Abstract
The research deals with an exploration of high dimensional environmental data using unsupervised learning algorithms and the concept of local fractality. The proposed methodology is applied to geospatial data used for the wind speed prediction in a complex mountainous region. It is shown, that the approach provides important additional information on data manifold useful in data analysis, data visualisation and predictive modelling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kanevski, M., Pozdnoukhov, A., Timonin, V.: Machine Learning of Spatial Environmental Data. Theory, Applications and Software. EPFL Press, Lausanne (2009)
Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman, San Francisco (1982)
Theiler, J.: Estimating fractal dimension. JOSA A Opt. Soc. Am. 7, 1055–1073 (1990)
Turcotte, D.L.: Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge (1997)
Camastra, F.: Intrinsic dimension estimation: advances and open problems. Inf. Sci. 328, 26–41 (2015)
Seuront, L.: Fractals and Multifractals in Ecology and Aquatic Science. CRC Press, Boca Raton (2009)
Ghanbarian, B., Hunt, A.: Fractals: Concepts and Applications in Geosciences. CRC Press, Boca Raton (2017)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, New York (2009). https://doi.org/10.1007/978-0-387-84858-7
Hennig, Ch., Meila, M., Murtagh, F., Rocci, R.: Handbook of Cluster Analysis. CRC, Boca Raton, Florida (2015)
Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, Hoboken (2009)
Golay, J., Kanevski, M.: Unsupervised feature selection based on the Morisita estimator of intrinsic dimension. Knowl.-Based Syst. 135, 125–134 (2017)
Golay, J., Leuenberger, M., Kanevski, M.: Feature selection for regression problems based on the Morisita estimator of intrinsic dimension. Pattern Recogn. 70, 126–138 (2017)
Ripley, B.: Spatial Statistics. Wiley, Hoboken (1981)
Kantz, H., Schreiber, Th.: Nonlinear time Series Analysis. Cambridge University Press, Cambridge (2004)
Vicsek, T.: Mass multifractals. Physica A 168(1), 490–497 (1990)
Kanevski, M. (ed.): Advanced Mapping of Environmental Data. iSTE & Wiley, London (2008)
Facco, E., d’Errico, M., Rodriguez, A., Laio, A.: Estimating the intrinsic dimension of datasets by a minimal neighborhood information. Sci. Rep. 7, 1–8 (2017)
Carter, K., Raich, R., Hero III, A.: On local intrinsic dimension estimation and its applications. IEEE Trans. Signal Process. 58, 650–663 (2009)
Houle, M.: Local intrinsic dimensionality I: an extreme-value-theoretic foundation for similarity applications, In: Beecks, C., Borutta, F., Kröger, P., Seidl, T. (eds.) Similarity Search and Applications. International Conference on Similarity Search and Applications, pp. 64–79. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68474-1_5
Allegra, M., Facco, E., Denti, F., et al.: Data segmentation based on the local intrinsic dimension. Sci. Rep. 10, 16449 (2020)
Gionis, A., Hinneburg, A., Papadimitriou, S., Tsaparas, P.: Dimension induced clustering. In: Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, pp. 51–60 (2005)
Kanevski, M., Pereira, M.: Local fractality: the case of forest fires in Portugal. Physica A 479(5), 400–410 (2017)
Ramsay, J., Silverman, B.: Functional Data Analysis, 2nd edn. Springer, New York (2009). https://doi.org/10.1007/b98888
Laib, M., Kanevski, M., FractalTools: R library for estimating fractal dimension. https://github.com/mlaib/FractalTools. Accessed 20 Oct 2020
Robert, S., Foresti, L., Kanevski, M.: Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks. Int. J. Climatol. 33(7), 1793–1804 (2013)
Golay, J., Kanevski, M.: A new estimator of intrinsic dimension based on the multipoint Morisita index. Pattern Recogn. 48, 4070–4081 (2015)
Charrad, M., Ghazzali, N., Boiteau, V., Niknafs, A.: NbClust: an R package for determining the relevant number of clusters in a data set. J. Stat. Softw. 61(6), 1–36 (2014)
Acknowledgements
The research was partly supported by the Swiss National Research Program “Big Data” (PNR75), project “Hybrid Renewable Energy Potential for the Built Environment using Big Data: Forecasting and Uncertainty Estimation” (no. 4075-40_167285).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Kanevski, M., Laib, M. (2021). Unsupervised Learning of High Dimensional Environmental Data Using Local Fractality Concept. In: Del Bimbo, A., et al. Pattern Recognition. ICPR International Workshops and Challenges. ICPR 2021. Lecture Notes in Computer Science(), vol 12666. Springer, Cham. https://doi.org/10.1007/978-3-030-68780-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-68780-9_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-68779-3
Online ISBN: 978-3-030-68780-9
eBook Packages: Computer ScienceComputer Science (R0)