Generalized external indexes for comparing data partitions with overlapping categories

R. J.G.B. Campello*


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There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided.

TidsskriftPattern Recognition Letters
Udgave nummer9
Sider (fra-til)966-975
StatusUdgivet - 1. jul. 2010
Udgivet eksterntJa

Bibliografisk note

Funding Information:
This work was supported by the Brazilian National Research Council (CNPq) and also by the Research Foundation of the State of São Paulo (Fapesp), under Grants #06/50231-5 and #301063/2007-9 .


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