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Vectorization
Enables readers to develop foundational and advanced vectorization skills for scalable data science and machine learning and address real-world problems Offering insights across various domains such as computer vision and natural language processing, Vectorization covers the fundamental topics of vectorization including array and tensor operations, data wrangling, and batch processing. This book illustrates how the principles discussed lead to successful outcomes in machine learning projects, serving as concrete examples for the theories explained, with each chapter including practical case studies and code implementations using NumPy, TensorFlow, and PyTorch. Each chapter has one or two types of contents: either an introduction/comparison of the specific operations in the numerical libraries (illustrated as tables) and/or case study examples that apply the concepts introduced to solve a practical problem (as code blocks and figures). Readers can approach the knowledge presented by reading the text description, running the code blocks, or examining the figures. Written by the developer of the first recommendation system on the Peacock streaming platform, Vectorization explores sample topics including: Basic tensor operations and the art of tensor indexing, elucidating how to access individual or subsets of tensor elementsVectorization in tensor multiplications and common linear algebraic routines, which form the backbone of many machine learning algorithmsMasking and padding, concepts which come into play when handling data of non-uniform sizes, and string processing techniques for natural language processing (NLP)Sparse matrices and their data structures and integral operations, and ragged or jagged tensors and the nuances of processing them From the essentials of vectorization to the subtleties of advanced data structures, Vectorization is an ideal one-stop resource for both beginners and experienced practitioners, including researchers, data scientists, statisticians, and other professionals in industry, who seek academic success and career advancement.
R 4,559.00
Vectorization of Computer Programs with Applications to Computational Fluid Dynamics
The scope of the present book is to offer the most efficient tools for the vectorization of serial computer programs. Here, by vectorization we understand the adaptation of computer programs to the special architecture of modern available vector computers to exploit fully their potential, which will often result in remarkable performance improvements. The book is written primarily for users working in the various fields of computational physics, for scientists as well as for programmers running their jobs on a vector computer. The text may, however, also be of value to those who are interested in numerical algorithms. Although the examples discussed in chapter 9 have been taken from Computational Fluid Dynamics, the numerical methods are well-known, and are applied in many fields of Computational Physics. The book is divided into four parts. After a short introduction which outlines the limits of conventional serial computers in contrast to the possibilities offered by the new vector machines, the second part is addressed to the discussion of some main features of existing computer architectures. We restrict ourselves to the vector computers CRAY-1S and CDC-CYBER 205, although, in the meantime, many vector and parallel computers and array processors are available such as DENELCOR's Heterogeneous Element Processor (HEP), ICL's Distributed Array Processor (DAP), SPERRY UNIVAC's Array Processing System (APS), STAR TECHNOLOGIES ST-l00, FLOATING POINT SYSTEMS' Array Processor (FPS), FUJITSU's FACOM VP-l00 and VP-200, HITACHI's Integrated Array Processor (lAP), HITACHI's S 810/10 and S 810/20 and others.
R 3,120.51
Generalized Vectorization, Cross-Products, and Matrix Calculus
This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.
R 2,226.94
Generalized Vectorization, Cross-Products, and Matrix Calculus
This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.
R 5,017.00
Vector
A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions—sparking both controversy and discovery. The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word “vector” might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough—and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn’t have such a deep understanding of our world. Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it’s not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional “spaces,” and why you’re likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone. In exploring the evolution of vectors and tensors—and introducing the fascinating people who gave them to us—Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world—and how a clever mathematical construct can dramatically change discovery’s direction.
R 639.00
Vector Analysis for Computer Graphics
This book is a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating vector algebra. Even though vector analysis is a relatively recent development in the history of mathematics, it has become a powerful and central tool in describing and solving a wide range of geometric problems. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to, among others, lines, planes, intersections, rotating vectors, and vector differentiation.
R 2,402.95
Automatic SIMD Vectorization of SSA-based Control Flow Graphs
Ralf Karrenberg presents Whole-Function Vectorization (WFV), an approach that allows a compiler to automatically create code that exploits data-parallelism using SIMD instructions. Data-parallel applications such as particle simulations, stock option price estimation or video decoding require the same computations to be performed on huge amounts of data. Without WFV, one processor core executes a single instance of a data-parallel function. WFV transforms the function to execute multiple instances at once using SIMD instructions. The author describes an advanced WFV algorithm that includes a variety of analyses and code generation techniques. He shows that this approach improves the performance of the generated code in a variety of use cases.
R 2,204.76
Vector Analysis for Computer Graphics
This book is a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating vector algebra. Even though vector analysis is a relatively recent development in the history of mathematics, it has become a powerful and central tool in describing and solving a wide range of geometric problems. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to, among others, lines, planes, intersections, rotating vectors, and vector differentiation.
R 2,508.52
Vector Calculus
Using meaningful examples, credible applications, and incisive technology, this book strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. An engaging style and clear writing make the language of mathematics accessible, understandable, and enjoyable, with a high standard for mathematical rigor.A calculus book must tell the truth.This book is carefully written in the acceptedlanguageofmathematics in a readable exposition.It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.Technique is presented, yet so are ideas. The author helps students to master basic methods and how to discover and build their own concepts in a scientific subject. There is an emphasis on using modeling and numerical calculation. Additional features include:A Quick Quiz and Problems for Practice, Further Theory and Practice and Calculator/Computer Exercises appear at the end of each section. All exercise sets are step laddered. A Look Back and A Look Forward help students put the ideas in context. Every chapter ends with a section called Genesis and Development, giving history and perspective on key topics in the evolution of calculus. Boxed Insights clear up a point or answer commonly asked question. The text has an extra-large offering of examples. Examples are illustrated with meaningful and useful graphics.The goal is to empower students, enhance their critical thinking skills, and give them the intellectual equipment to proceed successfully in whatever major or discipline they ultimately choose to study. This text is intended to be a cornerstone of that process.The pedagogical features make the subject more interesting and accessible to students than other texts, while maintaining an appropriate rigor. —Daniel Cunningham, CSU-FresnoThis text is truly well written and organized. I do like the fact the book is quite rigorous, yet full of illustrative examples. —Bob Devaney, Boston University
R 6,805.59
Vectors, Pure and Applied
Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online.
R 2,772.90
Vector Analysis
Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to the treatment of time-dependent integrals over fields - is achieved by the introduction from the outset of a method of general parametrisation of curves and surfaces.
R 2,081.78
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Vector Calculus: Formulations, Applications And Python Codes
This unique compendium deals with the differentiation and integration of vector functions. It examines critical effects and extracts important features using powerful tools of differentiation and integration. Techniques and codes for computing the divergence, curl, and gradients of a given field function, which reveal the mathematical behavior of the vector field, are discussed. Green's theorem, Stokes's theorem, and Gauss's formula, along with their novel extensions, are presented in detail with applications such as the smoothed gradient method.Written in Jupyter notebook format, the book offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.
R 3,590.00
Vector and Tensor Analysis
Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved.
R 11,172.92
Desingularization Strategies of Three-Dimensional Vector Fields
For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2"/I>i"/I>s, xi=x'i, i>s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the problem of reduction of singularities in characteristic p.Hence the book is potentially interesting both in the context of resolution of singularities and in that of vector fields and dynamical systems.
R 1,135.97
Vector and Tensor Analysis
Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved.
R 3,863.70
Introduction to Vector Analysis
The principal changes that I have made in preparing this revised edition of the book are the following. (i) Carefuily selected worked and unworked examples have been added to six of the chapters. These examples have been taken from class and degree examination papers set in this University and I am grateful to the University Court for permission to use them. (ii) Some additional matter on the geometrieaI application of veetors has been incorporated in Chapter 1. (iii) Chapters 4 and 5 have been combined into one chapter, some material has been rearranged and some further material added. (iv) The chapter on int~gral theorems, now Chapter 5, has been expanded to include an altemative proof of Gauss's theorem, a treatmeot of Green's theorem and a more extended discussioo of the classification of vector fields. (v) The only major change made in what are now Chapters 6 and 7 is the deletioo of the discussion of the DOW obsolete pot funetioo. (vi) A small part of Chapter 8 on Maxwell's equations has been rewritten to give a fuller account of the use of scalar and veetor potentials in eleetromagnetic theory, and the units emploYed have been changed to the m.k.s. system.
R 1,528.90
Vectors, Pure and Applied
Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online.
R 7,832.51
Vector Variational Inequalities and Vector Optimization
This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
R 6,979.59
Vector Analysis and Cartesian Tensors, Third edition
This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.
R 5,332.68
Recent Advances and Historical Development of Vector Optimization
In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.
R 3,203.15
Introduction to Vector Analysis
The first eight chapters of this book were originally published in 1966 as the successful Introduction to Elementary Vector Analysis. In 1970, the text was considerably expanded to include six new chapters covering additional techniques (the vector product and the triple products) and applications in pure and applied mathematics. It is that version which is reproduced here. The book provides a valuable introduction to vectors for teachers and students of mathematics, science and engineering in sixth forms, technical colleges, colleges of education and universities.
R 3,091.91
Vector Optimization
Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu tion in 1896). Typical examples of vector optimization model include maxi mization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational in equality problems, rather than optimization problems, unless further assump tions are imposed. The vector variational inequality was introduced by Gi- nessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Nemeth (1980) has been an interesting topic in the last decade. Fan Ky's minimax theorems and minimax inequalities for real-valued func tions have played a key role in optimization theory, game theory and math ematical economics. An extension was proposed to vector payoffs was intro duced by Blackwell (1955).
R 4,030.00
Vectors in Three-Dimensional Space
This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book will also appeal to mathematical physicists and to mathematically inclined engineers.
R 2,159.80
Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization
This book gathers papers presented at the 13th International Workshop on Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization (WSOM+), which was held in Barcelona, Spain, from the 26th to the 28th of June 2019. Since being founded in 1997, the conference has showcased the state of the art in unsupervised machine learning methods related to the successful and widely used self-organizing map (SOM) method, and extending its scope to clustering and data visualization. In this installment of the AISC series, the reader will find theoretical research on SOM, LVQ and related methods, as well as numerous applications to problems in fields ranging from business and engineering to the life sciences. Given the scope of its coverage, the book will be of interest to machine learning researchers and practitioners in general and, more specifically, to those looking for the latest developments in unsupervised learning and data visualization.
R 6,228.00
Vector Space Projections
A guide to the theory and application of methods ofprojections. With the rise of powerful personal computers, methods of vectorspace projections have moved rapidly from the realm of theory intowidespread use. This book reflects the growing interest in theapplication of these methods to problem solving in science andengineering. It brings together material previously scattered indisparate papers, book chapters, and articles, and offers asystematic treatment of vector space projections. Written by two leading authorities in the field, thisself-contained volume provides a tutorial on projection methods andhow to apply them in science and engineering. It details effectiveproblem-solving strategies, and explores key applications incommunication and signal processing, neural networks and patternrecognition, and optics and image processing. This book: * Reviews the fundamentals of vector space theory * Covers principles and applications of vector space projections ingeneral, and projections onto convex sets in particular * Provides real-world examples solvable on PCs and modestworkstations * Features more than 100 illustrations * Includes end-of-chapter exercises and references. This extremely useful reference for practicing engineers,scientists, and educators can also be used for graduate-level studyin science, mathematics, and engineering. Portions of the book havebeen used as material in short courses on applications of vectorspace projections.
R 6,804.00
Rotation Sequences and the Theory of Vectors and Coordinates
This book applies rotation theory to problems involving vectors and coordinates, with an approach that combines easily visualised procedures with smart mathematics. It constructs rotation theory from the ground up, building from basic geometry through to the motion and attitude equations of rockets, and the tensor analysis of relativity. The author replaces complicated pictures of superimposed axes with a simple and intuitive procedure of rotating a model aircraft, to create rotation sequences that are easily turned into mathematics. He combines the best of the 'active' and 'passive' approaches to rotation into a single coherent theory, and discusses many potential traps for newcomers. This volume will be useful to astronomers and engineers sighting planets and satellites, computer scientists creating graphics for movies, and aerospace engineers designing aircraft; also to physicists and mathematicians who study its abstract aspects.
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Vectors and Functions of Several Variables
This comprehensive textbook explores the topics of vector functions and functions of several variables. With over 500 exercises and problems, carefully chosen for their challenging, interesting, and educational value, this book is an ideal resource for undergraduate students of mathematics, statistics, computer science, engineering and the basic sciences. The material is organized into 10 chapters, each of which begins with necessary definitions, concepts and theorems to provide a solid foundation for understanding the topic. In addition, the book includes detailed solutions to all exercises and problems to help students test their understanding and reinforce their learning. Overall, this book is an excellent choice for anyone seeking a thorough introduction to calculus.
R 3,114.00
Geometrical Vectors
This text introduces an approach for mastering the concepts of vectors and vector analysis which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear co-ordinates. It separates those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, this text provides a guide for any student of vector analysis. Clear line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.
R 1,148.00
Vector Semantics
This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use. In spite of the fact that these two schools both have ‘linguistics’ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings.
R 1,832.00
Advances in Self-Organizing Maps and Learning Vector Quantization
This book contains the articles from the international conference 11th Workshop on Self-Organizing Maps 2016 (WSOM 2016), held at Rice University in Houston, Texas, 6-8 January 2016. WSOM is a biennial international conference series starting with WSOM'97 in Helsinki, Finland, under the guidance and direction of Professor Tuevo Kohonen (Emeritus Professor, Academy of Finland). WSOM brings together the state-of-the-art theory and applications in Competitive Learning Neural Networks: SOMs, LVQs and related paradigms of unsupervised and supervised vector quantization.The current proceedings present the expert body of knowledge of 93 authors from 15 countries in 31 peer reviewed contributions. It includes papers and abstracts from the WSOM 2016 invited speakers representing leading researchers in the theory and real-world applications of Self-Organizing Maps and Learning Vector Quantization: Professor Marie Cottrell (Universite Paris 1 Pantheon Sorbonne, France), Professor Pablo Estevez (University of Chile and Millennium Instituteof Astrophysics, Chile), and Professor Risto Miikkulainen (University of Texas at Austin, USA). The book comprises a diverse set of theoretical works on Self-Organizing Maps, Neural Gas, Learning Vector Quantization and related topics, and an excellent variety of applications to data visualization, clustering, classification, language processing, robotic control, planning, and to the analysis of astronomical data, brain images, clinical data, time series, and agricultural data.
R 6,228.00
R 579.00
Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization
In this collection, the reader can find recent advancements in self-organizing maps (SOMs) and learning vector quantization (LVQ), including progressive ideas on exploiting features of parallel computing. The collection is balanced in presenting novel theoretical contributions with applied results in traditional fields of SOMs, such as visualization problems and data analysis. Besides, the collection further includes less traditional deployments in trajectory clustering and recent results on exploiting quantum computation. The presented book is worth interest to data analysis and machine learning researchers and practitioners, specifically those interested in being updated with current developments in unsupervised learning, data visualization, and self-organization.
R 6,965.08
Introductory Theory of Topological Vector SPates
This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.
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Vector Optimization
Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.
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R 250.00
Variable Ordering Structures in Vector Optimization
This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
R 1,540.94
Vector Analysis
This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.
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Vector Calculus in Regional Development Analysis
Methods used for regional development analysis are employed mainly to make forecasts and comparisons. Forecasting models of various types (e.g. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular. These models were proposed by Sims in 1980. On the contrary, taxonomic methods (that are in the center of attention as far as the present publication is concerned) are most often employed to make comparisons. Linear ordering methods, including standard methods, are the most popular among ta- nomic methods. They are based on different distance and similarity measures, which leads to the fact that they do not always provide reliable information. When, for example, one construes the standard for a base year and then compares it with data for other years, it may turn out that the measure determined will have worse values than the standard for a real object (region, micro region) although this object is better from the standard. Hence, one must look for new methods employed in regional development analysis or improve hitherto existing ones in such a way so that information obtained re?ects the reality to a larger extent. The main aim of the present publication is to work out methodological basis for regional development analysis based on vector calculus together with assumptions about computer system supporting the implementation of the method suggested.
R 4,096.85
