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Chapter 8 Geocomputation Part B: Artificial Neural Networks (ANNs) & Genetic Algorithms (GAs)

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3 rd editionwww.spatialanalysisonline.com2 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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3 rd editionwww.spatialanalysisonline.com3 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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3 rd editionwww.spatialanalysisonline.com4 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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3 rd editionwww.spatialanalysisonline.com5 Artificial Neural Networks Hence at each output node (hidden or final) a two-step process takes place:

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3 rd editionwww.spatialanalysisonline.com6 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 w ij are weights to be determined, b 1 =1, and the x i are the observed input values

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3 rd editionwww.spatialanalysisonline.com7 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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3 rd editionwww.spatialanalysisonline.com8 Artificial Neural Networks We can now compute the output layer values as the weighted sum Suppose we have known input values x 1 =1, x 2 =-3, x 3 =5, and known outputs of 0 and 1. Can we select the weights to ensure the inputs generate the known outputs? Suggestion:

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3 rd editionwww.spatialanalysisonline.com9 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 e 2 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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3 rd editionwww.spatialanalysisonline.com10 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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3 rd editionwww.spatialanalysisonline.com11 Artificial Neural Networks MLP: Example 1 function approximation source datafitted solution curveRMSE vs epochs

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3 rd editionwww.spatialanalysisonline.com12 Artificial Neural Networks MLP Example 2: LCM

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3 rd editionwww.spatialanalysisonline.com13 Artificial Neural Networks MLP Example 2: LCM

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3 rd editionwww.spatialanalysisonline.com14 Artificial Neural Networks MLP Example 2: LCM

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3 rd editionwww.spatialanalysisonline.com15 Artificial Neural Networks MLP Example 2: LCM weights matrix

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3 rd editionwww.spatialanalysisonline.com16 Artificial Neural Networks MLP Example 3: Spatial interaction model Generalised model: T ij =f(O i,D j,d ij ) Sample data format (log transformed):

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3 rd editionwww.spatialanalysisonline.com17 Artificial Neural Networks MLP Example 3: Spatial interaction model

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3 rd editionwww.spatialanalysisonline.com18 Artificial Neural Networks Radial Basis Function Networks Basic functional form: Gaussian RBF:

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3 rd editionwww.spatialanalysisonline.com19 Artificial Neural Networks Self organising function maps SOM as an output space Neighbourhood relations Grid size, form and topology

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3 rd editionwww.spatialanalysisonline.com20 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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3 rd editionwww.spatialanalysisonline.com21 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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3 rd editionwww.spatialanalysisonline.com22 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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3 rd editionwww.spatialanalysisonline.com23 Artificial Neural Networks Self organising function maps – Idrisi

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3 rd editionwww.spatialanalysisonline.com24 Artificial Neural Networks Self organising function maps – Idrisi

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3 rd editionwww.spatialanalysisonline.com25 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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3 rd editionwww.spatialanalysisonline.com26 Genetic Algorithms GAs: Example 1 - TSP chromosome genes allele=12 (ID of town in TSP problem set) 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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3 rd editionwww.spatialanalysisonline.com27 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 = [ ] and the crossover point is 3, the following children are generated: child 1 = [a b c ] child 2= [1 2 3 d e f g h] Mutation Local search Termination

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3 rd editionwww.spatialanalysisonline.com28 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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