Functional data clustering: a survey
Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of methods working directly on the evaluation points of the curves. The second groups is defined by filtering methods which first approximate the cu...
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| Vydané v: | Advances in data analysis and classification Ročník 8; číslo 3; s. 231 - 255 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2014
Springer Verlag |
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| ISSN: | 1862-5347, 1862-5355 |
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| Abstract | Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of methods working directly on the evaluation points of the curves. The second groups is defined by filtering methods which first approximate the curves into a finite basis of functions and second perform clustering using the basis expansion coefficients. The third groups is composed of methods which perform simultaneously dimensionality reduction of the curves and clustering, leading to functional representation of data depending on clusters. The last group consists of distance-based methods using clustering algorithms based on specific distances for functional data. A software review as well as an illustration of the application of these algorithms on real data are presented. |
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| AbstractList | The main contributions to functional data clustering are reviewed. Most approaches used for clustering functional data are based on the following three methodologies: dimension reduction before clustering, nonparametric methods using specific distances or dissimilarities between curves and model-based clustering methods. These latter assume a probabilistic distribution on either the principal components or coefficients of functional data expansion into a finite dimensional basis of functions. Numerical illustrations as well as a software review are presented.
Nous présentons dans cet article une revue des méthodes de classification automatique pour données fonctionelles. Ces techniques peuvent être classées en trois catégories: les méthodes procédant à une étape de réduction de dimension avant la classification, les méthodes non paramétriques qui utilisent des techniques de classification automatique classiques couplées à des distances ou dissimilarités spécifiques aux données fonctionnelles, et enfin, les techniques à base de modèles génératifs. Ces dernières supposent un modèle probabiliste soit sur les scores d'une analyse en composantes principales fonctionnelle, soit sur les coefficients des approximations des courbes dans une base de fonctions de dimension finie. Une illustration numérique ainsi qu'une revue des logiciels disponibles sont également présentées. Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of methods working directly on the evaluation points of the curves. The second groups is defined by filtering methods which first approximate the curves into a finite basis of functions and second perform clustering using the basis expansion coefficients. The third groups is composed of methods which perform simultaneously dimensionality reduction of the curves and clustering, leading to functional representation of data depending on clusters. The last group consists of distance-based methods using clustering algorithms based on specific distances for functional data. A software review as well as an illustration of the application of these algorithms on real data are presented. |
| Author | Preda, Cristian Jacques, Julien |
| Author_xml | – sequence: 1 givenname: Julien surname: Jacques fullname: Jacques, Julien email: julien.jacques@polytech-lille.fr organization: Laboratoire Paul Painlevé, UMR CNRS 8524, Université Lille 1 and Inria Lille-Nord Europe – sequence: 2 givenname: Cristian surname: Preda fullname: Preda, Cristian organization: Laboratoire Paul Painlevé, UMR CNRS 8524, Université Lille 1 and Inria Lille-Nord Europe |
| BackLink | https://inria.hal.science/hal-00771030$$DView record in HAL |
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| Keywords | 62M99 Basis expansion Functional data 62-07 62H30 Clustering Functional principal component analysis |
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| Snippet | Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of... The main contributions to functional data clustering are reviewed. Most approaches used for clustering functional data are based on the following three... |
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| SubjectTerms | Chemistry and Earth Sciences Computer Science Data Mining and Knowledge Discovery Economics Finance Health Sciences Humanities Insurance Law Management Mathematics Mathematics and Statistics Medicine Physics Regular Article Statistical Theory and Methods Statistics Statistics for Business Statistics for Engineering Statistics for Life Sciences Statistics for Social Sciences Statistics Theory |
| Title | Functional data clustering: a survey |
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