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Author: Dan A. Simovici
Publisher: Springer Science & Business Media
ISBN: 1447164075
Category : Computers
Languages : en
Pages : 834
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Book Description
Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the first edition. We strived to make the book self-contained and only a general knowledge of mathematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.
Author: Dan A. Simovici
Publisher: Springer Science & Business Media
ISBN: 1447164075
Category : Computers
Languages : en
Pages : 834
Get Book
Book Description
Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the first edition. We strived to make the book self-contained and only a general knowledge of mathematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.
Author: Dan A. Simovici
Publisher: Springer Science & Business Media
ISBN: 1848002017
Category : Computers
Languages : en
Pages : 615
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Book Description
This volume was born from the experience of the authors as researchers and educators,whichsuggeststhatmanystudentsofdataminingarehandicapped in their research by the lack of a formal, systematic education in its mat- matics. The data mining literature contains many excellent titles that address the needs of users with a variety of interests ranging from decision making to p- tern investigation in biological data. However, these books do not deal with the mathematical tools that are currently needed by data mining researchers and doctoral students. We felt it timely to produce a book that integrates the mathematics of data mining with its applications. We emphasize that this book is about mathematical tools for data mining and not about data mining itself; despite this, a substantial amount of applications of mathematical c- cepts in data mining are presented. The book is intended as a reference for the working data miner. In our opinion, three areas of mathematics are vital for data mining: set theory,includingpartially orderedsetsandcombinatorics;linear algebra,with its many applications in principal component analysis and neural networks; and probability theory, which plays a foundational role in statistics, machine learning and data mining. Thisvolumeisdedicatedtothestudyofset-theoreticalfoundationsofdata mining. Two further volumes are contemplated that will cover linear algebra and probability theory. The ?rst part of this book, dedicated to set theory, begins with a study of functionsandrelations.Applicationsofthesefundamentalconceptstosuch- sues as equivalences and partitions are discussed. Also, we prepare the ground for the following volumes by discussing indicator functions, ?elds and?-?elds, and other concepts.
Author:
Publisher:
ISBN: 9814476234
Category :
Languages : en
Pages :
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Book Description
Author: Jeff M. Phillips
Publisher: Springer Nature
ISBN: 3030623416
Category : Mathematics
Languages : en
Pages : 299
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Book Description
This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.
Author: Dan A Simovici
Publisher: World Scientific
ISBN: 981127035X
Category : Computers
Languages : en
Pages : 1002
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Book Description
This updated compendium provides the linear algebra background necessary to understand and develop linear algebra applications in data mining and machine learning.Basic knowledge and advanced new topics (spectral theory, singular values, decomposition techniques for matrices, tensors and multidimensional arrays) are presented together with several applications of linear algebra (k-means clustering, biplots, least square approximations, dimensionality reduction techniques, tensors and multidimensional arrays).The useful reference text includes more than 600 exercises and supplements, many with completed solutions and MATLAB applications.The volume benefits professionals, academics, researchers and graduate students in the fields of pattern recognition/image analysis, AI, machine learning and databases.
Author: Paul E. Green
Publisher: Academic Press
ISBN: 1483214044
Category : Mathematics
Languages : en
Pages : 391
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Book Description
Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.
Author: Simovici Dan A
Publisher: World Scientific
ISBN: 9813229705
Category : Computers
Languages : en
Pages : 984
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Book Description
This compendium provides a self-contained introduction to mathematical analysis in the field of machine learning and data mining. The mathematical analysis component of the typical mathematical curriculum for computer science students omits these very important ideas and techniques which are indispensable for approaching specialized area of machine learning centered around optimization such as support vector machines, neural networks, various types of regression, feature selection, and clustering. The book is of special interest to researchers and graduate students who will benefit from these application areas discussed in the book.
Author: Felici, Giovanni
Publisher: IGI Global
ISBN: 1599045303
Category : Computers
Languages : en
Pages : 394
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Book Description
"This book focuses on the mathematical models and methods that support most data mining applications and solution techniques, covering such topics as association rules; Bayesian methods; data visualization; kernel methods; neural networks; text, speech, and image recognition; an invaluable resource for scholars and practitioners in the fields of biomedicine, engineering, finance, manufacturing, marketing, performance measurement, and telecommunications"--Provided by publisher.
Author: Paolo Giudici
Publisher: John Wiley & Sons
ISBN: 0470871393
Category : Computers
Languages : en
Pages : 379
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Book Description
Data mining can be defined as the process of selection, explorationand modelling of large databases, in order to discover models andpatterns. The increasing availability of data in the currentinformation society has led to the need for valid tools for itsmodelling and analysis. Data mining and applied statistical methodsare the appropriate tools to extract such knowledge from data.Applications occur in many different fields, including statistics,computer science, machine learning, economics, marketing andfinance. This book is the first to describe applied data mining methodsin a consistent statistical framework, and then show how they canbe applied in practice. All the methods described are eithercomputational, or of a statistical modelling nature. Complexprobabilistic models and mathematical tools are not used, so thebook is accessible to a wide audience of students and industryprofessionals. The second half of the book consists of nine casestudies, taken from the author's own work in industry, thatdemonstrate how the methods described can be applied to realproblems. Provides a solid introduction to applied data mining methods ina consistent statistical framework Includes coverage of classical, multivariate and Bayesianstatistical methodology Includes many recent developments such as web mining,sequential Bayesian analysis and memory based reasoning Each statistical method described is illustrated with real lifeapplications Features a number of detailed case studies based on appliedprojects within industry Incorporates discussion on software used in data mining, withparticular emphasis on SAS Supported by a website featuring data sets, software andadditional material Includes an extensive bibliography and pointers to furtherreading within the text Author has many years experience teaching introductory andmultivariate statistics and data mining, and working on appliedprojects within industry A valuable resource for advanced undergraduate and graduatestudents of applied statistics, data mining, computer science andeconomics, as well as for professionals working in industry onprojects involving large volumes of data - such as in marketing orfinancial risk management.
Author: Panos M. Pardalos
Publisher: American Mathematical Soc.
ISBN: 9780821870402
Category : Computers
Languages : en
Pages : 252
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Book Description
Data mining aims at finding interesting, useful or profitable information in very large databases. The enormous increase in the size of available scientific and commercial databases (data avalanche) as well as the continuing and exponential growth in performance of present day computers make data mining a very active field. In many cases, the burgeoning volume of data sets has grown so large that it threatens to overwhelm rather than enlighten scientists. Therefore, traditional methods are revised and streamlined, complemented by many new methods to address challenging new problems. Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion or a measure of discrimination) as well as the constraints imposed on the solution (e.g., find a partition, a covering or a hierarchy in clustering). It also provides powerful mathematical tools to build highly performing exact or approximate algorithms. This book is based on lectures presented at the workshop on "Data Mining and Mathematical Programming" (October 10-13, 2006, Montreal) and will be a valuable scientific source of information to faculty, students, and researchers in optimization, data analysis and data mining, as well as people working in computer science, engineering and applied mathematics.
