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974 tulosta hakusanalla "Vector"

Learning to Classify Text Using Support Vector Machines

Learning to Classify Text Using Support Vector Machines

Thorsten Joachims

Springer-Verlag New York Inc.
2012
nidottu
Based on ideas from Support Vector Machines (SVMs), Learning To Classify Text Using Support Vector Machines presents a new approach to generating text classifiers from examples. The approach combines high performance and efficiency with theoretical understanding and improved robustness. In particular, it is highly effective without greedy heuristic components. The SVM approach is computationally efficient in training and classification, and it comes with a learning theory that can guide real-world applications. Learning To Classify Text Using Support Vector Machines gives a complete and detailed description of the SVM approach to learning text classifiers, including training algorithms, transductive text classification, efficient performance estimation, and a statistical learning model of text classification. In addition, it includes an overview of the field of text classification, making it self-contained even for newcomers to the field. This book gives a concise introduction to SVMs for pattern recognition, and it includes a detailed description of how to formulate text-classification tasks for machine learning.
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Quadratic Forms in Infinite Dimensional Vector Spaces

Quadratic Forms in Infinite Dimensional Vector Spaces

Herbert Gross

Springer-Verlag New York Inc.
2013
nidottu
For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du­ ring this period, to wit, the results on denumerably infinite spaces (" ~O- forms") . Certain among the resul ts included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I in­ clude results contained in the Ph.D.theses by my students w. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ -dimensional 0 spaces ideally serves the purpose. First, these spaces show a large nurober of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro­ cedure by induction in the finite dimensional Situation. Third, the student acquires a good feeling for the linear algebra in infinite di­ mensions because it is impossible to camouflage problems by topological expedients (in dimension ~O it is easy to see, in a given case, wheth­ er topological language is appropriate or not) .
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Grassmann Algebra Volume 1: Foundations: Exploring extended vector algebra with Mathematica

Grassmann Algebra Volume 1: Foundations: Exploring extended vector algebra with Mathematica

John Browne

Createspace Independent Publishing Platform
2012
nidottu
Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, ... multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollst ndig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grass-mann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.
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Linear Algebra over Division Ring: Vector Space

Linear Algebra over Division Ring: Vector Space

Aleks Kleyn

Createspace Independent Publishing Platform
2014
nidottu
In this book I treat linear maps of vector space over division ring.The set of linear maps of left vector space over division ring D is right vector space over division ring D. The concept of twin representations follows from the joint consideration of vector space V and vector space of linear transformations of the vector space V.Considering of twin representations of division ring in Abelian group leads to the concept of D-vector space and their linear map. Based on polylinear map I considered definition of tensor product of rings and tensor product of D-vector spaces.
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Void Rivals Volume 3: The Key to Vector Theta

Void Rivals Volume 3: The Key to Vector Theta

Robert Kirkman

Image Comics
2025
nidottu
The worlds of G.I. JOE and TRANSFORMERS collide with the red hot VOID RIVALS in this new volume from Robert Kirkman (Invincible, The Walking Dead) and Lorenzo De Felici (Kroma, Oblivion Song). THE ENERGON UNIVERSE IS HOTTER THAN EVER Hot Rod and Pythona make their way to the Sacred Ring Will their arrival bring hope or spell certain doom for the Void Rivals? Meanwhile, Darak's loyalty is put to the test on Agorria. Will he be able to prove his worth to his father -- or will another unexpected arrival incite war on his homeworld? Collects issues #13-18. The game-changing team of Robert Kirkman (The Walking Dead, Invincible) and Lorenzo De Felici (Kroma, Oblivion Song) continue their critically acclaimed series exploring the most unexpected corners of the Energon Universe.
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Invariant & Quasiinvariant Measures in Infinite-Dimensional Topological Vector Spaces

Invariant & Quasiinvariant Measures in Infinite-Dimensional Topological Vector Spaces

Gogi Pantsulaia

Nova Science Publishers Inc
2007
sidottu
This monograph deals with certain aspects of the general theory of systems. The author develops the ergodic theory, which is the theory of quaslinvariant and invariant measures in such infinite-dimensional vector spaces which appear as models of various (physical, economic, genetic, linguistic, social, etc.) processes. The methods of ergodic theory are successful as applied to study properties of such systems. A foundation for ergodic theory was stimulated by the necessity of a consideration of statistic mechanic problems and was directly connected with the works of G. Birkhoff, Kryloff and Bogoliuboff, E. Hoph and other famous mathematicians.
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The Less Is More Linear Algebra of Vector Spaces and Matrices

The Less Is More Linear Algebra of Vector Spaces and Matrices

Daniela Calvetti; Erkki Somersalo

SOCIETY FOR INDUSTRIAL APPLIED MATHEMATICS,U.S.
2023
nidottu
Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)—arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.
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Modelo Black-Litterman con Support Vector Regression: una alternativa para los fondos de pensiones obligatorios colombianos

Modelo Black-Litterman con Support Vector Regression: una alternativa para los fondos de pensiones obligatorios colombianos

Julián Andrés Buriticá Mejía

Amazon Digital Services LLC - Kdp Print Us
2021
nidottu
El modelo pensional colombiano se caracteriza por ser intergeneracional, raz n por la cual se ha visto afectado por tres grandes problemas estructurales: inequidad, baja cobertura e insostenibilidad financiera. Frente a este panorama, el Estado ha reaccionado con medidas de tipo normativo que han aliviado algunos de estos problemas; sin embargo, estas regulaciones prudenciales han impactado la finalidad inherente a un fondo de inversi n, es decir, la generaci n de riqueza para garantizar el consumo intertemporal de la poblaci n colombiana en edad de retiro. En consecuencia, los fondos de pensiones en Colombia requieren que, bajo el marco de las diferentes regulaciones, se estudien nuevas alternativas de estructuraci n de sus portafolios que les permitan un eficiente manejo de los recursos de retiro para su poblaci n. En este sentido, se cre una frontera y un portafolio eficientes mediante la aplicaci n de Support Vector Machine sobre el modelo Black-Litterman para los fondos de pensiones obligatorios colombianos, con el fin de comprobar la utilidad de los algoritmos de aprendizaje en los diferentes mbitos financieros. Los resultados muestran que es posible su aplicabilidad al modelo de estructuraci n de portafolios Black-Litterman mediante mejoras a la matriz de las distribuciones a priori, puntualmente con el uso de Support Vector Regression, que gener portafolios mejor diversificados frente al modelo media varianza de Markowitz, y que son adaptables a los fondos de pensiones obligatorios colombianos.
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An Illustrative Guide to Multivariable and Vector Calculus

An Illustrative Guide to Multivariable and Vector Calculus

Stanley J. Miklavcic

Springer Nature Switzerland AG
2020
sidottu
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
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An Illustrative Guide to Multivariable and Vector Calculus

An Illustrative Guide to Multivariable and Vector Calculus

Stanley J. Miklavcic

Springer Nature Switzerland AG
2021
nidottu
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
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A Treatise on the Magnetic Vector Potential

A Treatise on the Magnetic Vector Potential

Kristján Óttar Klausen

Springer Nature Switzerland AG
2020
sidottu
The connection between the electric and magnetic fields is fundamental to our understanding of light as electromagnetic waves. The magnetic vector potential lies at the heart of this relation. The idea emerged in the early days of research in electromagnetism but was dismissed for more than half a century until the formulation of quantum electrodynamics. The magnetic vector potential is a pivotal concept with ties to many aspects of physics and mathematics. This book unravels the nature of the magnetic vector potential, highlights its connection to quantum mechanics and superconductivity, and explores the analogy with hydrodynamics.
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Optimal Control of Dynamic Systems Driven by Vector Measures

Optimal Control of Dynamic Systems Driven by Vector Measures

N. U. Ahmed; Shian Wang

Springer Nature Switzerland AG
2021
sidottu
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions foroptimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
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Optimal Control of Dynamic Systems Driven by Vector Measures

Optimal Control of Dynamic Systems Driven by Vector Measures

N. U. Ahmed; Shian Wang

Springer Nature Switzerland AG
2022
nidottu
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions foroptimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
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Narrow Operators on Function Spaces and Vector Lattices

Narrow Operators on Function Spaces and Vector Lattices

Mikhail Popov; Beata Randrianantoanina

De Gruyter
2012
sidottu
Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.
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Advances in Self-Organizing Maps and Learning Vector Quantization

Advances in Self-Organizing Maps and Learning Vector Quantization

Springer International Publishing AG
2014
nidottu
The book collects the scientific contributions presented at the 10th Workshop on Self-Organizing Maps (WSOM 2014) held at the University of Applied Sciences Mittweida, Mittweida (Germany, Saxony), on July 2–4, 2014. Starting with the first WSOM-workshop 1997 in Helsinki this workshop focuses on newest results in the field of supervised and unsupervised vector quantization like self-organizing maps for data mining and data classification.This 10th WSOM brought together more than 50 researchers, experts and practitioners in the beautiful small town Mittweida in Saxony (Germany) nearby the mountains Erzgebirge to discuss new developments in the field of unsupervised self-organizing vector quantization systems and learning vector quantization approaches for classification. The book contains the accepted papers of the workshop after a careful review process as well as summaries of the invited talks. Among these book chapters there are excellent examples of the use of self-organizing maps in agriculture, computer science, data visualization, health systems, economics, engineering, social sciences, text and image analysis and time series analysis. Other chapters present the latest theoretical work on self-organizing maps as well as learning vector quantization methods, such as relating those methods to classical statistical decision methods.All the contribution demonstrate that vector quantization methods cover a large range of application areas including data visualization of high-dimensional complex data, advanced decision making and classification or data clustering and data compression.
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Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Eric Ouellette

Springer International Publishing AG
2015
sidottu
This Thesis describes the first measurement of, and constraints on, Higgs boson production in the vector boson fusion mode, where the Higgs decays to b quarks (the most common decay channel), at the LHC. The vector boson fusion mode, in which the Higgs is produced simultaneously with a pair of quark jets, provides an unparalleled opportunity to study the detailed properties of the Higgs, including the possibility of parity and CP violation, as well as its couplings and mass. It thus opens up this new field of study for precision investigation as the LHC increases in energy and intensity, leading the way to this new and exciting arena of precision Higgs research.
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Advances in Self-Organizing Maps and Learning Vector Quantization

Advances in Self-Organizing Maps and Learning Vector Quantization

Springer International Publishing AG
2016
nidottu
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.
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