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Partitioning Data Sets
Edited by: Ingemar J. Cox, Pierre Hansen, and Bela Julesz
A co-publication of the AMS and DIMACS.

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1995; 408 pp; hardcover
Volume: 19
ISBN-10: 0-8218-6606-0
ISBN-13: 978-0-8218-6606-1
List Price: US$109
Member Price: US$87.20
Order Code: DIMACS/19
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Partitioning data sets into disjoint groups is a problem arising in many domains. The theory of cluster analysis aims to find groups that are both homogeneous (entities in the same group that are similar) and well separated (entities in different groups that are dissimilar). There has been rapid expansion in the axiomatic foundations and the computational complexity of such problems and in the design and analysis of exact or heuristic algorithms to solve them. Applications have burgeoned in psychology, computer vision, target tracking, and other areas. This book contains papers presented at the workshop Partioning Data Sets held at DIMACS in April 1993. Some of the papers cover the main paradigms of the field of cluster analysis methods and algorithms. Other topics include partitioning problems arising from multitarget tracking and surveillance and from computer and human vision. The multiplicity of approaches, methods, problems, and algorithms make for lively and informative reading.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).


This book is directed to a multidisciplinary audience who are interested in the problems associated with partitioning data.

Table of Contents

Part 1. Cluster Analysis Methods
  • J.-P. Barthélemy and B. Leclerc -- The median procedure for partitions
  • P. Bertrand -- Structural properties of pyramidal clustering
  • W. Cai and D. W. Matula -- Partitioning by maximum adjacency search of graphs
  • E. Diday -- From data to knowledge: Probabilist objects for a symbolic data analysis
  • S. Gélinas, P. Hansen, and B. Jaumard -- A labeling algorithm for minimum sum of diameters partitioning of graphs
  • W. Goddard, E. Kubicka, G. Kubicki, and F. R. McMorris -- Agreement subtrees, metric and consensus for labeled binary trees
  • P. Hansen, B. Jaumard, and N. Mladenovic -- How to choose \(K\) entities among N
  • M. F. Janowitz and R. Wille -- On the classification of monotone-equivariant cluster methods
  • F. D. Murtagh -- Contiguity-constrained hierarchical clustering
Part 2. Target Tracking
  • A. Kumar, Y. Bar-Shalom, and E. Oron -- Image segmentation based on optimal layering for precision tracking
  • A. B. Poore -- Multidimensional assignments and multitarget tracking
Part 3. Computer Vision
  • I. J. Cox, J. H. Rehg, S. L. Hingorani, and M. L. Miller -- Grouping edges: An efficient Bayesian multiple hypothesis approach
  • D. W. Jacobs -- Finding salient convex groups
  • A. Jepson and M. J. Black -- Mixture models for optical flow computation
  • Y. Yang and A. L. Yuille -- Multilevel detection of stereo disparity surfaces
Part 4. Human Vision
  • I. Biederman -- Some problems of visual shape recognition to which the application of clustering mathematics might yield some potential benefits
  • J. Feldman -- Perceptual models of small dot clusters
  • B. Julesz -- Subjective contours in early vision and beyond
  • D. Kersten and S. Madarasmi -- The visual perception of surfaces, their properties, and relationships
  • S. W. Zucker -- Visual computations and dot cluster
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