Generalized external indexes for comparing data partitions with overlapping categories

Campello, R.J.G.B. (2010) Generalized external indexes for comparing data partitions with overlapping categories. Pattern Recognition Letters, 31 (9). pp. 966-975.

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Abstract

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.

Item ID: 47617
Item Type: Article (Research - C1)
ISSN: 1872-7344
Keywords: clustering, overlapping, partitions, validity, indexes
Funders: Brazilian National Research Council (CNPq), São Paulo Research Foundation (FAPESP)
Projects and Grants: FAPESP grant #06/50231-5, FAPESP grant #301063/2007-9
Date Deposited: 08 Mar 2017 07:40
FoR Codes: 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010401 Applied Statistics @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%
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