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Neural Networks

Neural Networks. and. Pattern Recognition. Giansalvo EXIN Cirrincione. unit #1. Neural network definition. A neural network is a parallel distributed processor with adaptive capabilities (weights or states). nucleus. cell body. axon. dendrites. The neuron. The neuron. The neuron.

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Neural Networks

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  1. Neural Networks and

  2. Pattern Recognition

  3. Giansalvo EXIN Cirrincione

  4. unit #1

  5. Neural network definition A neural network is a parallel distributed processor with adaptive capabilities (weights or states)

  6. nucleus cell body axon dendrites The neuron

  7. The neuron

  8. The neuron

  9. The neuron

  10. The neuron Other activation functions

  11. input units hidden units output units The neuron

  12. Neural networks general

  13. Neural networks perceptron

  14. Neural networks feedforward multilayer perceptron

  15. Neural networks radial basis function

  16. Neural networks self-organizing map

  17. Neural networks recurrent Hopfield network

  18. Learning supervised unsupervised renforcement

  19. target teacher input supervised learning training set sum-of-squares error function output error

  20. supervised learning

  21. teacher input unsupervised learning training set self organization

  22. Pattern Recognition

  23. Pattern recognition is the science that concerns the description or classification (recognition) of measurements • PR approaches: • statistical (StatPR) • syntactic (SyntPR) • neural (NeurPR) • PR applications: • image analysis • computer vision • seismic analysis • radar signal classification/analysis • face recognition • speech recognition/understanding • fingerprint identification • character recognition • handwriting analysis • electrocardiographic analysis • medical diagnosis • PR overlaps: • adaptive signal processing • artificial intelligence • neural modeling • optimization/estimation theory • automata theory • fuzzy sets • structural modeling • formal languages

  24. PR may be characterized as an information reduction, information mapping or information labelling process

  25. to allow patterns from different classes to share attributes overlap also probabilistic abstract representation of pattern mappings • observations • measured patterns • features

  26. Given measurement mi identify and invert mappings M and Gi for all i cluster analysis limit ambiguity In practice, these mappings are not functions; even if they were, they are seldom 1:1, onto or invertible

  27. scatter plot similarity measures

  28. feature space

  29. classification description It assigns input data into one or more of c prespecified classes based on extraction of significant features or attributes and the processing or analysis of these attributes recognition noise pattern class DEFINITIONS

  30. DEFINITIONS classification description It is the ability to classify. Often PR problems are formulated with a c+1st class corresponding to the unclassifiable or don’t know or can’t decide class recognition noise pattern class

  31. DEFINITIONS classification description It is alternative to classification where a structural description of the input pattern is desired. It is common to resort to linguistic or structural models in description recognition noise pattern class

  32. DEFINITIONS classification description It is a set of patterns (hopefully sharing some common attributes) known to originate from the same source C. recognition noise pattern class

  33. DEFINITIONS classification description • Generalized concept including: • distorsions or errors in the input • errors in preprocessing • errors in feature extraction • errors in training data recognition noise pattern class

  34. decision boundaries A classifier partitions feature space into class-labeled decision regions

  35. PR neural approach a supervised example

  36. neural networks stat PR From the perspective of PR, neural networks can be regarded as an extension of the many conventional techniques which have been developed over several decades. Historically, many concepts in neural computing have been inspired by studies of biological networks. The perspective of stat PR, however, offers a much more direct and principled route to many of the same concepts.

  37. neural networks stat PR Example #1 The sum-and-threshold model of a neuron arises naturally as the optimal discriminant function needed to distinguish two classes whose distributions are normal with equal covariance matrices Historically, many concepts in neural computing have been inspired by studies of biological networks. The perspective of stat PR, however, offers a much more direct and principled route to many of the same concepts.

  38. neural networks stat PR Example #2 The logistic sigmoid is precisely the function needed to allow the output of a network to be interpreted as probability, when the distribution of hidden unit activations is governed by a member of the exponential family. Historically, many concepts in neural computing have been inspired by studies of biological networks. The perspective of stat PR, however, offers a much more direct and principled route to many of the same concepts.

  39. FINE

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