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Multiresolution clustering of dependent functional data with application to climate reconstruction
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-7917-5687
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Stat, E-ISSN 2049-1573, Vol. 8, no 1, article id e240Article in journal (Refereed) Published
Abstract [en]

We propose a new nonparametric clustering method for dependent functional data, the double clustering bagging Voronoi method. It consists of two levels of clustering. Given a spatial lattice of points, a function is observed at each grid point. In the first‐level clustering, features of the functional data are clustered. The second‐level clustering takes dependence into account, by grouping local representatives, built from the resulting first‐level clusters, using a bagging Voronoi strategy. Depending on the distance measure used, features of the functions may be included in the second‐step clustering, making the method flexible and general. Combined with the clustering method, a multiresolution approach is proposed that searches for stable clusters at different spatial scales, aiming to capture latent structures. This provides a powerful and computationally efficient tool to cluster dependent functional data at different spatial scales, here illustrated by a simulation study. The introduced methodology is applied to varved lake sediment data, aiming to reconstruct winter climate regimes in northern Sweden at different time resolutions over the past 6,000 years.

Place, publisher, year, edition, pages
John Wiley & Sons, 2019. Vol. 8, no 1, article id e240
Keywords [en]
bagging Voronoi strategy, climate reconstruction, clustering, dependency, functional data
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-164004DOI: 10.1002/sta4.240ISI: 000506857900010Scopus ID: 2-s2.0-85081025918OAI: oai:DiVA.org:umu-164004DiVA, id: diva2:1360319
Funder
Swedish Research Council, 340-2013-5203Swedish Research Council, 2016-02763Available from: 2019-10-11 Created: 2019-10-11 Last updated: 2023-03-24Bibliographically approved
In thesis
1. Non-parametric methods for functional data
Open this publication in new window or tab >>Non-parametric methods for functional data
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Icke-parametriska metoder för funktionella data
Abstract [en]

In this thesis we develop and study non-parametric methods within three major areas of functional data analysis: testing, clustering and prediction. The thesis consists of an introduction to the field, a presentation and discussion of the three areas, and six papers.

In Paper I, we develop a procedure for testing for group differences in functional data. In case of significant group differences, the test procedure identifies which of the groups that significantly differ, and also the parts of the domain they do so, while controlling the type I error of falsely rejecting the null hypothesis. In Paper II, the methodology introduced in Paper I is applied to knee kinematic curves from a one-leg hop for distance to test for differences within and between three groups of individuals (with and without knee deficits). It was found that two of the groups differed in their knee kinematics. We also found that the individual kinematic patterns differed between the two legs in one of the groups. In Paper III, we test for group differences in three groups with respect to joint kinematics from a vertical one-leg hop using a novel method that allows accounting for multiple joints at the same time. The aim of Paper III, as one of few within the field of biomechanics, is to illustrate how different choices prior to the analysis can result in different contrasting conclusions. Specifically, we show how the conclusions depend on the choice of type of movement curve, the choice of leg for between-group comparisons and the included joints.

In Paper IV, we present a new non-parametric clustering method for dependent functional data, the double clustering bagging Voronoi method. The objective of the method is to identify latent group structures that slowly vary over domain and give rise to different frequency patterns of functional data object types. The method uses a bagging strategy based on random Voronoi tessellations in which local representatives are formed and clustered. Combined with the clustering method, we also propose a multiresolution approach which allows identification of latent structures at different scales. A simulated dataset is used to illustrate the method's potential in finding stable clusters at different scales. The method is also applied to varved lake sediment data with the aim of reconstructing the climate over the past 6000 years, at different resolutions. In Paper V, we expand and modify the bagging strategy used in Paper IV, by considering different methods of generating the tessellations and clustering the local representatives of the tessellations. We propose new methods for clustering dependent categorical data (e.g., labelled functional data) along a one-dimensional domain, which we also compare in a simulation study. 

In Paper VI, two kriging approaches to predict spatial functional processes are compared, namely functional kriging and spatio-temporal kriging. A simulation study is conducted to compare their prediction performance and computational times. The overall results show that prediction performance is about the same for stationary spatio-temporal processes while functional kriging works better for non-stationary spatio-temporal processes. Furthermore, the computational time for (ordinary) kriging for functional data, was considerably lower than spatio-temporal kriging. Conditions are also formulated under which it is proved that the two functional kriging methods: ordinary kriging for functional data and pointwise functional kriging coincide.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2020. p. 32
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 72/20
Keywords
functional data analysis, testing, clustering, prediction, inference, bagging Voronoi strategy, kriging, dependency
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-175594 (URN)978-91-7855-374-7 (ISBN)978-91-7855-375-4 (ISBN)
Public defence
2020-10-30, Aula Biologica, Biologihuset, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2020-10-09 Created: 2020-10-05 Last updated: 2020-10-06Bibliographically approved

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Abramowicz, KonradSchelin, LinaSjöstedt de Luna, SaraStrandberg, Johan

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