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:PreliminariesLinear SpacesAlgebra of Convex SetsTopology:TopologyMetric Space TopologiesTopological Linear SpacesMeasure and Integration:Measurable Spaces and MeasuresIntegrationFunctional Analysis and Convexity:Banach SpacesDifferentiability of Functions Defined on Normed SpacesHilbert Spacesli>Convex FunctionsApplications:OptimizationIterative AlgorithmsNeural NetworksRegressionSupport Vector Machines
Readership: Researchers, academics, professionals and graduate students in artificial intelligence, and mathematical modeling.
Measure Theory;Banach Spaces;Hilbert Spaces;Convexity;Support Vector Machines;Neural Networks;Regression;Optimization00