UID:
almahu_9949972299802882
Format:
XII, 615 p.
,
online resource.
Edition:
1st ed. 2008.
ISBN:
9781848002012
Series Statement:
Advanced Information and Knowledge Processing,
Content:
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.
Note:
Set Theory -- Sets, Relations, and 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 -- The Vapnik-Chervonenkis Dimension.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9781848002005
Additional Edition:
Printed edition: ISBN 9781848820487
Additional Edition:
Printed edition: ISBN 9781849967518
Language:
English
DOI:
10.1007/978-1-84800-201-2
URL:
https://doi.org/10.1007/978-1-84800-201-2
