation

Download Backpropagation PDF Online Free

Author :
Publisher : Psychology Press
ISBN 13 : 1134775814
Total Pages : 576 pages
Book Rating : 4.1/5 (347 download)

DOWNLOAD NOW!


Book Synopsis Backpropagation by : Yves Chauvin

Download or read book Backpropagation written by Yves Chauvin and published by Psychology Press. This book was released on 2013-02-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composed of three sections, this book presents the most popular training algorithm for neural networks: backpropagation. The first section presents the theory and principles behind backpropagation as seen from different perspectives such as statistics, machine learning, and dynamical systems. The second presents a number of network architectures that may be designed to match the general concepts of Parallel Distributed Processing with backpropagation learning. Finally, the third section shows how these principles can be applied to a number of different fields related to the cognitive sciences, including control, speech recognition, robotics, image processing, and cognitive psychology. The volume is designed to provide both a solid theoretical foundation and a set of examples that show the versatility of the concepts. Useful to experts in the field, it should also be most helpful to students seeking to understand the basic principles of connectionist learning and to engineers wanting to add neural networks in general -- and backpropagation in particular -- to their set of problem-solving methods.

Data Analytics on Graphs

Download Data Analytics on Graphs PDF Online Free

Author :
Publisher :
ISBN 13 : 9781680839821
Total Pages : 556 pages
Book Rating : 4.8/5 (398 download)

DOWNLOAD NOW!


Book Synopsis Data Analytics on Graphs by : Ljubisa Stankovic

Download or read book Data Analytics on Graphs written by Ljubisa Stankovic and published by . This book was released on 2020-12-22 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at readers with a good grasp of the fundamentals of data analytics, this book sets out the fundamentals of graph theory and the emerging mathematical techniques for the analysis of a wide range of data acquired on graph environments. This book will be a useful friend and a helpful companion to all involved in data gathering and analysis.

Graph Machine Learning

Download Graph Machine Learning PDF Online Free

Author :
Publisher : Packt Publishing Ltd
ISBN 13 : 1800206755
Total Pages : 338 pages
Book Rating : 4.8/5 (2 download)

DOWNLOAD NOW!


Book Synopsis Graph Machine Learning by : Claudio Stamile

Download or read book Graph Machine Learning written by Claudio Stamile and published by Packt Publishing Ltd. This book was released on 2021-06-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Build machine learning algorithms using graph data and efficiently exploit topological information within your models Key Features Implement machine learning techniques and algorithms in graph data Identify the relationship between nodes in order to make better business decisions Apply graph-based machine learning methods to solve real-life problems Book Description Graph Machine Learning will introduce you to a set of tools used for processing network data and leveraging the power of the relation between entities that can be used for predictive, modeling, and analytics tasks. The first chapters will introduce you to graph theory and graph machine learning, as well as the scope of their potential use. You'll then learn all you need to know about the main machine learning models for graph representation learning: their purpose, how they work, and how they can be implemented in a wide range of supervised and unsupervised learning applications. You'll build a complete machine learning pipeline, including data processing, model training, and prediction in order to exploit the full potential of graph data. After covering the basics, you'll be taken through real-world scenarios such as extracting data from social networks, text analytics, and natural language processing (NLP) using graphs and financial transaction systems on graphs. You'll also learn how to build and scale out data-driven applications for graph analytics to store, query, and process network information, and explore the latest trends on graphs. By the end of this machine learning book, you will have learned essential concepts of graph theory and all the algorithms and techniques used to build successful machine learning applications. What you will learn Write Python scripts to extract features from graphs Distinguish between the main graph representation learning techniques Learn how to extract data from social networks, financial transaction systems, for text analysis, and more Implement the main unsupervised and supervised graph embedding techniques Get to grips with shallow embedding methods, graph neural networks, graph regularization methods, and more Deploy and scale out your application seamlessly Who this book is for This book is for data scientists, data analysts, graph analysts, and graph professionals who want to leverage the information embedded in the connections and relations between data points to boost their analysis and model performance using machine learning. It will also be useful for machine learning developers or anyone who wants to build ML-driven graph databases. A beginner-level understanding of graph databases and graph data is required, alongside a solid understanding of ML basics. You'll also need intermediate-level Python programming knowledge to get started with this book.

Computational Intelligence And Its Applications: Evolutionary Computation, Fuzzy Logic, Neural Network And Support Vector Machine Techniques

Download Computational Intelligence And Its Applications: Evolutionary Computation, Fuzzy Logic, Neural Network And Support Vector Machine Techniques PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 1908977078
Total Pages : 318 pages
Book Rating : 4.9/5 (89 download)

DOWNLOAD NOW!


Book Synopsis Computational Intelligence And Its Applications: Evolutionary Computation, Fuzzy Logic, Neural Network And Support Vector Machine Techniques by : Hung Tan Nguyen

Download or read book Computational Intelligence And Its Applications: Evolutionary Computation, Fuzzy Logic, Neural Network And Support Vector Machine Techniques written by Hung Tan Nguyen and published by World Scientific. This book was released on 2012-07-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational intelligence techniques and their applications — fast-growing and promising research topics that have drawn a great deal of attention from researchers over the years. It brings together many different aspects of the current research on intelligence technologies such as neural networks, support vector machines, fuzzy logic and evolutionary computation, and covers a wide range of applications from pattern recognition and system modeling, to intelligent control problems and biomedical applications. Fundamental concepts and essential analysis of various computational techniques are presented to offer a systematic and effective tool for better treatment of different applications, and simulation and experimental results are included to illustrate the design procedure and the effectiveness of the approaches./a

Neural Network Methods for Natural Language Processing

Download Neural Network Methods for Natural Language Processing PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3031021657
Total Pages : 20 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!


Book Synopsis Neural Network Methods for Natural Language Processing by : Yoav Goldberg

Download or read book Neural Network Methods for Natural Language Processing written by Yoav Goldberg and published by Springer Nature. This book was released on 2022-06-01 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural networks are a family of powerful machine learning models. This book focuses on the application of neural network models to natural language data. The first half of the book (Parts I and II) covers the basics of supervised machine learning and feed-forward neural networks, the basics of working with machine learning over language data, and the use of vector-based rather than symbolic representations for words. It also covers the computation-graph abstraction, which allows to easily define and train arbitrary neural networks, and is the basis behind the design of contemporary neural network software libraries. The second part of the book (Parts III and IV) introduces more specialized neural network architectures, including 1D convolutional neural networks, recurrent neural networks, conditioned-generation models, and attention-based models. These architectures and techniques are the driving force behind state-of-the-art algorithms for machine translation, syntactic parsing, and many other applications. Finally, we also discuss tree-shaped networks, structured prediction, and the prospects of multi-task learning.

Discrete Mathematics of Neural Networks

Download Discrete Mathematics of Neural Networks PDF Online Free

Author :
Publisher : SIAM
ISBN 13 : 089871480X
Total Pages : 137 pages
Book Rating : 4.8/5 (987 download)

DOWNLOAD NOW!


Book Synopsis Discrete Mathematics of Neural Networks by : Martin Anthony

Download or read book Discrete Mathematics of Neural Networks written by Martin Anthony and published by SIAM. This book was released on 2001-01-01 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.