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"Offering a fundamental basis in kernel-based learning theory, this book covers both statistical and algebraic principles. It provides over 30 major theorems for kernel-based supervised and unsupervised learning models. The first of the theorems establishes a condition, arguably necessary and sufficient, for the kernelization of learning models. In addition, several other theorems are devoted to proving mathematical equivalence between seemingly unrelated models. With over 25 closed-form and iterative algorithms, the book provides a step-by-step guide to algorithmic procedures and analysing which factors to consider in tackling a given problem, enabling readers to improve specifically designed learning algorithms, build models for new applications and develop efficient techniques suitable for green machine learning technologies. Numerous real-world examples and over 200 problems, several of which are Matlab-based simulation exercises, make this an essential resource for graduate students and professionals in computer science, electrical and biomedical engineering. Solutions to problems are provided online for instructors"-- "Provides an overview of the broad spectrum of applications and problem formulations for kernel-based unsupervised and supervised learning methods. The dimension of the original vector space, along with its Euclidean inner product, often proves to be highly inadequate for complex data analysis. In order to provide a more e
Support vector machines. --- Machine learning. --- Kernel functions. --- Functions, Kernel --- Functions of complex variables --- Geometric function theory --- Learning, Machine --- Artificial intelligence --- Machine theory --- SVMs (Algorithms) --- Algorithms --- Kernel functions --- Supervised learning (Machine learning) --- COMPUTERS / Computer Vision & Pattern Recognition. --- Support vector machines --- Machine learning
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In the context of Geographical Information Systems (GIS) the book offers a timely review of Map Projections. The first chapters are of foundational type. We introduce the mapping from a left Riemann manifold to a right one specified as conformal, equiaerial and equidistant, perspective and geodetic. In particular, the mapping from a Riemann manifold to a Euclidean manifold ("plane") and the design of various coordinate systems are reviewed . A speciality is the treatment of surfaces of Gaussian curvature zero. The largest part is devoted to the mapping the sphere and the ellipsoid-of-revolution to tangential plane, cylinder and cone (pseudo-cone) using the polar aspect, transverse as well as oblique aspect. Various Geodetic Mappings as well as the Datum Problem are reviewed. In the first extension we introduce optimal map projections by variational calculus for the sphere, respectively the ellipsoid generating harmonic maps. The second extension reviews alternative maps for structures , namely torus (pneu), hyperboloid (cooling tower), paraboloid (parabolic mirror), onion shape (church tower) as well as clothoid (Hight Speed Railways) used in Project Surveying. Third, we present the Datum Transformation described by the Conformal Group C10 (3) in a threedimensional Euclidean space , a ten parameter conformal transformation. It leaves infinitesimal angles and distance ratios equivariant. Numerical examples from classical and new map projections as well as twelve appendices document the Wonderful World of Map Projections.
Map projection --- Cartography --- Conformal mapping --- Data processing. --- Mathematics. --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Transformations (Mathematics) --- Cartography, Primitive --- Chartography --- Map-making --- Mapmaking --- Mapping (Cartography) --- Mathematical geography --- Surveying --- Maps --- Projection --- Geographical information systems. --- Physical geography. --- Geography. --- Geographical Information Systems/Cartography. --- Geophysics/Geodesy. --- Geography, general. --- Cosmography --- Earth sciences --- World history --- Geography --- Geographical information systems --- GIS (Information systems) --- Information storage and retrieval systems --- Geophysics. --- Geological physics --- Terrestrial physics --- Physics
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This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
Analytic functions. --- Cauchy transform. --- Geometric function theory. --- Function theory, Geometric --- Cauchy-Hilbert transform --- Cauchy's transform --- Transform, Cauchy --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Mathematics. --- Functions of complex variables. --- Potential theory (Mathematics). --- Calculus of variations. --- Functions of a Complex Variable. --- Potential Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Functions of complex variables --- Series, Taylor's --- Transformations (Mathematics) --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mechanics --- Complex variables --- Elliptic functions --- Functions of real variables --- Isoperimetrical problems --- Variations, Calculus of
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This book discusses the advanced kernel learning algorithms and its application on face recognition. The book focuses on the theoretical deviation, the system framework and experiments involving kernel based face recognition. This authors aim to solve the parameter selection problems endured by kernel learning algorithms, and presents kernel optimization method with the data dependent kernel. This text extends the definition of data-dependent kernel and applies it to kernel optimization. Included within are algorithms of kernel based face recognition and the feasibility of the kernel based face recognition method.
Human face recognition (Computer science) --- Kernel functions. --- Pattern recognition systems. --- Pattern classification systems --- Pattern recognition computers --- Functions, Kernel --- Face recognition, Human (Computer science) --- Facial pattern recognition (Computer science) --- Engineering. --- Image processing. --- Computational intelligence. --- Electrical engineering. --- Signal, Image and Speech Processing. --- Communications Engineering, Networks. --- Computational Intelligence. --- Image Processing and Computer Vision. --- Electric engineering --- Engineering --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Construction --- Industrial arts --- Technology --- Pattern perception --- Computer vision --- Functions of complex variables --- Geometric function theory --- Optical pattern recognition --- Telecommunication. --- Computer vision. --- Machine vision --- Vision, Computer --- Image processing --- Pattern recognition systems --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Signal processing. --- Speech processing systems. --- Optical data processing. --- Computational linguistics --- Electronic systems --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment --- Machine learning. --- Algorithms.
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