On Automatic Mapping of Environmental Data Using Adaptive General Regression Neural Network Mikhail Kanevski and Vadim Tim...
Contents <ul><li>Automatic mapping algorithms, some criteria </li></ul><ul><li>General Regression Neural Network (GRNN). D...
SIMPLE  PROBLEM: AUTOMATIC INTERPOLATION (from measurements to maps)  Interpolator Automatic
Advanced automatic mapping algorithms: some necessary and important  properties <ul><li>Detection of patterns (Yes/No). Di...
Possible solution: GRNN <ul><li>General Regression  </li></ul><ul><li>Neural Network </li></ul>
GRNN is a modification of  Nadaraya-Watson nonparametric regressor (GRNN is a winner of the SIC2004 – Spatial Interpolatio...
Regression = conditional mean where  is a conditional distribution of Z given x.
where joint pdf  can be estimated using Parzen-Rozenblatt kernel density estimator ( K(.) is a kernel ): Conditional pdf i...
Therefore the regression can be represented as follows:
There are different valid kernels.  For an isotropic Gaussian kernel
In a more general setting of  adaptive/anisotropic kernel we have:
General Regression Neural Network INPUTS INTEGRATION LAYER IMAGE   LAYER OUTPUT GRNN estimate using  measurements Z k :
GRNN Training:  find kernel bandwidths by minimising  <ul><li>Cross-validation </li></ul><ul><ul><li>Leave-one-out </li></...
GRNN: influence of bandwidth True function Too large, oversmoothing Too small, overfitting Optimal
Some useful properties of GRNN <ul><li>When bandwidth is small:  </li></ul><ul><ul><li>->   nearest neighbour estimator </...
Case study – precipitation mapping Swiss DEM and Precipitation Monitoring Network
Data (raw and shuffled)  and  corresponding training curves
The same is valid for Adaptive GRNN:  variables (features, inputs) which are irrelevant are “filtered out” automatically b...
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...
3D and 4D modelling results
Quality of model?  Analysis of the residuals using… GRNN! CV error = 92.8; sigma=inf
GRNN Mapping & uncertainties  (illustrative example)
Geokernels.org
The research was partly supported by Swiss NSF grants  N 200021-126505 and N 200020-121835   www.unil.ch/igar   2009 Thank...
Conclusions   and   perspectives <ul><li>IT WAS SHOWN THAT: </li></ul><ul><li>Adaptive GRNN is an efficient modelling algo...
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9A_1_On automatic mapping of environmental data using adaptive general regression neural network

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

  1. 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. 2. Contents <ul><li>Automatic mapping algorithms, some criteria </li></ul><ul><li>General Regression Neural Network (GRNN). Description </li></ul><ul><li>Training of GRNN </li></ul><ul><li>Illustrative case study </li></ul><ul><li>Adaptive GRNN and its useful properties </li></ul><ul><li>Conclusions and perspectives </li></ul>
  3. 3. SIMPLE PROBLEM: AUTOMATIC INTERPOLATION (from measurements to maps) Interpolator Automatic
  4. 4. Advanced automatic mapping algorithms: some necessary and important properties <ul><li>Detection of patterns (Yes/No). Discrimination between noise and structures </li></ul><ul><li>Universal, nonlinear modelling tool </li></ul><ul><li>Adaptive, data-driven </li></ul><ul><li>Automatic feature selection </li></ul><ul><li>Robust, stable </li></ul><ul><li>Characterize uncertainties </li></ul><ul><li>Quality of mapping. Analysis of the residuals </li></ul><ul><li>Computationally efficient </li></ul>
  5. 5. Possible solution: GRNN <ul><li>General Regression </li></ul><ul><li>Neural Network </li></ul>
  6. 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. 7. Regression = conditional mean where is a conditional distribution of Z given x.
  8. 8. where joint pdf can be estimated using Parzen-Rozenblatt kernel density estimator ( K(.) is a kernel ): Conditional pdf is defined by:
  9. 9. Therefore the regression can be represented as follows:
  10. 10. There are different valid kernels. For an isotropic Gaussian kernel
  11. 11. In a more general setting of adaptive/anisotropic kernel we have:
  12. 12. General Regression Neural Network INPUTS INTEGRATION LAYER IMAGE LAYER OUTPUT GRNN estimate using measurements Z k :
  13. 13. GRNN Training: find kernel bandwidths by minimising <ul><li>Cross-validation </li></ul><ul><ul><li>Leave-one-out </li></ul></ul><ul><ul><li>Leave-k-out </li></ul></ul><ul><li>Data splitting </li></ul><ul><ul><li>Training/testing </li></ul></ul><ul><li>Algorithms: gradient descents; Genetic Algorithms, Simulated Annealing,… </li></ul>
  14. 14. GRNN: influence of bandwidth True function Too large, oversmoothing Too small, overfitting Optimal
  15. 15. Some useful properties of GRNN <ul><li>When bandwidth is small: </li></ul><ul><ul><li>-> nearest neighbour estimator </li></ul></ul><ul><li>When all bandwidths are larger than the region of the study: </li></ul><ul><ul><li>-> there is no structure and </li></ul></ul><ul><li>When bandwidth for some coordinate i is large, this coordinate will be filtered out: </li></ul><ul><li>-> </li></ul>
  16. 16. Case study – precipitation mapping Swiss DEM and Precipitation Monitoring Network
  17. 17. Data (raw and shuffled) and corresponding training curves
  18. 18. The same is valid for Adaptive GRNN: variables (features, inputs) which are irrelevant are “filtered out” automatically by large corresponding bandwidths.
  19. 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. 20. 3D and 4D modelling results
  21. 21. Quality of model? Analysis of the residuals using… GRNN! CV error = 92.8; sigma=inf
  22. 22. GRNN Mapping & uncertainties (illustrative example)
  23. 23. Geokernels.org
  24. 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. 25. Conclusions and perspectives <ul><li>IT WAS SHOWN THAT: </li></ul><ul><li>Adaptive GRNN is an efficient modelling algorithm for processing of environmental data </li></ul><ul><li>GRNN is a useful DATA/RESIDUALS exploratory tool </li></ul><ul><li>Feature selection capability is important for automatic data processing </li></ul><ul><li>FUTURE TRENDS </li></ul><ul><li>More efficient algorithms for high dimensional and large data sets </li></ul><ul><li>New advanced models (space-time). Uncertainties </li></ul><ul><li>More case studies in high dimensional spaces </li></ul><ul><li>Implementation in decision support systems </li></ul>

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