Defining subjects distance in hierarchical cluster analysis by copula approach

Bonanomi, Andrea; Ruscone, Marta Nai; Osmetti, Silvia Angela

doi:10.1007/s11135-016-0444-9

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…In this section, we assess the proposed model with hierarchical cluster analysis using simulated data. We compare the results obtained with our distance measure based on a mixture of copulae with those based on classical Spearman's correlation and Spearman's grade correlation of Clayton copula . In Table we consider 10 rankings representing the judgments of 10 consumers on six aspects of a product, attributing “1” to the most important aspect and “6” to the least important one.…”

Section: Examplementioning

confidence: 99%

“…Plots of a mixture copula of Gumbel ( 1 = 1.5) and Clayton( 2 = 10) with = 0.5 on the left side and = 0.2 on the right side correlation and Spearman's grade correlation of Clayton copula [3]. In Table 4 we consider 10 rankings representing the judgments of 10 consumers on six aspects of a product, attributing "1" to the most important aspect and "6" to the least important one.…”

Section: Examplementioning

confidence: 99%

“…In this context, since the most important dependence measures can be expressed by copula functions, ref. propose a distance measure for ranking data based on copula functions with (lower) tail dependence for emphasizing the agreement of top ranks when they are considered more important than lower ranks.…”

Section: Introductionmentioning

confidence: 99%

“…In this way, mixture of copulae is a generalization of the previous approaches presented in ref. , where there was the choice of only one family of copulae, in order to emphasize only a particular dependence structure.…”

Section: Introductionmentioning

confidence: 99%

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Dissimilarity measure for ranking data via mixture of copulae*

Bonanomi

Ruscone

Osmetti

2019

Statistical Analysis

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We define a new distance measure for ranking data using a mixture of copula functions. Our distance measure evaluates the dissimilarity of subjects' ranking preferences to segment them via hierarchical cluster analysis. The proposed distance measure builds upon Spearman grade correlation coefficient on a copula transformation of rank denoting the level of importance assigned by subjects on the classification of k objects. These mixtures of copulae enable flexible modeling of the different types of dependence structures found in data and the consideration of various circumstances in the classification process. For example, by using mixtures of copulae with lower and upper tail dependence, we can emphasize the agreement on extreme ranks when they are considered important.

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Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dissimilarity measure for ranking data via mixture of copulae*

Bonanomi

Ruscone

Osmetti

2019

Statistical Analysis

Self Cite

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A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data

D’Urso

Vitale

2022

J Classif

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We propose two robust fuzzy clustering techniques in the context of preference rankings to group judges into homogeneous clusters even in the case of contamination due to outliers or, more generally, noisy data. The two fuzzy C-Medoids clustering methods, based on the same suitable exponential transformation of the Kemeny distance, belong to two different approaches and differ in the way they introduce the fuzziness in the membership matrix, the one based on the “m” exponent and the other on the Shannon entropy. As far as the Kemeny distance is concerned, it is equivalent to the Kendall distance in the case of complete rankings but differs from the latter in the way of handling tied rankings. Simulations prove that our methods are able to recover the natural structure of the groups neutralizing the effect of possible noises and outliers. Two applications to real datasets are also provided.

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