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Abramowicz, K., Schelin, L., Sjöstedt de Luna, S. & Strandberg, J. (2019). Multiresolution clustering of dependent functional data with application to climate reconstruction. Stat, 8(1), Article ID e240.
Open this publication in new window or tab >>Multiresolution clustering of dependent functional data with application to climate reconstruction
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
Keywords
bagging Voronoi strategy, climate reconstruction, clustering, dependency, functional data
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-164004 (URN)10.1002/sta4.240 (DOI)
Funder
Swedish Research Council, 340-2013-5203Swedish Research Council, 2016-02763
Available from: 2019-10-11 Created: 2019-10-11 Last updated: 2019-10-14Bibliographically approved
Strandberg, J., Sjöstedt de Luna, S. & Mateu, J. (2019). Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches. Stochastic environmental research and risk assessment (Print), 33(10), 1699-1719
Open this publication in new window or tab >>Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches
2019 (English)In: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 33, no 10, p. 1699-1719Article in journal (Refereed) Published
Abstract [en]

We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Functional kriging, Prediction, Spatial functional random processes, Spatio-temporal kriging
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-164996 (URN)10.1007/s00477-019-01705-y (DOI)000491084300003 ()
Funder
Swedish Research Council, 340-2013-5203
Available from: 2019-11-08 Created: 2019-11-08 Last updated: 2019-11-08Bibliographically approved
Hébert-Losier, K., Pini, A., Vantini, S., Strandberg, J., Abramowicz, K., Schelin, L. & Häger, C. (2015). One-leg hop kinematics 20years following anterior cruciate ligament rupture: Data revisited using functional data analysis. Clinical Biomechanics, 30(10), 1153-1161
Open this publication in new window or tab >>One-leg hop kinematics 20years following anterior cruciate ligament rupture: Data revisited using functional data analysis
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2015 (English)In: Clinical Biomechanics, ISSN 0268-0033, E-ISSN 1879-1271, Vol. 30, no 10, p. 1153-1161Article in journal (Refereed) Published
Abstract [en]

BACKGROUND: Despite interventions, anterior cruciate ligament ruptures can cause long-term deficits. To assist in identifying and treating deficiencies, 3D-motion analysis is used for objectivizing data. Conventional statistics are commonly employed to analyze kinematics, reducing continuous data series to discrete variables. Conversely, functional data analysis considers the entire data series.

METHODS: Here, we employ functional data analysis to examine and compare the entire time-domain of knee-kinematic curves from one-leg hops between and within three groups. All subjects (n=95) were part of a long-term follow-up study involving anterior cruciate ligament ruptures treated ~20years ago conservatively with physiotherapy only or with reconstructive surgery and physiotherapy, and matched knee-healthy controls.

FINDINGS: Between-group differences (injured leg, treated groups; non-dominant leg, controls) were identified during the take-off and landing phases, and in the sagittal (flexion/extension) rather than coronal (abduction/adduction) and transverse (internal/external) planes. Overall, surgical and control groups demonstrated comparable knee-kinematic curves. However, compared to controls, the physiotherapy-only group exhibited less flexion during the take-off (0-55% of the normalized phase) and landing (44-73%) phase. Between-leg differences were absent in controls and the surgically treated group, but observed during the flight (4-22%, injured leg>flexion) and the landing (57-85%, injured leg<internal rotation) phases in the physiotherapy-only group.

INTERPRETATION: Functional data analysis identified specific functional knee-joint deviations from controls persisting 20years post anterior cruciate ligament rupture, especially when treated conservatively. This approach is suggested as a means for comprehensively analyzing complex movements, adding to previous analyses.

National Category
Physiotherapy
Identifiers
urn:nbn:se:umu:diva-111923 (URN)10.1016/j.clinbiomech.2015.08.010 (DOI)000366790400022 ()26365484 (PubMedID)2-s2.0-84941709869 (Scopus ID)
Available from: 2015-11-26 Created: 2015-11-26 Last updated: 2018-06-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1098-0076

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