Dynamic clustering of interval data using a Wasserstein-based distance

Irpino, Antonio; Verde, Rosanna

doi:10.1016/j.patrec.2008.04.008

Cited by 110 publications

(73 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, a basic belief assignment (BBA) is represented by a set of belief intervals, which can also be considered as a set of interval numbers or data. For two different BBAs, we calculate the distance between their corresponding focal element's belief intervals using the distance of interval numbers [12]. Based on the interval distance values corresponding to different focal elements, we propose an Euclidean-family distance based on sum of squares, and a Chebyshev-family distance based on the maximum selection, respectively.…”

Section: Introductionmentioning

confidence: 99%

New Distance Measures of Evidence Based on Belief Intervals

Han

Dezert²,

Yang

2014

Belief Functions: Theory and Applications

View full text Add to dashboard Cite

Abstract.A distance or dissimilarity of evidence represents the degree of dissimilarity between bodies of evidence, which has been widely used in the applications based on belief functions theory. In this paper, new distance measures are proposed based on belief intervals [Bel, P l]. For a basic belief assignment (BBA), the belief intervals of different focal elements are first calculated, respectively, which can be considered as interval numbers. Then, according to the distance of interval numbers, we can calculate the distance values between the corresponding belief intervals of the same focal elements in two given BBAs. Based on these distance values of belief intervals, new distance measures of evidence can be obtained using Euclidean and Chebyshev approaches, respectively. Some experiments and related analyses are provided to show the rationality and efficiency of the proposed measures.

show abstract

Section: Introductionmentioning

confidence: 99%

New Distance Measures of Evidence Based on Belief Intervals

Han

Dezert²,

Yang

2014

Belief Functions: Theory and Applications

View full text Add to dashboard Cite

show abstract

“…From a computational point of view, the difficulties of computing an exact value for S 2 W (Y ) is related to the possibility of computing the ρ i,j . Irpino and Verde [15], Irpino et al [14] proposed a closed form for computing the squared Wasserstein distance between two histogram-valued data and from that formation it is also possible to derive the closed form related to ρ i,j . The computation is also done in a time that is linear with respect to the number of bins of the histograms.…”

Section: Definitionmentioning

confidence: 99%

“…Another result presented in [15,14] is related to the variance decomposition in a framework of clustering analysis of histogram-valued data. [15,14], after showing that the ℓ 2 Wasserstein distance is an extension of the Euclidean distance between quantile functions, the authors showed that it was possible to obtain a decomposition of the variability of a set of histograms according to the Huygens theorem of decomposition of the inertia and used such properties for extending some clustering methods for standard data to histogram-valued data.…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

Basic statistics for distributional symbolic variables: a new metric-based approach

Irpino

Verde

2014

Adv Data Anal Classif

Self Cite

View full text Add to dashboard Cite

In data mining it is usual to describe a group of measurements using summary statistics or through their empirical distribution functions. Each summary of a group of measurements is the representation of a typology of individuals (sub-populations) or of the evolution of the observed variable for each individual. Therefore, typologies or individuals are expressible through multi-valued descriptions (intervals, frequency distributions). Symbolic Data Analysis, a relatively new statistical approach, aims at the treatment of such kinds of data. In the conceptual framework of Symbolic Data Analysis, the paper aims at presenting new basic statistics for numeric multi-valued data. First of all, we propose how to consider all numerical multi-valued descriptions as special cases of distributional data, i.e. as data described by distributions. Secondly, we extend some classic univariate (mean, variance, standard deviation) and bivariate (covariance and correlation) basic statistics taking into account the nature, the source and the interpretation of the variability of such data. As opposed to those proposed in the literature, the novel statistics are based on a distance between distributions, the ℓ2 Wasserstein distance. Using a clinic dataset, we compare the proposed approach to the existing one showing the main differences in terms of interpretation of results.

show abstract

“…Several distances between interval objects have been extended to distances between hyperrectangles and remain a subject of research in automatic classification. These include the distance based on city block distance [1], Hausdorff distance between hyperrectangles, Wasserstein based distance [2], and single adaptive distance [3]. Finally, the third type of reduction leads to new uncorrelated variables but poses significant mathematical problems such as the search for compromise space and the number of observations to be used for the reduction of each entry table (see [4,5]).…”

Section: Introductionmentioning

confidence: 99%

Classification of the Entities Represented by Samples from Gaussian Distribution

Rebbouh

2016

Advances in Decision Sciences

View full text Add to dashboard Cite

This paper aims to cluster entities which are described by a data matrix. Under the assumption of normality of observations contained in each table, each entity is represented by samples from Gaussian distribution, that is, a number of measurements in the data matrix, the sample mean vector, and the sample covariance. We propose a new distance based on Mahalanobis's discriminant score to measure the similarity between objects. The present study is thought to be an important and interesting topic of research not only in the quest for an adequate model of the data representation but also in the choice of the distance index between entities that would allow justifying the homogeneity of any observed classes.

show abstract

Dynamic clustering of interval data using a Wasserstein-based distance

Cited by 110 publications

References 12 publications

New Distance Measures of Evidence Based on Belief Intervals

New Distance Measures of Evidence Based on Belief Intervals

Basic statistics for distributional symbolic variables: a new metric-based approach

Classification of the Entities Represented by Samples from Gaussian Distribution

Contact Info

Product

Resources

About