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Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
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Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)

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Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland) …

Kernel based models for geo- and environmental sciences- Alexei Pozdnoukhov – National Centre for Geocomputation, National University of Ireland , Maynooth (Ireland)
Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)

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  • 1. Kernel Methods (Support Vector Machines) for Environmental and Geo- Sciences Alexei Pozdnoukhov Lecturer National Centre for Geocomputation National University of Ireland, Maynooth +353 (0)1 7086146 Alexei.Pozdnoukhov@nuim.ie
  • 2. Machine Learning
  • 3. Learning From Data • Environmental monitoring Current rate of data acquisition is about 0.5Tb/day (increasing at 82% per year) • Remote Sensing Data NASA holds more than 10Pb of data, increasing by 10x every 5 years. ESA data stream is about 0.5Tb/year, likely to increase by 20x in next 5 years. • GIS, DEM • Sensor Networks • Field Measurements
  • 4. Clustering Cluster 1 Cluster 2
  • 5. Dimensionality Reduction
  • 6. Classification Binary Multi-Class
  • 7. Regression y Input, x
  • 8. Curse of Dimensionality Sensor Network Sensor Network Need more data? Batteries Recharged at WSN Human activity Remote Sensing Wireless Sensor Network Geographical Information
  • 9. Detecting Events Observed environment: Events: Very Rare, Extreme high-dimensional input space • High-dimensional spaces: risk of overfitting • Robust to noise in both inputs/outputs • Non-linear and non-parametric • Computationally effective for real-time processing and LBS dissemination
  • 10. Curse of Dimensionality
  • 11. Statistical Learning Theory • Models that can generalise from data • Good predictive abilities • Complexity can be controlled
  • 12. Statistical Learning Theory • Occam’s Razor Principle (14th century) One should not increase, beyond what is necessary, the number of entities required to explain anything • When many solutions are available for a given problem, we should select the simplest one. • But what do we mean by simple? • We will use prior knowledge of the problem to solve to define what is a simple solution (example of a prior: smoothness).
  • 13. Occam’s Razor and Classification Model 1 Model 2 Model 3 Complexity √√ √ ×× Training error ×× √ √√ Overall - √ -
  • 14. Structural Risk Minimization • Define a set of learning functions, {S} • Order it in terms of complexity, {S1, …, SN} • Select the optimal S* F = {f(x,α), α∈Λ}
  • 15. Classification Support Vector Machine SVM
  • 16. Separating Hyperplane x - input patterns w - weight vector b - threshold f w,b ( x ) = sign ( w ⋅ x + b) How powerful are linear decision functions?
  • 17. VC-dimension in classification Shattering • the number of samples which can be discriminated by the function for all possible class memberships – shattered. 3 samples: x x x 4 samples: x ? x VC-dimension h of the linear decision functions in RN equals N+1 That is, the power of linear decision functions is beyond our control…?
  • 18. Support Vector Machine Decision function is a margin hyperplane(*)  1, (w⋅ x) − b ≥ 1 f (x,{w, b}) =   −1, (w⋅ x) − b ≤ −1 Intuition: Large Margin is good. Lemma: Given that the N-dimensional data {xl, x2, …xL} lie inside a finite enclosing sphere of the radius R, the VC-dimension h of the margin-based decision functions (*) follows the inequality: h ≤ min R2 w , N  +1 2   The complexity (VC-dimension) can be controlled with ||w||2 !!
  • 19. Separating Hyperplane: Max Margin To maximize the margin ρ, one would like to minimize ||w||, or ||w||2.  1, (w ⋅ x) − b ≥ 1 fw,b ( x) =  f w,b ( x) = sign (( w ⋅ x) + b)  −1, (w ⋅ x) − b ≤ −1
  • 20. Optimization Problem, Lagrangian { 1 2 min w 2 ⇒ yi ( w ⋅ xi + b) ≥ 1, i = 1,..., L. { L w − ∑ α i ( yi ( w ⋅ xi + b) − 1) 2 Lp = 1 2 i =1 L ⇒ ∑α ⋅ y i =1 i i = 0, L w = ∑ αi ⋅ yi ⋅ xi i =1 KKT conditions: αi > 0 - Support Vectors α i ( yi ( w ⋅ xi + b) − 1) = 0, ∀i αi = 0
  • 21. Optimization Problem: Dual Variables. L L LD = ∑ α i − 1 ∑ α iα j yi y j ( xi ⋅ x j ) 2 i =1 i , j =1 L ∑α y i =1 i i =0 α i ≥ 0, i = 1,...L  L  f ( x ) = sign ( w ⋅ x + b) = sign  ∑ α i yi ( x ⋅ xi ) + b   i =1  • inputs are presented as dot products • Quadratic Programming • convex problem, nice theoretical field • unique solution, good solvers
  • 22. Soft margin hyperplane: allowing for the training error. error { L w + C ∑ξi 1 2 min 2 i =1 yi ( w ⋅ xi + b) ≥ 1 − ξ i , i = 1,..., L. ξ i ≥ 0, i = 1,...L { L L LD = ∑ α i − 1 2 ∑α α i j yi y j ( xi ⋅ x j ) i =1 i , j =1 C - regularization parameter L ∑α y i i =0 trade-off between i =1 margin maximization 0 ≤ αi ≤ C , i = 1,...L & training error
  • 23. Support Vector Terminology αi = 0 Normal Samples 0 < αi < C Support Vectors αi = C Support Vectors untypical or noisy C - regularization parameter  L  f ( x ) = sign  ∑ α i yi ( x ⋅ xi ) + b   i =1  trade-off between margin maximization & training error
  • 24. Support Vector Algorithm Kernel Trick If data is not linearly separable, it can be projected into (sufficiently) high dimensional space. There it is much easier to separate! Example. K ( x, x′) = ( x ⋅ x′) 2  x12   x1     x  →  2 x1 x2   2   x2 2     x → Φ( x) ? The algorithm was formulated in terms of dot products! x ⋅ x′ → Φ ( x ) ⋅ Φ ( x′) ⇔ x ⋅ x′ → K ( x, x′) •K is symmetric •K is positive-definite
  • 25. Nonlinear SVM. Kernel trick. f ( x ) = wx + b → L f ( x ) = ∑ yiα i K ( x, xi ) + b i =1 Any linear algorithm, formulated in terms of dot products of input data, can be modified into a non-linear one using the kernel trick. trick • Support Vector Machine • Kernel Ridge Regression • Kernel Principle Component Analysis • Kernel Fischer Discriminant Analysis • etc.
  • 26. Nonlinear SVM. Kernel types. • Polynomial kernel: K ( x, y ) = ( x ⋅ y + 1) p 2 x− y − • Radial Basis Function kernel: K ( x, y ) = e 2σ 2 f ( x ) = sign ( ∑ yiαi K ( x, xi ) + b) i∈SV
  • 27. Nonlinear SVM. Optimization problem. L L LD = ∑ α i − 1 ∑ α iα j yi y j K ( xi , x j ) 2 i =1 i , j =1 L ∑α y i =1 i i =0 0 ≤ α i ≤ C , i = 1,...L L b = yi − ∑ yiα i K ( xi , x j ) f ( x ) = sign( ∑ yiαi K ( x, xi ) + b) i =0 i∈SV K is positive-definite, still QP programming, hence unique solution!
  • 28. Support Vector Machine http://www.geokernels.org/teaching/svm
  • 29. SVM: Software.
  • 30. Examples
  • 31. SV Porosity Mapping Data description 200 training samples “+” 94 validation samples minimum = 0.0 median = 0.515 max = 1.000 mean = 0.53 variance = 0.048 The original continuous data were transformed into 2-class data according to the 0.5 threshold: If fpor ≥ 0.5, then y = +1 If fpor < 0.5, then y = -1
  • 32. SV Porosity Mapping Data: 2-class transformation • class “+1”, ≥ 0.5 o class “-1”, < 0.5 + validation data
  • 33. SV Porosity Mapping Data loading 150 training samples 50 testing samples Prediction Grid
  • 34. SV Porosity Mapping Hyper-parameters tuning 2 x − x′ • Gaussian RBF kernel is selected. − K ( x, x′) = e 2σ 2 • Two hyper-parameters: C and σ. • Grid search: testing error analysis for every pair of paramaters. The range of σ min(σ) - minimum distance between data samples max(σ) - max distance between data samples The range of log(C) min(C) - some small value, 1 or less max(C) – depends on data, 1e3-1e6 Start calculation using testing data Save results to file
  • 35. SV Porosity Mapping Hyper-parameters tuning Training error surface Log(C) Gaussian RBF kernel bandwidth • increase with kernel bandwidth • decrease with C
  • 36. SV Porosity Mapping Hyper-parameters tuning Testing error surface Log(C) Gaussian RBF kernel bandwidth Complex structure, but generally, if the range is selected reasonably and data splitting is correct, there exist a region of minima – optimal values.
  • 37. SV Porosity Mapping Hyper-parameters tuning Normalized number of Support Vectors Log(C) Gaussian RBF kernel bandwidth Represents the complexity of the model, the more complex one has more SVs.
  • 38. What are the parameters for the final model? Hyper-parameters selection Testing error C=3 σ = 0.09 Training error Normalized NSV
  • 39. What are the parameters for the final model? Hyper-parameters selection Testing error C = 18 σ = 0.13 Training error Normalized NSV
  • 40. SV Porosity Mapping Dependence on Parameters C = 10 σ 0.02 0.06 0.1 0.2 0.3 0.4 0.5
  • 41. SV Porosity Mapping Dependence on Parameters C=100 C=10 C=1 C=0.1 σ = 0.1
  • 42. SV Porosity Mapping Predictive Mapping and Support Vectors Predictive mapping + MARGIN + Normal SV, 0<α<C. + Critical SV, α=C.
  • 43. Applications for Natural Hazards • Topo-climatic mapping • Landslides • Snow avalanches prediction
  • 44. Weather observations • 110 meteo stations • Measurements, up to every 10min • Altitude: 270m-3580m • Temperature • Precipitation • Humidity • Air Pressure • Wind Speed • Insolation • Etc. Spatio-temporal prediction mapping?
  • 45. Temperature Inversion Can only be explained using terrain surface characteristics (convexity, slope, etc.)
  • 46. Physical Models at local scales • Terrain roughness is too high for physical models, computational speed, precision, uncertainty estimation… PDE on smoothed terrain + empirical correction vModel ( x, y ) = vPhysical + cRidges + cCanyons + cValues + cFlatAreas + cSea ... Can this information be extracted directly from data?
  • 47. Modelling Scheme Data Predictive Modeling with Machine Learning DEM Non-linear dependencies Noise, Outliers Spatio-Temporal Mapping F E A T U …. R Feature E Selection/Extraction S Analysis Decision Support
  • 48. Temperature vs. Elevation Mean Monthly Mean Daily Linear Locally Linear Regionalized Mean Hourly Mean Hourly Explained Non-linear Regionalized Temperature Inversion
  • 49. DEM Features Large Scale Difference of Gaussians Short Scale Difference of Gaussians Slope Local Variance
  • 50. Temperature Inversion Mapping Probability of Inversion Temperature
  • 51. Visual Validation
  • 52. Operational setting http://www.geokernels.org/services/meteo
  • 53. Applications • Topo-climatic mapping • Landslides • Snow avalanches prediction • Remote Sensing
  • 54. Landslide inventory SFI (SRC-ID 07/SRC/I1168)
  • 55. Method I Factor 1 Probability density estimation Factor 2 SFI (SRC-ID 07/SRC/I1168)
  • 56. Model vs. Training Data SFI (SRC-ID 07/SRC/I1168)
  • 57. What is wrong with this susceptibility map? SFI (SRC-ID 07/SRC/I1168)
  • 58. Method II Classification Stable Factor 1 Unstable Factor 2 SFI (SRC-ID 07/SRC/I1168)
  • 59. Predictive models SFI (SRC-ID 07/SRC/I1168)
  • 60. A model should fit the observed landslides, and … SFI (SRC-ID 07/SRC/I1168)
  • 61. Applications • Topo-climatic mapping • Landslides • Snow avalanches prediction • Remote Sensing
  • 62. Lochaber, Scotland • 1842 days of weather conditions (11 features) recording, 1991-2007 • 1135 days with documented avalanche events • 797 safe days, 245 with avalanches • 260 days unknown (mainly bad weather)
  • 63. Spatial Data Training data: 722 events, winters 1991-2005 Validation data: 72 events, winters 2006-2007 • 47 avalanche paths, x, y, z, slope, aspect, date • DEM, 10m resolution, 5km x 5km
  • 64. Lochaber weather observations • Snow index 0-10 • No-settle cumulative Snow over a season • Rain at 900m binary [0, 1] • Snow drift binary [0, 1] • Air temperature -10,… +10 • Wind speed 0, … 25 m/s • Wind Direction 0o-360o • Cloudness [25, 50, 75, 100] • Foot penetration 0, … 50 • Snow temperature 0, … -10 • Insolation cumulative over season
  • 65. Classification Problem Z Slope Aspect: SN-WE [Spatialized Weather Features] +1 720 …over all the documented avalanche events… Z Slope Aspect: SN-WE [Spatialized Weather Features] +1 Z Slope Aspect: SN-WE [Spatialized Weather Features] -1 44000 …over all the 47 gullies for documented days without avalanches… Z Slope Aspect: SN-WE [Spatialized Weather Features] -1 4 + 22 = 26
  • 66. Wind Speed and Direction Wind speed weighting: Correction for slope: Correction for curvature: Terrain-corrected wind direction:
  • 67. Snow accumulation Simple heuristics based on wind speed gradients If Snow index > 0 If Snow drift = 1 Snow accumulation = F(Wind Speed, Wind Direction)
  • 68. Results DEM Avalanche Danger
  • 69. Results wind Animation in 3D
  • 70. Applications • Topo-climatic mapping • Landslides • Snow avalanches prediction • Remote Sensing
  • 71. Inhabited areas Ground truth is known: population census Testing Training
  • 72. Inhabited areas Ground truth is known: population census
  • 73. Inhabited areas: examples
  • 74. Inhabited areas: examples
  • 75. Inhabited areas: examples
  • 76. Inhabited areas: examples
  • 77. Inhabited areas: examples
  • 78. Inhabited areas: examples
  • 79. Pre-processing and Features Mathematical morphology (image closing)
  • 80. Pre-processing and Features SIFT
  • 81. Pre-processing and Features Gaussian Mixture Model
  • 82. Pre-processing and Features
  • 83. Testing: inhabited areas
  • 84. Inhabited areas
  • 85. Inhabited areas
  • 86. Summary and Conclusions • Statistical Learning Theory • Classification Problem • Support Vector Machines and Kernel Methods • GeoSpatial Data Classification with SVM
  • 87. Open PhD positions at NCG Thank you! Alexei Pozdnoukhov Alexei.Pozdnoukhov@nuim.ie SFI (SRC-ID 07/SRC/I1168)

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