Your SlideShare is downloading. ×
9A_1_On automatic mapping of environmental data using adaptive general regression neural network
Upcoming SlideShare
Loading in...5

Thanks for flagging this SlideShare!

Oops! An error has occurred.


Introducing the official SlideShare app

Stunning, full-screen experience for iPhone and Android

Text the download link to your phone

Standard text messaging rates apply

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


Published on

Session 9A, Paper 1

Session 9A, Paper 1

  • Be the first to comment

  • Be the first to like this

No Downloads
Total Views
On Slideshare
From Embeds
Number of Embeds
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

No notes for slide


  • 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] ,
  • 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.
  • 24. The research was partly supported by Swiss NSF grants N 200021-126505 and N 200020-121835 2009 Thank you for your attention! 2004 2008
  • 25. Conclusions and perspectives
    • 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
    • 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