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