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1 Image Classification MSc Image Processing Assignment March 2003

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2 Summary Introduction Classification using neural networks Perceptron Multilayer perceptron Applications

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3 Introduction Definition Assignment of a physical object to one of several pre-specified categories Unsupervised Supervised For more details See Image Processing course

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4 Classification Supervised Pattern recognition Algebraic Unsupervised k-means Fuzzy k-mean ParametricNon-parametricNeural nets Bayes Minimum distance K-nearest neighbour Decision trees SVM Classification

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5 Neural nets Inspired by the human brain Useful for Classification Regression Optimization …

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6 Model x=(x 1 …x n ) input vector w=(w 0 …w n ) weight vector f activation function x1x1 xnxn wnwn w1w1 f y=f( w i x i + w 0 )

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7 Perceptron f=sign 1 w 1 x 1 +w 2 x 2 +w 0 =0 2 inputs

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8 Perceptron (2) Example: AND function x1x1 x2x x1x1 x2x2 w 2 =1 w 1 =1 sign w 0 =1 w 1 =1 x2x2 -1+x1+x2=0 + - x1x1

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9 Algorithm Minimise set of misclassified examples Gradient ascent Converges if data linearly separable Demo Perceptron (3)

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10 Perceptron (4) XOR problem Problem when Data non-linearly separable Solution: change activation function For more details Matlab classification toolbox

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11 Multilayer Perceptron (MLP) Able to model complex non-linear functions Hidden layers with neurons Backpropagation algorithm inputs outputs

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12 MLP (2) f=sigmoid w0w0 w1w1 w2w2 y x1x1 x2x2

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13 MLP demo Matlab Classification Toolbox Handwritten digits classification Discriminate between 10 digits

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14 MLP demo (2) Pre-processing Feature extraction Choice of neural network Training Test For more details See our program 10 neurons OUTPUTOUTPUT FEATURESFEATURES 8 features Input layer 1 st hidden layer Output layer 2 nd hidden layer

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15 MLP performance Able to model complex, nonlinear mapping and classification Can be trained by examples, no mathematical description needed In practice, shows good results

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16 MLP limitations Extensive training data must be available Computation time Curse of dimensionality Generalisation Overfitting To go further See Neural Network Toolbox, demo on generalisation

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17 A few applications Medicine Defence Radar & Sonar Finance …

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18 Thank you.

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