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9A_1_On automatic mapping of environmental data using adaptive general regression neural network

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Session 9A, Paper 1

Session 9A, Paper 1


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  • 1. On Automatic Mapping of Environmental Data Using Adaptive General Regression Neural Network Mikhail Kanevski and Vadim Timonin GISRUK 2010, UCL, London [email_address] , [email_address] , www.unil.ch/igar
  • 2. Contents
    • Automatic mapping algorithms, some criteria
    • General Regression Neural Network (GRNN). Description
    • Training of GRNN
    • Illustrative case study
    • Adaptive GRNN and its useful properties
    • Conclusions and perspectives
  • 3. SIMPLE PROBLEM: AUTOMATIC INTERPOLATION (from measurements to maps) Interpolator Automatic
  • 4. Advanced automatic mapping algorithms: some necessary and important properties
    • Detection of patterns (Yes/No). Discrimination between noise and structures
    • Universal, nonlinear modelling tool
    • Adaptive, data-driven
    • Automatic feature selection
    • Robust, stable
    • Characterize uncertainties
    • Quality of mapping. Analysis of the residuals
    • Computationally efficient
  • 5. Possible solution: GRNN
    • General Regression
    • Neural Network
  • 6. GRNN is a modification of Nadaraya-Watson nonparametric regressor (GRNN is a winner of the SIC2004 – Spatial Interpolation Competition organised by EU JRC, Ispra)
  • 7. Regression = conditional mean where is a conditional distribution of Z given x.
  • 8. where joint pdf can be estimated using Parzen-Rozenblatt kernel density estimator ( K(.) is a kernel ): Conditional pdf is defined by:
  • 9. Therefore the regression can be represented as follows:
  • 10. There are different valid kernels. For an isotropic Gaussian kernel
  • 11. In a more general setting of adaptive/anisotropic kernel we have:
  • 12. General Regression Neural Network INPUTS INTEGRATION LAYER IMAGE LAYER OUTPUT GRNN estimate using measurements Z k :
  • 13. GRNN Training: find kernel bandwidths by minimising
    • Cross-validation
      • Leave-one-out
      • Leave-k-out
    • Data splitting
      • Training/testing
    • Algorithms: gradient descents; Genetic Algorithms, Simulated Annealing,…
  • 14. GRNN: influence of bandwidth True function Too large, oversmoothing Too small, overfitting Optimal
  • 15. Some useful properties of GRNN
    • When bandwidth is small:
      • -> nearest neighbour estimator
    • When all bandwidths are larger than the region of the study:
      • -> there is no structure and
    • When bandwidth for some coordinate i is large, this coordinate will be filtered out:
    • ->
  • 16. Case study – precipitation mapping Swiss DEM and Precipitation Monitoring Network
  • 17. Data (raw and shuffled) and corresponding training curves
  • 18. The same is valid for Adaptive GRNN: variables (features, inputs) which are irrelevant are “filtered out” automatically by large corresponding bandwidths.
  • 19. An example with added artificial coordinate 4135 191 7474 6949 420 4D (3D+Noise) 192 7601 7011 419 3D σ Znoise σ z σ y σ x Sigma values (metres) Cross-Validation error Model
  • 20. 3D and 4D modelling results
  • 21. Quality of model? Analysis of the residuals using… GRNN! CV error = 92.8; sigma=inf
  • 22. GRNN Mapping & uncertainties (illustrative example)
  • 23. Geokernels.org
  • 24. The research was partly supported by Swiss NSF grants N 200021-126505 and N 200020-121835 www.unil.ch/igar 2009 Thank you for your attention! 2004 2008
  • 25. Conclusions and perspectives
    • IT WAS SHOWN THAT:
    • Adaptive GRNN is an efficient modelling algorithm for processing of environmental data
    • GRNN is a useful DATA/RESIDUALS exploratory tool
    • Feature selection capability is important for automatic data processing
    • FUTURE TRENDS
    • More efficient algorithms for high dimensional and large data sets
    • New advanced models (space-time). Uncertainties
    • More case studies in high dimensional spaces
    • Implementation in decision support systems