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Chapter 8. Geocomputation Part B: Artificial Neural Networks (ANNs) & Genetic Algorithms (GAs). Geocomputation: ANNs. In this presentation on geocomputation: ANNs discussed include Multi-level perceptrons (MLPs) Radial basis function neural networks (RBFNNs)

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chapter 8

Chapter 8

Geocomputation Part B:

Artificial Neural Networks (ANNs) & Genetic Algorithms (GAs)

www.spatialanalysisonline.com

geocomputation anns
Geocomputation: ANNs

In this presentation on geocomputation:

ANNs discussed include

  • Multi-level perceptrons (MLPs)
  • Radial basis function neural networks (RBFNNs)
  • Self organising feature maps (SOFMs)

ANNs are particularly concerned with

  • Function approximation and interpolation
  • Image analysis and classification
  • Spatial interaction modelling

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geocomputation evolutionary computing
Geocomputation: Evolutionary computing

In this presentation on geocomputation:

EC elements discussed include

  • Genetic algorithms (GAs)
  • Genetic programming (GP)

EC is particularly concerned with

  • Complex problem solving using GAs
  • Model design using GP methods

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geocomputation
Geocomputation
  • Artificial Neural Networks (ANNs)
    • A computational model based on emulating biological neural networks
    • A form of non-linear modelling tool
    • Often a 3-layer network structure is used:

input, hidden, output

    • The output layer of such structures are typically modified weighted sums of intermediate layers, which are modified weighted sums of the input layer

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artificial neural networks
Artificial Neural Networks

Hence at each output node (hidden or final) a two-step process takes place:

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artificial neural networks6
Artificial Neural Networks
  • Simple 3-layer feedforward ANN
  • Fully inter-connected; each connection is given a weight, w
  • Known as a Multi-level perceptron (MLP)
  • In this case: 3 input nodes, 5 hidden nodes, 2 output nodes and 2 bias nodes (bias, B, is similar to the constant term in regression models)
  • At hidden node 1 we have:

where the wij are weights to be determined, b1=1, and the xi are the observed input values

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artificial neural networks7
Artificial Neural Networks

is simply a linear weighted sum of the inputs. To generate a non-linear output it must be modified by some (well behaved) non-linear function, g(), e.g. the logistic function:

i.e.

Sample activation functions

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artificial neural networks8
Artificial Neural Networks

We can now compute the output layer values as the weighted sum

Suppose we have known input values x1=1, x2=-3, x3=5, and known outputs of 0 and 1. Can we select the weights to ensure the inputs generate the known outputs?

Suggestion: <build your own worked example & program here>

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artificial neural networks9
Artificial Neural Networks
  • Learning
    • Supervised learning
      • Split training/test data sets (control data)
      • Known inputs and output (target) values for training data
      • (Network output-Target output) = Error signal, e
      • Systematically adjust weights to minimise sum of e2
      • Adjustment typically based on backpropagation and gradient descent
      • Used in many classification/pattern recognition applications and in function approximation
    • Unsupervised learning
      • No training data
      • Must create clusters by analysing dataset for patterns/clusters

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artificial neural networks10
Artificial Neural Networks
  • Some basic issues:
    • local vs global minimisation
    • Initialisation and selection
    • Data normalisation and coding
    • Momentum
    • Model design and over-fitting
    • Overtraining
    • Interpolation vs Extrapolation/Forecasting

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artificial neural networks11
Artificial Neural Networks
  • MLP: Example 1 function approximation

source data

fitted solution curve

RMSE vs epochs

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artificial neural networks12
Artificial Neural Networks
  • MLP Example 2: LCM

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artificial neural networks13
Artificial Neural Networks
  • MLP Example 2: LCM

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artificial neural networks14
Artificial Neural Networks
  • MLP Example 2: LCM

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artificial neural networks15
Artificial Neural Networks
  • MLP Example 2: LCM

weights matrix

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artificial neural networks16
Artificial Neural Networks
  • MLP Example 3: Spatial interaction model
    • Generalised model: Tij=f(Oi,Dj,dij)
    • Sample data format (log transformed):

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artificial neural networks17
Artificial Neural Networks
  • MLP Example 3: Spatial interaction model

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artificial neural networks18
Artificial Neural Networks
  • Radial Basis Function Networks

Basic functional form:

Gaussian RBF:

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artificial neural networks19
Artificial Neural Networks
  • Self organising function maps
    • SOM as an output space
    • Neighbourhood relations
    • Grid size, form and topology

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artificial neural networks20
Artificial Neural Networks
  • Self organising function maps
    • Dimensional reductions
    • Mapped output – similar vectors (units) are close to each other
    • Typically an unsupervised procedure
    • Spatial mapping of SOM can follow using simple assignment to best matching unit (BMU)

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artificial neural networks21
Artificial Neural Networks
  • Self organising function maps
    • Choose a grid size, form and topology
    • Train the network
      • Identify the best matching units
      • Modify the BMU and its neighbours (spatially biased learning rule)
    • Map the trained network

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artificial neural networks22
Artificial Neural Networks
  • Self organising function maps – some issues
    • Initialisation
    • Pre-processing
    • Normalisation
    • Missing data
    • Masking and weighting
    • Learning and tuning
    • Distance metrics
    • Neighbourhood functions (kernels)
    • Learning rate functions

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artificial neural networks23
Artificial Neural Networks
  • Self organising function maps – Idrisi

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artificial neural networks24
Artificial Neural Networks
  • Self organising function maps – Idrisi

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genetic algorithms
Genetic Algorithms
  • Solutions are represented as individuals
    • Individuals are modelled as chromosomes
    • Chromosomes are comprised of genes
    • Genes have values known as alleles
    • Chromosomes have a measurable fitness
    • New chromosomes (children) are created by reproduction and mutation processes
    • The fittest individuals survive
    • The creation process is then iterated

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genetic algorithms26
Genetic Algorithms
  • GAs: Example 1 - TSP

allele=12 (ID of town in TSP problem set)

chromosome

genes

  • Each chromosome contains complete list of towns
  • create a set of m randomly permuted strings and compute lengths, d
  • evaluate the fitness of each string (e.g. 1/d)
  • select random pairs of tours (biased by fitness)
  • combine pairs by crossover operation
  • evaluate fitness of offspring
  • apply replacement rule (fittest retained) and iterate till stable

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genetic algorithms27
Genetic Algorithms
  • GA components
    • Encoding or representation – binary, list, tree etc
    • Fitness function selection – use of rank transforms
    • Population initialisation
    • Selection: roulette, tournament, uniform random
    • Reproduction
    • Crossover e.g. A = [a b c d e f g h] B = [1 2 3 4 5 6 7 8]

and the crossover point is 3, the following children are generated:

child 1 = [a b c 4 5 6 7 8] child 2= [1 2 3 d e f g h]

    • Mutation
    • Local search
    • Termination

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genetic algorithms28
Genetic Algorithms
  • GAs: application areas
    • TSP (as above)
    • Clustering
    • Map labelling
    • Optimum location with capacity constraints
    • Concept can be extended to alleles that are expressions or program elements rather than numerical values  Genetic programming

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