Proximity Matrix Reorganization and Hierarchical Clustering (From Confirmatory and Exploratory Analysis of the Spatio and Temporal Properties of Crime Data, P 104-123, 1981, by Reginald G Golledge and Lawrence J Hubert - See NCJ-78709)

• NCJ Number: 78713
• Author(s): L J Hubert; R G Golledge; G D Richardson
• Date Published: 1981
• Length: 20 pages
• Grant Number(s): 79-NI-AX-0057; SOC-77-28227
• Sponsoring Agency: National Science Foundation; National Institute of Justice (NIJ); US Dept of Justice NIJ Pub
• Corporate Author: University of California, Santa Barbara
• Publication Format: Document
• Publication Type: Statistics
• Language: English
• Country: United States of America
• Note: Available on microfiche from NCJRS as NCJ-78709.

Annotation

Proximity matrix reorganization and hierarchical clustering are discussed as aspects of confirmatory and exploratory analysis of the spatio-temporal properties of crime data.

Abstract

Connections between hierarchical clustering and the seriation of objects along a continuum that depend on the patterning of entries in a proximity matrix are indicated. Based on the similarity between the central notion of an ultrametric in hierarchical clustering and what is called an anti-Robinson property in seriation, it is suggested that both data analysis procedures are compatible. Preliminary seriation of a proximity matrix may help verify the adequacy of the results obtained from a hierarchical clustering or suggest better alternatives. A numerical example using criminal justice data is included. The superiority of either seriation or a a particular method of hierarchical clustering is not clear. The presentation aims to show how they are complementary in seeking to justify a particular analysis. Seriation procedures based on clustering have also been suggested in the literature (see Schuler and Ulrich, 1972). Tabular data, mathematical equations, and 22 references are provided. (Author summary modified)