Clustering multivariate functional data using unsupervised binary trees
•An effective model-based clustering algorithm for multivariate functional data.•The algorithm is recursive and based on a set of binary trees.•The number of clusters is determined in a data-driven way.•New data are easily classified. A model-based clustering algorithm is proposed for a general clas...
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| Published in: | Computational statistics & data analysis Vol. 168; p. 107376 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.04.2022
Elsevier |
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| ISSN: | 0167-9473, 1872-7352 |
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| Abstract | •An effective model-based clustering algorithm for multivariate functional data.•The algorithm is recursive and based on a set of binary trees.•The number of clusters is determined in a data-driven way.•New data are easily classified.
A model-based clustering algorithm is proposed for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with errors at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout. |
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| AbstractList | •An effective model-based clustering algorithm for multivariate functional data.•The algorithm is recursive and based on a set of binary trees.•The number of clusters is determined in a data-driven way.•New data are easily classified.
A model-based clustering algorithm is proposed for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with errors at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout. We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout. A model-based clustering algorithm is proposed for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with errors at discrete, and possibly random, points in the definition domain. The idea is to build a set of binary trees by recursive splitting of the observations. The number of groups are determined in a data-driven way. The new algorithm provides easily interpretable results and fast predictions for online data sets. Results on simulated datasets reveal good performance in various complex settings. The methodology is applied to the analysis of vehicle trajectories on a German roundabout. |
| ArticleNumber | 107376 |
| Author | Golovkine, Steven Patilea, Valentin Klutchnikoff, Nicolas |
| Author_xml | – sequence: 1 givenname: Steven orcidid: 0000-0002-5994-2671 surname: Golovkine fullname: Golovkine, Steven email: steven.golovkine@ensai.fr organization: Groupe Renault & Ensai, CREST - UMR 9194, Rennes, France – sequence: 2 givenname: Nicolas surname: Klutchnikoff fullname: Klutchnikoff, Nicolas email: nicolas.klutchnikoff@univ-rennes2.fr organization: Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France – sequence: 3 givenname: Valentin surname: Patilea fullname: Patilea, Valentin email: valentin.patilea@ensai.fr organization: Ensai, CREST - UMR 9194, Rennes, France |
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| Keywords | Gaussian mixtures Model-based clustering Multivariate functional principal components Multivariate Functional Principal Components |
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| Snippet | •An effective model-based clustering algorithm for multivariate functional data.•The algorithm is recursive and based on a set of binary trees.•The number of... A model-based clustering algorithm is proposed for a general class of functional data for which the components could be curves or images. The random functional... We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional... |
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| SubjectTerms | algorithms data analysis data collection Gaussian mixtures Machine Learning Model-based clustering Multivariate functional principal components Statistics |
| Title | Clustering multivariate functional data using unsupervised binary trees |
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