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. TOC:Set Theory.- Sets, Relations, Functions.- Algebras.- 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.- Clustering.- Combinatorics.- Combinatorics.- Combinatorics and the Vapnik-Chervonenkis Dimension.- A: Asymptotics.- B: Convex Sets and Functions.- C: A Characterization of a Function.- References.- Topic Index.