On clustering of non-stationary meteorological time series

Dynamics of Atmospheres and Oceans

Volumn 49, Issue 2-3, 2010, Pages 164-187

  Horenko, Illia ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Clustering; Finite element method; Non stationary time series analysis; Regularization

Indexed keywords

APRIORI; CLUSTER STATE; DISTINGUISHABILITY; FINITE MIXTURE MODELS; FUZZY CLUSTERING METHOD; GLOBAL TEMPERATURES; NON-STATIONARY TIME SERIES; NONSTATIONARY; NUMERICAL FEATURES; OPTIMAL NUMBER; PROBABILITY MODELS; QUALITY OF DATA; REGRESSION MODEL; STATIONARITY; TEMPERATURE DATA; TOY MODELS;

CLUSTER ANALYSIS; FINITE ELEMENT METHOD; FUZZY CLUSTERING; FUZZY SYSTEMS; HIDDEN MARKOV MODELS; PROBABILITY DENSITY FUNCTION; REGRESSION ANALYSIS; SANITARY SEWERS; TIME SERIES; TIME SERIES ANALYSIS;

CLUSTERING ALGORITHMS;

ALGORITHM; DATA QUALITY; FINITE ELEMENT METHOD; METEOROLOGY; NUMERICAL MODEL; OPTIMIZATION; TIME SERIES ANALYSIS; WEATHER FORECASTING;

EID: 75149146645     PISSN: 03770265     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dynatmoce.2009.04.003     Document Type: Article

References (46)

1. Arioli M. The use of QR factorization in sparse quadratic programming and backward error issues. SIAM J. Matrix Anal. Appl. 21 3 (2000) 825-839
2. Benzi R., Parisi G., Sutera A., and Vulpiani A. Stochastic resonance in climatic change. Tellus 3 (1982) 10-16
3. Bezdek J.C. Pattern Recognition with Fuzzy Objective Function Algorithms (1981), Plenum Press, New York
4. Bezdek J.C., Hathaway R.H., Sabin M.J., and Tucker W.T. Convergence theory for fuzzy c-mens: counterexamples and repairs. IEEE Trans. Syst. 17 (1987) 873-877
5. Bilmes, J.A., 1998. A Gentle Tutorial of the EM Algorithm and its Applications to Parameter Estimation for Gaussian Mixture and Hidden Markov Models. Thechnical Report. International Computer Science Institute, Berkeley.
6. Braess D. Finite Elements: Theory, Fast Solvers and Applications to Solid Mechanics (2007), Cambridge University Press
7. Cheng X., and Wallace J.M. Cluster analysis of the northern hemisphere wintertime 500-hPa height field: spatial patterns. J. Atmos. Sci. 50 (1993) 2674-2696
8. Christiansen B. Atmospheric circulation regimes: can cluster analysis provide the number?. J. Climate 20 10 (2007) 2229-2250
9. Corti S., Molteni F., and Palmer T.N. Signature of recent climate change in frequencies of natural atmospheric circulation regimes. Nature 398 (1999) 799-802
10. Davison A., and Hinkley D. Bootstrap Methods and their Applications (2006), Cambridge Series in Statistical and Probability Mathematics
11. Deuflhard P. Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms volume 35 of Computational Mathematics (2004), Springer, Heidelberg
12. Efimov V.V., Prusov A.V., and Shokurov M.V. Patterns of interannual variability defined by a cluster analysis and their relation with enso. Quart. J. R. Meteorol. Soc. 121 (1995) 1651-1679
13. Franzke, C., Crommelin, D., Fischer, A., Majda, A., 2008. A hidden markov model perspective on regimes and metastability in atmospheric flows. J. Climate 21, 1740-1757.
14. Fruhwirth-Schnatter S. Finite Mixture and Markov Switching Models (2006), Springer
15. Gardiner H. Handbook of Stochastical Methods (2004), Springer, Berlin
16. Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H., 1987. A Schur-complement method for sparse quadratic programming. Technical Report. STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB.
17. Hathaway R.H., and Bezdek J.C. Switching regression models and fuzzy clustering. IEEE Trans. Fuzzy Syst. 1 (1993) 195-204
18. Höppner F., Klawonn F., Kruse R., and Runkler T. Fuzzy Cluster Analysis (1999), John Wiley and Sons, New York
19. Horenko, I., 2008. Finite element approach to clustering of multidimensional time series. SIAM J. Sci. Comp. (available at biocomputing.mi.fu-berlin.de).
20. Horenko, I., in press. On simultaneous data-based dimension reduction and hidden phase identification. J. Atmos. Sci. (available at biocomputing.mi.fu-berlin.de).
21. Horenko I., Klein R., Dolaptchiev S., and Schuette Ch. Automated generation of reduced stochastic weather models i: simultaneous dimension and model reduction for time series analysis. SIAM Mult. Mod. Sim. 6 4 (2008) 1125-1145
22. Horenko, I., Dolaptchiev, S., Eliseev, A.V., Mokhov, I.I., Klein, R., in press. Metastable decomposition of high-dimensional meteorological data with gaps. J. Atmos. Sci. (available at biocomputing.mi.fu-berlin.de).
23. Huisinga W., Meyn S., and Schuette Ch. Phase transitions and metastability in Markovian and molecular systems. Ann. Appl. Prob. 14 1 (2004) 419-458
24. Kedem B., and Fokianos K. Regression Models for Time Series Analysis (2002), Wiley Series in Probability and Statistics
25. Kimoto M., and Ghil M. Multiple flow regimes in the northern hemisphere winter. Part I. Methodology and hemispheric regimes. J. Atmos. Sci. 50 (1993) 2625-2644
26. Kimoto M., and Ghil M. Multiple flow regimes in the northern hemisphere winter. Part II. Sectorial regimes and preferred transitions. J. Atmos. Sci. 50 (1993) 2645-2673
27. Loader C. Local likelihood density estimation. Ann. Stat. (1996) 24
28. Loader C. Local Regressions and Likelihood (1999), Springer, New Yorck
29. Majda A., Franzke C., Fischer A., and Crommelin D. Distinct metastable atmospheric regimes despite nearly gaussian statistics: a paradigm model. PNAS 103 22 (2006) 8309-8314
30. McLachlan G., and Peel D. Finite Mixture Models (2000), Wiley, New York
31. Metzner P., Horenko I., and Schuette Ch. Generator estimation of Markov Jump processes based on incomplete observations nonequidistant in time. Phys. Rev. E 76 (2007) 0667021
32. Mokhov I.I., and Semenov V.A. Bimodality of the probability density functions of subseasonal variations in surface air temperature. Izvestiya Atmos. Ocean. Phys. 33 (1997) 702-708
33. Mokhov I.I., Petukhov V.K., and Semenov V.A. Multiple intraseasonal temperature regimes and their evolution in the iap ras climate model. Izvestiya Atmos. Ocean. Phys. 34 (1998) 145-152
34. Monahan A.H. Nonlinear principal component analysis by neural networks: theory and application to the lorenz system. J. Climate 13 (2000) 821-835
35. Nicolis C. Stochastic aspects of climatic transitions-response to a periodic forcing. Tellus 34 (1982) 1
36. Noe F. Probability distributions of molecular observables computed from Markov models. J. Chem. Phys. 128 (2008) 1
37. Paillard D. The timing of pleistocene glaciations from a simple multiple-state climate model. Nature 391 (1998) 378-381
38. Palmer T.N. A nonlinear dynamical perspective on climate prediction. J. Climate 12 (1999) 575-591
39. Philipp A., Della-Marta P.M., Jacobeit J., Fereday D.R., Jones P.D., Moberg A., and Wanner H. Long term variability of daily north Atlantic-European pressure patterns since 1850 classified by simulated annealing clustering. J. Climate 20 16 (2007) 4065-4095
40. Preminger A., Ben-Zion U., and Wettstein D. The extended switching regression model: allowing for multiple latent state variables. J. Forecast. 26 (2007) 457-473
41. Schütte Ch., and Huisinga W. Biomolecular conformations can be identified as metastable sets of molecular dynamics. In: Ciaret P.G., and Lions J.-L. (Eds). Handbook of Numerical Analysis, vol. X (2003), Elsevier 699-744
42. Simmons, A., Gibson, J., 2000. The ERA 40 project plan. In: ERA 40 Project Rep. Ser. 2000. European Center for Medium-Range Weather Forcasting, Reading.
43. Stephenson D., Hannachi A., and O'Neil A. On the existence of multiple climate regimes. Quart. J. R. Meteorol. Soc. 130 (2004) 583-605
44. Sura P., Newmann M., Penland G., and Sardeshmukh D. Multiplicative noise and non-Gaussianity: a paradigm for atmospheric regimes?. J. Atmos. Sci. 62 (2005) 1391-1409
45. Tsonis A.A., and Elsner J.B. Multiple attractors, fractal basins and longterm climate dynamics. Beit. Phys. Atmos. 63 (1990) 171-176
46. Viterbi A.J. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans. Informat. Theory 13 (1967) 260-269