Publisher's Synopsis
The maturing of the field of data mining has brought about an increased level of mathematical sophistication. Such disciplines like topology, combinatorics, partially ordered sets and their associated algebraic structures (lattices and Boolean algebras), and metric spaces are increasingly applied in data mining research. This book presents these mathematical foundations of data mining integrated with applications to provide the reader with a comprehensive reference.
Mathematics is presented in a thorough and rigorous manner offering a detailed explanation of each topic, with applications to data mining such as frequent item sets, clustering, decision trees also being discussed. More than 400 exercises are included and they form an integral part of the material. Some of the exercises are in reality supplemental material and their solutions are included. The reader is assumed to have a knowledge of elementary analysis.
Features and topics:
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
This wide-ranging, thoroughly detailed volume is self-contained and intended for researchers and graduate students, and will prove an invaluable reference tool.
