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Mathematical tools for data mining : set theory, partial orders, combinatorics (2nd ed.)
Simovici D., Djeraba C., Springer Publishing Company, Incorporated, London, UK, 2014. 831 pp. Type: Book (978-1-447164-06-7)
Date Reviewed: Sep 18 2014

The goal of this book is to present the basic mathematical theory and principles used in data mining tools and techniques. Accordingly, a variety of foundational theoretical concepts are covered, including set theory, combinatorics, linear algebra, matrix theory and properties of matrices, topology and measure theory, graph theory, and clustering algorithms. A chapter on the relevant theoretical concepts from relational databases theory is also included.

The application of mathematical concepts to data mining problems is indicated in various books and would be obvious to a reader who started with one or another data mining text describing problems, algorithms, and solution techniques, but describing such problems and solution techniques is not a focus of this book, and descriptions of problem areas and solutions are provided only in outline where they are mentioned. The reader will indeed find algorithms described in pseudocode, but these are similar to a typical textbook on the theory of computer science (CS) in their use of mathematical notation and natural language statements to describe complex operations or single steps.

The range of topics addressed is broad and consistent with the stated goal of describing the basic mathematical tools. It should be understood that this is not a comprehensive collection of foundational concepts and techniques, but is limited to mathematical foundations. Basic ideas from other domains, such as probability theory, machine learning, and databases, are not within the scope of this text. Prior exposure to undergraduate mathematics such as that usually part of an undergraduate CS or mathematics degree program is a prerequisite for complete understanding of the material. The intended audience is analyst practitioners rather than programmers. Graduate or advanced undergraduate students with prior coursework in mathematics will find this book a useful collection of the fundamental mathematical ideas; readers new to data mining but with college mathematics training should also find it a useful adjunct to more traditional data mining texts and as a refresher text.

The exposition of concepts is clear and readable. Comfort with mathematical notation is necessary, since the book makes significant use of such notation. Several exercises are included, with solutions being provided in outline.

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Reviewer:  R. M. Malyankar Review #: CR142730 (1412-1020)
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