- Full Description
This book integrates the mathematics of data mining with its applications, offering the reader a reference to the mathematical tools required for data mining. Dedicated to the study of set-theoretical foundations of data mining, this book is focused on set theory and several closely related areas: partially ordered sets and lattice theory, metric spaces and combinatorics. The book is structured into 4 parts and presents a comprehensive discussion of the subject. Features and topics include: - Study of functions and relations, - Applications are provided throughout, - Presents graphs and hypergraphs, - Covers partially ordered sets, lattices and Boolean algebras, - Finite partially ordered sets, - Focuses on metric spaces, - Includes combinatorics, - Discusses the theory of the Vapnik-Chervonenkis dimension of collections of sets. Intended as a reference for the working data miner and researchers, a good knowledge of calculus is required to make the best use of this book, which will prove a useful reference.
- Table of Contents
Table of Contents
- Set Theory.
- Sets, Relations, Functions.
- Graphs and Hypergraphs.
- Partial Orders.
- Partially Ordered Sets.
- Lattices and Boolean Algebras.
- Topologies and Measures.
- Frequent Item Sets and Association Rules.
- Applications to Databases and Data Mining.
- Rough Sets.
- Metric Spaces.
- Dissimilarities, Metrics and Ultrametrics.
- Topologies and Measures on Metric Spaces.
- Dimensions of Metric Spaces.
- Combinatorics and the Vapnik
- Chervonenkis Dimension.
- A: Asymptotics.
- B: Convex Sets and Functions.
- C: A Characterization of a Function.
- Topic Index.
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