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.
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Editorial Reviews
Review
From the reviews: "The book is organized into four parts, with a total of 15 chapters. Each chapter … offers numerous exercises and references for further reading. … Overall, Simovici and Djeraba’s presentation of both the theoretical grounds and the practical aspects of the various data mining methodologies is good. … The book is intended for readers who have a data mining background … . It will help this audience to improve their knowledge of how different data mining strategies operate from a mathematical standpoint." (Aris Gkoulalas-Divanis, ACM Computing Reviews, February, 2009)
From the Back Cover
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.
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Most Helpful Customer Reviews
3.0 out of 5 stars
Good content, but too many typos to learn from,
By Jian Ye (San Leandro, ca United States) - See all my reviews
This review is from: Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics (Advanced Information and Knowledge Processing) (Paperback)
The book has very relevant material for me. But it is a shame to have so many typos. I find it very hard to learn from the book, because even some theorem statements have crucial errors. Could someone please suggest a good text book that contains: Set Theory, Partial Orders, and Combinatorics, which is similar to this one? Thanks.
1 of 2 people found the following review helpful:
5.0 out of 5 stars
Great textbook, excellent reference !!!,
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This review is from: Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics (Advanced Information and Knowledge Processing) (Hardcover)
This is a great textbook, and an excellent reference. Mathematical foundations of Data Mining are introduced in great detail. It is worth every penny. It may be the most serious book about data mining ever published.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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bibliographical comments, partition entropy, logical data analysis, differential constraints, completeness axiom, topological metric space, functional dependency schema, standard disjunctive normal form, metric hyperspace, tabular variable, equidistant tree, triangular axiom, sequential cover, hereditary collection, locally finite poset, graded poset, suppose that the statement, small inductive dimension, frequent item sets, dissimilarity space, standard transposition, edit transcript, levelwise algorithm, finite metric space, inductive dimensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Metric Spaces, Springer-Verlag London Limited, Partially Ordered Sets, The Hasse, Hierarchical Clustering, The Vapnik-Chervonenkis Dimension, Basic Notions of Graph Theory, Axiom of Choice, Ultranietric Spaces, The Cartesian, Temperature Humidity Wind, Functions Example, Special Classes of Lattices, Rough Sets, Elementary Conibinatorics, Fields of Sets, Temperature Wind, Resulting Tree, The Hausdorff-Besicovitch, Starting Tree Leaf Vertex, The Armstrong, Iterative Function System Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
bibliographical comments, partition entropy, logical data analysis, differential constraints, completeness axiom, topological metric space, functional dependency schema, standard disjunctive normal form, metric hyperspace, tabular variable, equidistant tree, triangular axiom, sequential cover, hereditary collection, locally finite poset, graded poset, suppose that the statement, small inductive dimension, frequent item sets, dissimilarity space, standard transposition, edit transcript, levelwise algorithm, finite metric space, inductive dimensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Metric Spaces, Springer-Verlag London Limited, Partially Ordered Sets, The Hasse, Hierarchical Clustering, The Vapnik-Chervonenkis Dimension, Basic Notions of Graph Theory, Axiom of Choice, Ultranietric Spaces, The Cartesian, Temperature Humidity Wind, Functions Example, Special Classes of Lattices, Rough Sets, Elementary Conibinatorics, Fields of Sets, Temperature Wind, Resulting Tree, The Hausdorff-Besicovitch, Starting Tree Leaf Vertex, The Armstrong, Iterative Function System Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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