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A Gentle Introduction to Mathematical Cluster Analysis

# A Gentle Introduction to Mathematical Cluster Analysis,Harel Barzilai,Alexander Kheyfits,Kathy Andrews

A Gentle Introduction to Mathematical Cluster Analysis
• 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. • 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 clus- tering 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.

## References (3)

### Cluster analysis and mathematical programming(Citations: 166)

Journal: Mathematical Programming , vol. 79, no. 1-3, pp. 191-215, 1997

### Algorithms for Clustering Data(Citations: 4196)

Published in 1988.

### A Survey of Recent Advances in Hierarchical Clustering Algorithms(Citations: 158)

Journal: The Computer Journal - CJ , vol. 26, no. 4, pp. 354-359, 1983