The Isolation Principle of Clustering: Structural Characteristics and Implementation
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The isolation principle rests on defining internal and external differentiation for each subset of at least two objects. Subsets with larger external than internal differentiation form isolated groups in the sense that they are internally cohesive and externally isolated. Objects that do not belong to any isolated group are termed solitary. The collection of all isolated groups and solitary objects forms a hierarchical (encaptic) structure. This ubiquitous characteristic of biological organization provides the motivation to identify universally applicable practical methods for the detection of such structure, to distinguish primary types of structure, to quantify their distinctiveness, and to simplify interpretation of structural aspects. A method implementing the isolation principle (by generating all isolated groups and solitary objects) is proven to be specified by single-linkage clustering. Basically, the absence of structure can be stated if no isolated groups exist, the condition for which is provided. Structures that allow for classifications in the sense of complete partitioning into disjoint isolated groups are characterized, and measures of distinctiveness of classification are developed. Among other primary types of structure, chaining (complete nesting) and ties (isolated groups without internal structure) are considered in more detail. Some biological examples for the interpretation of structure resulting from application of the isolation principle are outlined.
Key Words:isolaton principle internal differentiation external differentiation encapsis hierarchical structure cluster mehod single linkage classification measure of clustering structure degree of cluster isolation
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- Arabie, P. and L.J. Hubert (1996). An overview of combinatorial data analysis. In: P., L.J. Arabie, Hubert and G. DeSoete (eds). pp. 5–63.Google Scholar
- Arabie, P., L.J. Hubert and G. De Soete (eds.), (1996). Clustering and Classification. World Scientific, Singapore etc.Google Scholar
- Barthélemy, J.-P. and F. Brucker (2001). NP-hard approximation problems in overlapping clustering. Journal of Classification 18: 159–183.Google Scholar
- Gordon, A.D. (1996). Hierarchical classification. In: P. Arabie and L.J. Hubert, G. De Soete (eds.),. pp. 65–121.Google Scholar
- Jain, A.K. and R.C. Dubes (1988). Algorithms for Clustering Data. Prentice Hall.Google Scholar
- Jardine, N.J. and R. Sibson (1971). Mathematical Taxonomy. John Wiley & Sons, London etc.Google Scholar
- Kaufman, L. and P.J. Rousseeuw (1990). Finding Groups in Data. An Introduction to Cluster analysis. John Wiley & Sons, New York etc.Google Scholar
- Ludwig, J.A. and J.F. Reynolds (1988). Statistical Ecology – A Primer on Methods and Computing. John Wiley & Sons, New York, etc.Google Scholar
- Milligan, G.W. (1996). Clustering validation: results and implications for applied analysis. In: P. Arabie, L.J. Hubert and G. De Soete (eds.),. pp. 341–375.Google Scholar
- Muchnik, I.B. and I.A. Rybina (1989). Definitive conditions for isolation of classes in empiric classifications. Automatic Documentation and Mathematical Linguistics 23: 97–107.Google Scholar
- Prim, R.C. (1957). Shortest connection networks and some generalizations. Bell System Technical Journal 36: 1389–1401.Google Scholar