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\begin{center}
\vspace{.2in}
{\Large \bf DIMACS EDUCATIONAL MODULE SERIES}

\vspace{.7in}

{\Large \bf MODULE 03-7}\\
{\Large \bf A Gentle Introduction to Mathematical Cluster Analysis}\\
{\large \bf September, 2003}

\vspace{.3in}

{\bf Harel Barzilai}\\
{\bf Department of Mathematics and Computer Science}\\
{\bf Salisbury University}\\
{\bf Salisbury MD 21801}\\
{\bf phone: 410-543-6472}\\
{\bf email: hxbarzilai@salisbury.edu}\\
{\bf harel@barzilai.org}

\vspace{.15in}

{\bf Alexander Kheyfits}\\
{\bf Department of Mathematics and Computer Science}\\
{\bf Bronx Community College (CUNY)}\\
{\bf University Avenue at W. 181st Street}\\
{\bf Bronx, NY 10453}\\
{\bf phone: 718-289-5616}\\
{\bf email: alexander.kheyfits@bcc.cuny.edu}

\vspace{.15in}

{\bf Kathy Andrews}\\
{\bf Hillsdale College}\\
{\bf Department of Mathematics}\\
{\bf 33 E. College}\\
{\bf Hillsdale, MI 49242}\\
{\bf email: kjandrews42@comcast.net} 

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\begin{center}
{\large \bf Module Description Information}
\end{center}

\begin{itemize}
\item[] {\bf Title:}

A Gentle Introduction to Mathematical Cluster Analysis

\item[] {\bf Author(s):}

Harel Barzilai, Department of Mathematics and Ccomputer Science, Salisbury University

Alexander Kheyfits, Department of Mathematics and Computer Science,
Bronx Community College (CUNY)

Kathy Andrews, Department of Mathematics, Hillsdale College

\item[] {\bf Abstract:}

Mathematical Clustering or Cluster Analysis is a field which endeavors
to "classify". More precisely, given a discrete data set, this set is
classified into groupings, or clusters. The criteria for what makes a
"good" set of such clusters vary, however in general we want similar
data points to be made part of the same cluster, and data points
assigned to different clusters should have some important
features distinguishing them.

The basics notions and definitions of clustering are introduced, as
well as key algorithms used in the field, including the notion of a
"hierarchical" algorithm. The first chapter provides an overview of
the field as well as an introduction to "Agglomerative" hierarchical
algorithms; the second chapter describes "Divisive" hierarchical
algorithms; and the third chapter introduces Sequential clustering
algorithms.

A section of print References is provided for further exploration, as
well as as a section of Web References Cited (with full URLs), and
additionally an online page, "Online Resources for Further
Exploration" is available from the DIMACS page with sections on
Tutorials, Sample Applications, Researchers with Expertise,  and 
Software.

\item[] {\bf Informal Description:}

The types of algorithms surveyed in this module are listed in the
Abstract.

Prospective readers may be interested to note that the wide variety of
areas of application of this field include: business planning as well
as public, city and regional planning such as choosing the
locations for hospitals; taxonomic classification of species;
classification of chemical molecules into types; and even web pages
classified together as being of similar relevance to a search, or of
similar interest to a reader.

Students who complete this module will have been introduced to the
fundamentals of clustering through an informal and intuitive approach
which takes the reader gradually into the full formal definitions and
algorithms. They will also glimpse some of the applications of this
area, and will be provided with ample references for further study of
both applications, and the mathematical field of cluster analysis
itself.

\item[] {\bf Target Audience:}

This module is meant to be an "entry level" introduction for freshmen
and sophomore students. It can be used in Finite Mathematics, Discrete
Mathematics and Applied Mathematics courses, as well as in "Survey of
Mathematics" courses for strongly motivated liberal arts students. It
can also serve for guided self-study by mathematically inclined high
school students. The module may also be of interest in beginning
computer science courses, particularly courses with sections which
focus on algorithms

\item[] {\bf Prerequisites:}

The formal prerequisites include only high school mathematics through
algebra and functions or precalculus. Graph theory is not assumed,
and all but he most basic set-theoretic notation is defined within the
module itself.

\item[] {\bf Mathematical Field:}

Cluster analysis; Classification theory; Graph theory

\item[] {\bf Applications Areas:}

Classification theory; Biological, Chemical, and Ecological taxonomy
and classification; Data Mining; Internet analysis and search engine
algorithms.

\item[] {\bf Mathematics Subject Classification:}

Primary 91C20

Secondary 05C90, 90B80, 92B10

\item[] {\bf Contact Information:}

Harel Barzilai\\Department of Mathematics and Computer Science\\Salisbury University\\
Salisbury MD 21801\\410-543-6472\\hxbarzilai@salisbury.edu, harel@barzilai.org

Alexander Kheyfits\\Department of Mathematics and Computer Science\\
Bronx Community College (CUNY)\\University Avenue at W. 181st Street\\
Bronx, NY 10453\\718-289-5616\\alexander.kheyfits@bcc.cuny.edu

Kathy Andrews\\Hillsdale College\\Department of Mathematics\\33 E. College\\
Hillsdale, MI 49242\\301-552-6429\\keandrews@dmci.net

\item[] {\bf Other DIMACS modules related to this module:}

Module 03-1 by Alex Kheyfits.

(There may be others of which we are not yet aware)

\end{itemize}
\end{document}

