Abstract
In this paper we introduce a novel functional clustering method, the Bagging Voronoi K-Medoid Aligment (BVKMA) algorithm, which simultaneously clusters and aligns spatially dependent curves. It is a nonparametric statistical method that does not rely on distributional or dependency structure assumptions. The method is motivated by and applied to varved (annually laminated) sediment data from lake Kassjön in northern Sweden, aiming to infer on past environmental and climate changes. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnqvist P, Bigler C, Renberg I, Sjostedt de Luna S (2016) Functional clustering of varved lake sediment to reconstruct past seasonal climate. J Environ Ecol Stat (351). doi:10.1007/s10651-016-0351-1
Beniston M (2005) Warm winter spells in the Swiss Alps: strong heat waves in a cold season? A study focusing on climate observations at the Saentis high mountain site. Geophys Res Lett 32(1)
Comas C, Mehtätalo L, Miina J (2013) Analysing spacetime tree interdependencies based on individual tree growth functions. Stoch Environ Res Risk Assess 27(7):1673–1681
Dabo-Niang S, Yao AF, Pischedda L, Cuny P, Gilbert F (2010) Spatial mode estimation for functional random fields with application to bioturbation problem. Stoch Environ Res Risk Assess 24(4):487–497
Fernández-Pascual R, Espejo R, Ruiz-Medina M (2015) Moment and bayesian wavelet regression from spatially correlated functional data. Stoch Environ Res Risk Assess 30:523–557
Finazzi F, Haggarty R, Miller C, Scott M, Fasso A (2015) A comparison of clustering approaches for the study of the temporal coherence of multiple time series. Stoch Environ Res Risk Assess 29:463–475
Gaffney SJ, Smyth P (2004) Joint probabilistic curve clustering and alignment. In: Advances in neural information processing systems, pp 473–480
Giraldo R, Delicado P, Mateu J (2012) Hierarchical clustering of spatially correlated functional data. Stat Neerl 66(4):403–421
Ignaccolo R, Ghigo S, Giovenali E (2008) Analysis of air quality monitoring networks by functional clustering. Environmetrics 19(7):672–686
Ignaccolo R, Mateu J, Giraldo R (2014) Kriging with external drift for functional data for air quality monitoring. Stoch Environ Res Risk Assess 28(5):1171–1186
Leijonhufvud L, Wilson R, Moberg A, Söderberg J, Retsö D, Söderlind U (2010) Five centuries of Stockholm winter/spring temperatures reconstructed from documentary evidence and instrumental observations. Clim Change 101(1–2):109–141
Liu X, Müller HG (2004) Functional convex averaging and synchronization for time-warped random curves. J Am Stat Assoc 99(467):687–699
Mann ME, Zhang Z, Hughes MK, Bradley RS, Miller SK, Rutherford S, Ni F (2008) Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc Natl Acad Sci USA 105(36):13252–13257
Menafoglio A, Secchi P, Guadagnini A (2016) A class-kriging predictor for functional compositions with application to particle-size curves in heterogeneous aquifers. Math Geosci 48(4):463–485
Menafoglio A, Guadagnini A, Secchi P (2014) A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers. Stoch Environ Res Risk Assess 28(7):1835–1851
Ojala AE, Alenius T (2005) 10000 years of interannual sedimentation recorded in the Lake Nautajärvi (Finland) clastic-organic varves. Palaeogeogr, Palaeoclimatol, Palaeoecol 219(3):285–302
Ojala AE, Alenius T, Seppä H, Giesecke T (2008) Integrated varve and pollen-based temperature reconstruction from Finland: evidence for Holocene seasonal temperature patterns at high latitudes. Holocene 18(4):529–538
Pachauri RK, Allen MR, Barros VR, Broome J, Cramer W, Christ R, Church JA, Clarke L, Dahe Q, Dasgupta P, Dubash NK, Edenhofer O, Elgizouli I, Field CB, Forster P, Friedlingstein P, Fuglestvedt J, Gomez-Echeverri L, Hallegatte S, Hegerl G, Howden M, Jiang K, Cisneroz BJ, Kattsov V, Lee H, Mach KJ, Marotzke J, Mastrandrea MD, Meyer L, Minx J, Mulugetta Y, O’Brien K, Oppenheimer M, Pereira JJ, Pichs-Madruga R, Plattner GK, Pörtner HO, Power SB, Preston B, Ravindranath NH, Reisinger A, Riahi K, Rusticucci M, Scholes R, Seyboth K, Sokona Y, Stavins R, Stocker TF, Tschakert P, van Vuuren D, van Ypserle JP (2014) Climate change 2014: synthesis report. contribution of working groups I, II and III to the 5th assessment report of the intergovernmental panel on Climate Change. IPCC, Geneva, Switzerland
Petterson G (1999) Image analysis, varved lake sediments and climate reconstruction. Ph.D thesis, Umeå University
Petterson G, Renberg I, Geladi P, Lindberg A, Lindgren F (1993) Spatial uniformity of sediment accumulation in varved lake sediments in northern Sweden. J Paleolimnol 9(3):195–208
Petterson G, Odgaard B, Renberg I (1999) Image analysis as a method to quantify sediment components. J Paleolimnol 22(4):443–455
Petterson G, Renberg I, Sjöstedt-de Luna S, Arnqvist P, Anderson NJ (2010) Climatic influence on the inter-annual variability of late-Holocene minerogenic sediment supply in a boreal forest catchment. Earth Surf Process Landf 35(4):390–398
R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org/
Ramsay J, Silverman B (2005) Functional data analysis. Springer, New York
Romano E, Balzanella A, Verde R (2010) Classification as a tool for research. In: Proceedings of the 11th IFCS Biennial conference and 33rd annual conference of the Gesellschaft für Klassifikation e.V., Dresden, March 13-18, 2009, Springer, Heidelberg, chap clustering spatio-functional data: a model based approach, pp 167–175
Romano E, Mateu J, Giraldo R (2015) On the performance of two clustering methods for spatial functional data. AStA Adv Stat Anal 99(4):467–492
Salazar E, Giraldo R, Porcu E (2015) Spatial prediction for infinite-dimensional compositional data. Stoch Environ Res Risk Assess 29(7):1737–1749
Sangalli LM, Secchi P, Vantini S, Vitelli V (2010a) Functional clustering and alignment methods with applications. Commun Appl Ind Math 1(1):205–224
Sangalli LM, Secchi P, Vantini S, Vitelli V (2010b) K-mean alignment for curve clustering. Comput Stat Data Anal 54(5):1219–1233
Sangalli LM, Secchi P, Vantini S (2014) Analysis of aneurisk65 data: k-mean alignment. Electron J Stat 8(2):1891–1904
Secchi P, Vantini S, Vitelli V (2011) Spatial clustering of functional data. In: Recent advances in functional data analysis and related topics, Springer, New York, pp 283–289
Secchi P, Vantini S, Vitelli V (2013) Bagging Voronoi classifiers for clustering spatial functional data. Int J Appl Earth Obs Geoinf 22:53–64
Segerström U, Renberg I, Wallin JE (1984) Annual sediment accumulation and land use history; investigations of varved lake sediments. Verh int Ver Limnol 22:1396–1403
Stephens M (2000) Dealing with label switching in mixture models. J R Stat Soc 62(4):795–809
Tarpey T, Kinateder KK (2003) Clustering functional data. J Classif 20(1):093–114
Tiljander M, Saarnisto M, Ojala AE, Saarinen T (2003) A 3000-year palaeoenvironmental record from annually laminated sediment of Lake Korttajarvi, central Finland. Boreas 32(4):566–577
Vantini S (2012) On the definition of phase and amplitude variability in functional data analysis. Test 21(4):676–696
Acknowledgments
The authors would like to thank Christian Bigler for valuable comments and discussions. This work was supported by the Swedish Research Council, project D0520301.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abramowicz, K., Arnqvist, P., Secchi, P. et al. Clustering misaligned dependent curves applied to varved lake sediment for climate reconstruction. Stoch Environ Res Risk Assess 31, 71–85 (2017). https://doi.org/10.1007/s00477-016-1287-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-016-1287-6