On comparing two sequences of numbers and its applications to clustering analysis

R. J.G.B. Campello*, E. R. Hruschka


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A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall's indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index.

TidsskriftInformation Sciences
Udgave nummer8
Sider (fra-til)1025-1039
StatusUdgivet - 29. mar. 2009
Udgivet eksterntJa

Bibliografisk note

Funding Information:
The authors thank the Brazilian National Research Council (CNPq) and the Research Foundation of the State of São Paulo (Fapesp) for their financial support. The authors also thank their undergraduate student Lucas Vendramin for having programmed the codes used in the illustrative examples.


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