Dan A. Simovici

This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications.

Linear Algebra Tools for Data Mining

Richard L. Tenney

Formal languages provide the theoretical underpinnings for the study of programming languages as well as the foundations for compiler design. They are important in such areas as data transmission and compression, computer networks, etc. This book combines an algebraic approach with algorithmic aspects and decidability results and explores applications both within computer science and in fields where formal languages are finding new applications such as molecular and developmental biology. It contains more than 600 graded exercises. While some are routine, many of the exercises are in reality supplementary material. Although the book has been designed as a text for graduate and upper-level undergraduate students, the comprehensive coverage of the subject makes it suitable as a reference for scientists.

Theory of Formal Languages with Applications

Relational Database Systems provides a timely introduction to the type of systems that are the current mainstay of the database management field. This book serves as a text for advanced undergraduate and graduate students, as well as an informative reference for researchers and professionals in all database aspects of computer science. It presents important querying systems including SQL and QUEL, and covers their respective theoretical foundations in relational algebra, tuple calculus, and domain calculus. The presentation of SQL adheres to the ANSI standard; however, the book discusses the most popular SQL dialects; a separate chapter covers imbedded SQL. The text also contains references to many significant relational database products, including INGRES, ORACLE, DB2, PARADOX, and SYBASE. Relational Database Systems concentrates on those issues that are most relevant to database design and application development. Exercises that constitute important extensions of the material are provided at the end of each chapter. The book assumes a knowledge of programming languages and datastructures, and some mathematical induction. Includes coverage of embedded SQL, the most important existing application development tool Presents query systems within their theoretical context Discusses supporting mathematical theory Offers a comparison of SQL dialects Provides supplemental exercises for each chapter Contains references to significant relational database products, including INGRES, ORACLE, DB2, PARADOX, and SYBASE

Relational Database Systems

Chabane Djeraba

Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the first edition. We strived to make the book self-contained and only a general knowledge of mathematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.

Set Theory, Partial Orders, Combinatorics

Mathematical Tools for Data Mining

Chaabane Djeraba

This volume was born from the experience of the authors as researchers and educators,whichsuggeststhatmanystudentsofdataminingarehandicapped in their research by the lack of a formal, systematic education in its mat- matics. The data mining literature contains many excellent titles that address the needs of users with a variety of interests ranging from decision making to p- tern investigation in biological data. However, these books do not deal with the mathematical tools that are currently needed by data mining researchers and doctoral students. We felt it timely to produce a book that integrates the mathematics of data mining with its applications. We emphasize that this book is about mathematical tools for data mining and not about data mining itself; despite this, a substantial amount of applications of mathematical c- cepts in data mining are presented. The book is intended as a reference for the working data miner. In our opinion, three areas of mathematics are vital for data mining: set theory,includingpartially orderedsetsandcombinatorics;linear algebra,with its many applications in principal component analysis and neural networks; and probability theory, which plays a foundational role in statistics, machine learning and data mining. Thisvolumeisdedicatedtothestudyofset-theoreticalfoundationsofdata mining. Two further volumes are contemplated that will cover linear algebra and probability theory. The ?rst part of this book, dedicated to set theory, begins with a study of functionsandrelations.Applicationsofthesefundamentalconceptstosuch- sues as equivalences and partitions are discussed. Also, we prepare the ground for the following volumes by discussing indicator functions, ?elds and?-?elds, and other concepts.

Dan A. Simovici

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