Mathematical Analysis for Machine Learning and Data Mining

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.

Contents:

• Set-Theoretical and Algebraic Preliminaries:

  • Preliminaries
  • Linear Spaces
  • Algebra of Convex Sets

• Topology:

  • Topology
  • Metric Space Topologies
  • Topological Linear Spaces

• Measure and Integration:

  • Measurable Spaces and Measures
  • Integration

• Functional Analysis and Convexity:

  • Banach Spaces
  • Differentiability of Functions Defined on Normed Spaces
  • Hilbert Spaces

• Applications:

  • Optimization
  • Iterative Algorithms
  • Neural Networks
  • Regression
  • Support Vector Machines

Readership: Researchers, academics, professionals and graduate students in artificial intelligence, and mathematical modeling.
0