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Mathematical analysis for machine learning and data mining/ by Dan Simovici

By: Simovici, Dan [author].
Material type: TextTextPublisher: New Jersey: World Scientific, [2018]Description: xv, 968 pages, 23cm.ISBN: 9789813229686.Subject(s): Machine Learning-Mathematics | Data Mining-MathematicsDDC classification: 006.3101515
Contents:
Preface, Part I. Set-Theoretical and Algebraic Preliminaries Preliminaries Linear Spaces Algebra of Convex Sets Part II. Topology, Topology Metric Space Topologies Topological Linear Spaces Part III. Measure and Integration, Measurable Spaces and Measures Integration Part IV. Functional Analysis and Convexity, Banach Spaces Differentiability of Functions Defined on Normed Spaces Hilbert Spaces Convex Functions Part V. Applications, Optimization Iterative Algorithms Neural Networks Regression Support Vector Machines Bibliography, Index
Summary: 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.
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Includes bibliographical references and index

Preface,
Part I. Set-Theoretical and Algebraic Preliminaries
Preliminaries
Linear Spaces
Algebra of Convex Sets
Part II. Topology,
Topology
Metric Space Topologies
Topological Linear Spaces
Part III. Measure and Integration,
Measurable Spaces and Measures
Integration
Part IV. Functional Analysis and Convexity,
Banach Spaces
Differentiability of Functions Defined on Normed Spaces
Hilbert Spaces
Convex Functions
Part V. Applications,
Optimization
Iterative Algorithms
Neural Networks
Regression
Support Vector Machines
Bibliography,
Index

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.

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