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Neural network architectures and learning algorithms Author : Bogdan M. Wilamowski Source : IEEE INDUSTRIAL ELECTRONICS MAGAZINE Date : 2011/11/22 Presenter : 林哲緯 1

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Outline Neural Architectures Parity-N Problem Suitable Architectures Use Minimum Network Size Conclusion 2

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Neural Architectures 3 Lecture Notes for E Alpaydın 2010 Introduction to Machine Learning 2e © The MIT Press (V1.0)

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Neural Architectures 4 Lecture Notes for E Alpaydın 2010 Introduction to Machine Learning 2e © The MIT Press (V1.0)

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Neural Architectures 5 Lecture Notes for E Alpaydın 2010 Introduction to Machine Learning 2e © The MIT Press (V1.0)

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error back propagation(EBP) algorithm – multilayer perceptron (MLP) 6 Lecture Notes for E Alpaydın 2010 Introduction to Machine Learning 2e © The MIT Press (V1.0)

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multilayer perceptron (MLP) 7 Neural network architectures and learning algorithms, Wilamowski, B.M. MLP-type architecture 3-3-4-1(without connections across layers)

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neuron by neuron(NBN) algorithm – bridged multilayer perceptron (BMLP) – fully connected cascade (FCC) 8 Neural network architectures and learning algorithms, Wilamowski, B.M. arbitrarily connected network

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neuron by neuron(NBN) algorithm Levenberg–Marquardt(LM) algorithm – Improve nonlinear function of least square – Forward & Backward Computation Jacobian Matrix – Forward-Only Computation 9

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bridged multilayer perceptron (BMLP) 10 Neural network architectures and learning algorithms, Wilamowski, B.M. BMLP architecture 3=3=4=1(with connections across layers marked by dotted lines)

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fully connected cascade (FCC) 11 Neural network architectures and learning algorithms, Wilamowski, B.M. Bipolar neural network for parity-8 problem in a FCC architecture

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Outline Neural Architectures Parity-N Problem Suitable Architectures Use Minimum Network Size Conclusion 12

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parity-8 problem MLP 8*9 + 9 = 81 weights BMLP 4*9 + 8 + 4 + 1 = 49 weights 13 Neural network architectures and learning algorithms, Wilamowski, B.M.

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parity-8 problem 9 + 10 + 11 + 12 = 42 weights 14 Neural network architectures and learning algorithms, Wilamowski, B.M.

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parity-17 problem MLP architecture needs 18 neurons BMLP architecture with connections across hidden layers needs 9 neurons FCC architecture needs only 5 neurons 15

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parity-N problem MLP architectures BMLP architectures FCC architectures nn = neurons nw = weights 16 Neural network architectures and learning algorithms, Wilamowski, B.M.

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Outline Neural Architectures Parity-N Problem Suitable Architectures Use Minimum Network Size Conclusion 17

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suitable architectures For a limited number of neurons, FCC neural networks are the most powerful architectures, but this does not mean that they are the only suitable architectures 18

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suitable architectures if the two weights marked by red dotted lines – signal has to be propagated by fewer layers 19 Neural network architectures and learning algorithms, Wilamowski, B.M.

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Outline Neural Architectures Parity-N Problem Suitable Architectures Use Minimum Network Size Conclusion 20

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Use Minimum Network Size receive a close-to-optimum answer for all patterns that were never used in training generalization abilities 21

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Case Study 22 Neural network architectures and learning algorithms, Wilamowski, B.M. TSK fuzzy controller: (a) Required control surface (b) 8*6 = 48 defuzzification rules TSK fuzzy controller: (a) Trapezoidal membership functions (b) Triangular membership functions

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Case Study 23 Neural network architectures and learning algorithms, Wilamowski, B.M. (a) 3 neurons in cascade (12 weights), training error = 0.21049 (b) 4 neurons in cascade (18 weights), training error = 0.049061 (a) 5 neurons in cascade (25 weights), training error = 0.023973 (b) 8 neurons in cascade (52 weights), training error = 1.118E-005

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time complexity NBN algorithm can train neural networks 1,000 times faster than the EBP algorithm. 24 Neural network architectures and learning algorithms, Wilamowski, B.M. (a)EBP algorithm, average solution time of 4.2s, and average 4188.3 iterations (b)NBN algorithm, average solution time of 2.4ms, and average 5.73 iterations

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two-spiral problem 25 Neural network architectures and learning algorithms, Wilamowski, B.M. NBN algorithm using FCC architecture 244 iterations and 0.913s EBP algorithm using FCC architecture 30,8225 iterations and 342.7s

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Outline Neural Architectures Parity-N Problem Suitable Architectures Use Minimum Network Size Conclusion 26

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Conclusions FCC or BMLP architectures are not only more powerful but also easier to train use networks with a minimum number of neurons NBN have to invert a nw*nw matrix, but 500 weights are limit now. 27

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