A Review of Classification

Abstract

Summary The summarization of large quantities of multivariate data by clusters, undefined a priori, is increasingly practiced, often irrelevantly and unjustifiably. This paper attempts to survey the burgeoning bibliography, restricting itself to published, freely available, references of known provenance. A plethora of definitions of similarity and of cluster are presented. The principles, but not details of implementation, of the many empirical classification techniques currently in use are discussed, and limitations and shortcomings in their development and practice are pointed out. Methods based on well‐defined mathematical formulations of the problem are emphasized, and other ways of summarizing data are suggested as alternatives to classification. The growing tendency to regard numerical taxonomy as a satisfactory alternative to clear thinking is condemned.

Cluster analysis and mathematical programming

“…Agglomerative hierarchical clustering algorithms are among the oldest and still most used methods of cluster analysis [23,49]. They proceed from an initial partition in N single-entity clusters by successive mergings of clusters until all entities belong to the same cluster.…”

“…Results of hierarchical clustering can be represented graphically on a dendrogram [23] or an espalier [69] as shown in Figure 1. Then vertical lines correspond Diameter to entities or clusters and horizontal lines joining endpoints of vertical lines to mergings of clusters.…”

“…Partitions obtained by the coloring algorithm for minimum diameter may suffer from the dissection effect [23]: similar entities may be assigned to different clusters. To avoid both effects one may seek compromise solutions, i.e., efficient partitions for the split and diameter criteria.…”

SNP Subset Selection for Genetic Association Studies

“…Clustering algorithms divide SNPs into different clusters, where SNPs within the same cluster have a Cormack (1971) for a review). Two commonly used clustering algorithms are nearest neighbour and furthest neighbour.…”

Environmental impact assessment for hydroelectric power plants in Trentino (Italy) 1990-1997: similarity and clustering of studies, sites and projects

“…This coefficient, being a concordance measure, allows comparison between the different results obtained from the six algorithms tried. It ranges from zero to one, and increases whenever the distortion decreases in value (Cormack, 1971); usually, it has values between 0.6 and 0.95 (Sneath and Sokal, 1973). 19.…”