Fundamental theory and practical algorithms of weakly supervised classification, emphasizing an approach based on empirical risk minimization.Standard machine learning techniques require large amounts of labeled data to work well. When we apply machine learning to problems in the physical world, however, it is extremely difficult to collect such quantities of labeled data. This book presents theory and algorithms for weakly supervised learning, a paradigm of machine learning from weakly labeled data. Emphasizing an approach based on empirical risk minimization and drawing on state-of-the-art research in weakly supervised learning, the book provides both the fundamentals of the field and the advanced mathematical theories underlying them. It can be used as a reference for practitioners and researchers and in the classroom.The book first mathematically formulates classification problems, defines common notations, and reviews various algorithms for supervised binary and multiclass classif
Description logics (DLs) have a long tradition in computer science and knowledge representation, being designed so that domain knowledge can be described and so that computers can reason about this knowledge. DLs have recently gained increased importance since they form the logical basis of widely used ontology languages, in particular the web ontology language OWL. Written by four renowned experts, this is the first textbook on description logics. It is suitable for self-study by graduates and as the basis for a university course. Starting from a basic DL, the book introduces the reader to their syntax, semantics, reasoning problems and model theory and discusses the computational complexity of these reasoning problems and algorithms to solve them. It then explores a variety of reasoning techniques, knowledge-based applications and tools and it describes the relationship between DLs and OWL.
Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gröbner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials and systems of non-linear equations. A special feature is that Gröbner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experience teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student perfor
Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gröbner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials and systems of non-linear equations. A special feature is that Gröbner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experience teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student perfor
Paul Erdös was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdös himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.
Paul Erdös was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdös himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.
One of the most promising technologies to resolve the bottlenecks in traffic capacity of future wireless networks is multiple-input multiple-output (MIMO) communications and space-time processing. MIMO wireless technology has progressed from the stage of fundamental research to commercially available products within a decade. With over sixty contributors from the field, this book provides an extensive overview of the state-of-the-art in MIMO communications, ranging from its roots in antenna array processing to advanced cellular communication systems. A balanced treatment of three key areas -information theory, algorithms and systems studies, and implementation issues - has been assembled by four editors with a broad range of academic and industry experience. This comprehensive reference will appeal to practitioners, researchers, and graduate students in wireless communications.
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.
Genetic algorithms are playing an increasingly important role in studies of complexadaptive systems, ranging from adaptive agents in economic theory to the use of machine learningtechniques in the des
Graph drawing comprises all aspects of visualizing structural relations between objects. The range of topics dealt with extends from graph theory, graph algorithms, geometry, and topology to visual la
This book provides a comprehensive foundation of machine learning. To answer the questions of what to learn, how to learn, what to get from learning, and how to evaluate, as well as what is meant by learning, the book focuses on the fundamental basics of machine learning, its methodology, theory, algorithms, and evaluations, together with some philosophical thinking on comparison between machine learning and human learning for machinery intelligence.The book is organized as follows: Introduction (Chapter 1), Evaluation (Chapter 2), Supervised learning (Chapters 3, 4, and 5), Unsupervised learning (Chapter 6), Representation learning (Chapter 7), Problem decomposition (Chapter 8), Ensemble learning (Chapter 9), Deep learning (Chapter 10), Application (Chapter 11), and Challenges (Chapter 12).The book can be used as a textbook for college, undergraduate, graduate and PhD students majored in computer science, automation, electronic engineering, communication, ect. It can also be used as
Genetic algorithms are playing an increasingly important role in studies of complex adaptive systems, ranging from adaptive agents in economic theory to the use of machine learning techniques in the d
A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory
The expression 'Neural Networks' refers traditionally to a class of mathematical algorithms that obtain their proper performance while they 'learn' from examples or from experience. As a consequence,
A more intuitive approach to the mathematical foundations of computer scienceDiscrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and gra
Quantum physics allows entirely new forms of computation and cryptography, which could perform tasks currently impossible on classical devices, leading to an explosion of new algorithms, communications protocols and suggestions for physical implementations of all these ideas. As a result, quantum information has made the transition from an exotic research topic to part of mainstream undergraduate courses in physics. Based on years of teaching experience, this textbook builds from simple fundamental concepts to cover the essentials of the field. Aimed at physics undergraduate students with a basic background in quantum mechanics, it guides readers through theory and experiment, introducing all the central concepts without getting caught up in details. Worked examples and exercises make this useful as a self-study text for those who want a brief introduction before starting on more advanced books. Solutions are available online at www.cambridge.org/9781107014466.
Offering a new perspective, this textbook demystifies the operation of electric machines by providing an integrated understanding of electromagnetic fields, electric circuits, numerical analysis, and computer programming. It presents fundamental concepts in a rigorous manner, emphasising underlying physical modelling assumptions and limitations, and provides detailed explanations of how to implement the finite element method to explore these concepts using Python. It includes explanations of the conversion of concepts into algorithms, and algorithms into code, and examples building in complexity, from simple linear-motion electromagnets to rotating machines. Over 100 theoretical and computational end-of-chapter exercises test understanding, with solutions for instructors and downloadable Python code available online. Ideal for graduates and senior undergraduates studying electric machines, electric machine design and control, and power electronic converters and power systems engineerin
Boundaries and Hulls of Euclidean Graphs: From Theory to Practice presents concepts and algorithms for finding convex, concave and polygon hulls of Euclidean graphs. It also includes some implementati
This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide
