Advertisement

Learning wind fields with multiple kernels

  • Loris Foresti
  • Devis Tuia
  • Mikhail Kanevski
  • Alexei Pozdnoukhov
Original Paper

Abstract

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

Keywords

Multiple kernel learning Support vector regression Feature selection Wind resource estimation Topographic features/indices extraction 

Notes

Acknowledgements

The research is funded in part by the Swiss National Science Foundation projects “GeoKernels: kernel-based methods for geo- and environmental sciences (Phase II)” (No 200020-121835/1) and “Structured learning for remote sensing data analysis” (PBLAP2-127713/1). A. Pozdnoukhov acknowledges the support of Science Foundation Ireland under the National Development Plan, particularly through Stokes Award and Strategic Research Cluster grant (07/SRC/I1168). The authors would like to acknowledge Prof. S. Canu and Prof. A. Rakotomamonjy for the useful discussion and interesting comments.

References

  1. Andrienko N, Andrienko G (2006) Exploratory data analysis of spatial and temporal data. Springer, NYGoogle Scholar
  2. Ayotte KW (2008) Computational modelling for wind energy assessment. J Wind Eng Indus Aerodyn 96:1571–1590CrossRefGoogle Scholar
  3. Ayotte KW, Davy RJ, Coppin PA (2001) A simple temporal and spatial analysis of flow in complex terrain in the context of wind energy modeling. Boundary-Layer Meteorol 98:275–295CrossRefGoogle Scholar
  4. Bach FR, Lanckriet GRG, Jordan MI (2004) Multiple kernel learning, conic duality and the SMO algorithm. In: Proceedings of the 21th international conference on machine learning 69Google Scholar
  5. Baines PG (1997) Topographic effects in stratified flows. Cambridge University Press, CambridgeGoogle Scholar
  6. Beccali M, Cirrincione G, Marvuglia A, Serporta C (In press) Estimation of wind velocity over a complex terrain using the generalized mapping regressor. Applied EnergyGoogle Scholar
  7. Bishop C (2006) Pattern recognition and machine learning. Springer, NYGoogle Scholar
  8. Canu S, Grandvalet Y, Guigue V, and Rakotomamonjy A (2005) SVM and kernel methods matlab toolbox. Perception Systèmes et Information, INSA de Rouen, Rouen, FranceGoogle Scholar
  9. Cellura M, Cirrincione G, Marvuglia A, Miraoui A (2008) Wind speed spatial estimation for energy planning in Sicily: a neural kriging application. Renew Energy 33:1251–1266CrossRefGoogle Scholar
  10. Cressie N (1993) Statistics for spatial data, revised edn. Wiley, NYGoogle Scholar
  11. Eidsvik KJ (2005) A system for wind power estimation in mountainous terrain. Prediction of Askervein hill data. Wind Energy 8:237–249Google Scholar
  12. Eidsvik KJ, Holstad A, Lie I, Utnes T (2004) A prediction system for local wind variations in mountainous terrain. Boundary-Layer Meteorology 112:557–586CrossRefGoogle Scholar
  13. Evensen G (2006) Data assimilation: The ensemble Kalman filter. Springer, NYGoogle Scholar
  14. Faure P, Huard P (1965) Résolution de programmes mathématiques à fonction non linéaire par la méthode du gradient réduit, Revue Française de Recherche Opérationnelle 36Google Scholar
  15. Foresti L, Pozdnoukhov A, Tuia D and Kanevski M (In press) Extreme precipitation modelling using geostatistics and machine learning algorithms. Proceedings of the 7th international conference on geostatistics for environmental applicationsGoogle Scholar
  16. Foresti L, Tuia D, Pozdnoukhov A, Kanevski M (2009) Multiple kernel learning of environmental data. Case study: analysis and mapping of wind fields. Proceedings of the 19th international conference on artificial neural networks, Part II, pp 933–943Google Scholar
  17. Franck HP, Rathmann O, Mortensen NG, Landberg L (2001) The numerical wind atlas—the KAMM/WAsP method. Risoe National Laboratory publications, Danemark Risoe-R-1252(EN)Google Scholar
  18. Freeman WT and Adelson EH (1991) The design and use of steerable filters. IEEE Trans Pattern Anal Mach Intel 13:891–906CrossRefGoogle Scholar
  19. Freund RM (2004) Solution methods for quadratic optimization. Technical report, Massachusetts Institute of Technology, MAGoogle Scholar
  20. Gönen M, Alpaydin E (2008) Localized multiple kernel learning. Proceedings of the 25th international conference on machine learning, vol 307. pp 352–359CrossRefGoogle Scholar
  21. Gravdahl AR (1998) Meso scale modeling with a reynolds averaged navier-stokes solver: assessment of wind resources along the Norwegian coast. 31th IEA experts meeting. State of the Art on Wind Resource EstimationGoogle Scholar
  22. Guyon I, Weston J, Barnhill S, Vapnik V (2002) Gene selection for cancer classification using support vector machines. Mach Learn 46:389–422CrossRefGoogle Scholar
  23. Guyon I, Gunn S, Nikravesh M, Zadeh LA (eds) (2006) Feature extraction: foundations and applications. Springer, NYGoogle Scholar
  24. Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning, 2nd edn. Springer, NYGoogle Scholar
  25. Haykin S (1999) Neural Networks. Prentice Hall, IndiaGoogle Scholar
  26. Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35(1):73–101CrossRefGoogle Scholar
  27. Hughes GF (1968) On the mean accuracy of statistical pattern recognition. IEEE Trans Inf Theory 14(1):55–63CrossRefGoogle Scholar
  28. Kanevski M (ed) (2008) Advanced mapping of environmental data. ISTE Wiley, NYGoogle Scholar
  29. Kanevski M, Pozdnoukhov A, Timonin V (2009) Machine learning algorithms for spatial data analysis and modelling. EPFL Press, LausanneGoogle Scholar
  30. Lanckriet GRG, De Bie T, Cristianini N, Jordan MI, Noble WS (2004) A statistical framework for genomic data fusion. Bioinformatics 20(16):2626–2635CrossRefGoogle Scholar
  31. Landberg L, Myllerup L, Rathmann O, Petersen EL, Jorgensen BH, Badger J, Mortensen NG (2003) Wind resource estimation-an overview. Wind Energy 6:261–271CrossRefGoogle Scholar
  32. Lewis DP, Jebara T, Noble WS (2006) Support vector machine learning from heterogeneous data: an empirical analysis using protein sequence and structure. Bioinformatics 22:2753–2760CrossRefGoogle Scholar
  33. Lindsay JB, Rothwell J (2008) Modelling channeling and deflection of wind by topography. In: Zhou Q, Lees B (eds) Advances in digital terrain analysis. Springer, NY, pp 383–406Google Scholar
  34. Liston GE, Elder KA (2006) Meteorological distribution system for high-resolution terrestrial modeling (microMet). J Hydrometeorol 7:217–234CrossRefGoogle Scholar
  35. Longworth C, Gales MJF (2008) multiple kernel learning for speaker verification. IEEE conference on acoustic, speech and signal processing ICASSP, pp 1581–1584Google Scholar
  36. Martinez WL (2004) Exploratory data analysis with matlab. Chapman & Hall/CRC, LondonGoogle Scholar
  37. Mercer J (1905) Functions of positive and negative type and their connection with the theory of integral equations. Phil Trans R Soc CCIX:215–228Google Scholar
  38. Palma JMLM, Castro FA, Ribeiro LF, Rodrigues AH, Pinto AP (2008) Linear and nonlinear models in wind resource assessment and wind turbine micro-siting in complex terrain. J Eng Indus Aerodyn 96:2308–2326CrossRefGoogle Scholar
  39. Petersen EL, Mortensen NG, Landberg L, Hojstrup J, Frank HP (1998) Wind power meteorology. Wind Energy 1:2–22CrossRefGoogle Scholar
  40. Pozdnoukhov A, Kanevski M (2008) Multi-scale support vector algorithms for hot spot detection and modelling. Stoch Environ Res Risk Assess 22(5):647–660CrossRefGoogle Scholar
  41. Pozdnoukhov A, Kanevski M, Timonin V (2007) Prediction of wind power density using machine learning algorithms. Proceedings of the 12th annual conference of international association for mathematical GeologyGoogle Scholar
  42. Pozdnoukhov A, Foresti L and Kanevski M (2009) Data-driven topo-climatic mapping with machine learning methods. Nat Haz 3(50):497–518Google Scholar
  43. Rakotomamonjy A, Bach FR, Canu S, Grandvalet Y (2008) Simple MKL. J Mach Learn Res 9:2491–2521Google Scholar
  44. Rätsch G, Sonnenburg S, Schäfer C (2006) Learning interpretable SVMs for biological sequence classification. BMC Bioinformatics 7(Suppl 1):S9CrossRefGoogle Scholar
  45. Schaffner B, Remund J (eds) (2005) The alpine space wind map: modeling approach. Alpine Windharvest Report Series 7–2. Alpine windharvest partnership networkGoogle Scholar
  46. Schölkopf B (2001) The kernel trick for distances. In: Leen TK, Dietterich TG, and Tresp V (eds) NIPS. MIT Press, Cambridge, pp 301–307Google Scholar
  47. Schölkopf B, Smola A (2002) Learning with Kernels. MIT Press, CambridgeGoogle Scholar
  48. Smola A-J, Schölkopf B (1998) A Tutorial on support vector regression. NeuroCOLT2 technical report series, NC2-TR-1998-030Google Scholar
  49. Sonnenburg S, Schaefer G, Rätsch G, Schölkopf B (2006) Large scale multiple kernel learning. J Mach Learn Res 7:1531–1565Google Scholar
  50. Tuia D, Kanevski M (2008) Environmental monitoring network characterization and clustering. In: Kanevski (ed) Advanced mapping of environmental data. ISTE Wiley, NY, pp 19–47Google Scholar
  51. Tuia D, Camps-Valls G, Matasci G, Kanevski M (in press) Learning relevant image features with multiple kernel classification. IEEE Trans Geosci Remote SensGoogle Scholar
  52. Vapnik V (1995) The nature of statistical learning theory. Springer, NYGoogle Scholar
  53. Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, OxfordGoogle Scholar
  54. Wilson JP, Gallant JC (eds) (2000) Terrain analysis: principles and applications. Wiley, NYGoogle Scholar
  55. Zien A, Ong CS (2007) Multiclass multiple kernel learning. Proceedings of the 24th international conference on machine learning, vol 227. pp 1191–1198CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Geomatics and Analysis of RiskUniversity of LausanneLausanneSwitzerland
  2. 2.National Centre for GeocomputationNational University of IrelandMaynoothIreland

Personalised recommendations