Mathematical Analysis for Machine Learning and Data Mining

✍ Scribed by Dan A Simovici

• Publisher: World Scientific Publishing Co Pte Ltd
• Year: 2018
• Tongue: English
• Leaves: 968
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
Title Page
Copyright
Epigraph
Preface
Contents
Part I: Set-Theoretical and Algebraic
Preliminaries
1 Preliminaries
2 Linear Spaces
3 Algebra of Convex Sets
Part II: Topology
4 Topology
5 Metric Space Topologies
6 Topological Linear Spaces
Part III: Measure and Integration
7 Measurable Spaces and Measures
8 Integration
Part IV: Functional Analysis and Convexity
9 Banach Spaces
10 Differentiability of Functions Defined
on Normed Spaces
11 Hilbert Spaces
12 Convex Functions
Part V: Applications
13 Optimization
14 Iterative Algorithms
15 Neural Networks
16 Regression
17 Support Vector Machines
Bibliography
Index