Extending the rand, adjusted rand and jaccard indices to fuzzy partitions

Brouwer, Roelof K.

doi:10.1007/s10844-008-0054-7

Cited by 58 publications

(65 citation statements)

References 19 publications

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“…When putting elements independently of each other into clusters, however, this is a possible scenario. And indeed, this scenario contributes to the fuzzy Rand index according to (4) and (6).…”

Section: Campello and Frigui Et Almentioning

confidence: 87%

“…We start with the proposals of Campello [7] and Frigui et al [8], which are intimately connected in the sense that the latter can be seen as a special case of the former. Subsequently, an alternative extension of the Rand index is discussed, namely the one proposed by Brouwer [6], which is based on the idea of a "measure of bonding" between pairs of objects. While this approach is still quite similar to Campello and Frigui et al, the measure put forward by Anderson et al [2] proceeds from a different idea and takes the so-called contingency matrix of two fuzzy partitions as a point of departure.…”

Section: Generalizations Of the Rand Indexmentioning

confidence: 99%

“…An alternative extension of the Rand index was recently proposed by Brouwer [6]. His "measure of bonding" between pairs of objects arguably improves upon the comparison of objects as proposed by Frigui et al (and Campello).…”

Section: Brouwermentioning

confidence: 99%

“…It was already observed by Brouwer in [6] that the quantities a, b, c, d can directly be derived from C. For example, what is the number a = |C1| of tuples (x, x ) of objects that are both paired in P and in Q? If (x, x ) ∈ C1, then there are clusters Pi and Qj such that x and x are both in Pi and both in Qj, and hence both in Pi ∩ Qj.…”

Section: Anderson Et Almentioning

confidence: 99%

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Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Hüllermeier

Rifqi

Henzgen

et al. 2012

IEEE Trans. Fuzzy Syst.

104

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In this paper, we introduce a fuzzy extension of a class of measures for comparing clustering structures, namely measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast to previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure.

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Section: Campello and Frigui Et Almentioning

confidence: 87%

Section: Generalizations Of the Rand Indexmentioning

confidence: 99%

Section: Brouwermentioning

confidence: 99%

Section: Anderson Et Almentioning

confidence: 99%

See 2 more Smart Citations

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Hüllermeier

Rifqi

Henzgen

et al. 2012

IEEE Trans. Fuzzy Syst.

104

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“…Esse é o caso do popular índice ARI projetado para APEs. Apenas as medidas 13AGRI e 09BARI (Brouwer, 2009) apresentaram tal avaliação para todos os cená-rios considerados, o que inclui o contexto dos APEs; entretanto, 09BARI não atingiu o máximo 1 para o número correto de grupos na maioria dos cenários do primeiro experimento. As outras medidas exibiram preferência por certas soluções, fenômeno atribuível unicamente aos seus mecanismos de avaliação.…”

Section: Consideraçõesunclassified

Algoritmos e técnicas de validação em agrupamento de dados multi-representados, agrupamento possibilístico e bi-agrupamento

Horta¹

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Fuzzy Generalization and Comparisons for the Rand Index

Yang

Yeh

2017

Int. J. Intell. Syst.

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To generalize the Rand index (RI) from crisp partitions to fuzzy partitions, we first propose a graph method in which color edges in the graph for crisp partitions are used to determine the relation matrix between objects such that the matrix trace can be employed to calculate the RI. This approach is then introduced into fuzzy partitions to generalize the RI to the fuzzy RI (FRI). Compared with previous fuzzy generalizations, the most unique aspect of our method has the following important characteristics that for any two partition matrices M(1) and M(2), the result with M(1)=M(2) is the necessary and sufficient condition for the result that the FRI is equal to 1. This important characteristic renders our fuzzy generalization of the RI is not only able to determine the similarities between fuzzy partitions and crisp reference partitions, but also to identify the similarity between fuzzy partitions and fuzzy reference partitions. The method can even be used to explore and compare the similarities between various data sets and the same fuzzy reference partition. Finally, we use synthetic data and real data to give more demonstrations, and further perform comparisons of our method with those existing fuzzy extensions of the RI.

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Extending the rand, adjusted rand and jaccard indices to fuzzy partitions

Cited by 58 publications

References 19 publications

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Algoritmos e técnicas de validação em agrupamento de dados multi-representados, agrupamento possibilístico e bi-agrupamento

Fuzzy Generalization and Comparisons for the Rand Index

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