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Soft computing

Soft computing

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Soft computing

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  1. Soft computing Lecture 6 Introduction to neural networks

  2. Disadvantages of fuzzy systems • Difficulties of formalized of fuzzy sets and linguistic variables • Its description is subjective, • Its description depend on context, features of situation and inference, • Fuzzy systems are keeping knowledge base systems with its main disadvantage – orientation on formalizing of knowledge by anybody (expert) and unable to learn • Way out is to use neural networks instead of its or together with its

  3. motor cortex association cortex visual cortex to motor output

  4. Signal: action potential (spike) action potential 10 000 neurons 3 km wires 1mm

  5. Formal neuron by MacCallock-Pitts xi – binary signal

  6. Non-binary inputs or

  7. Geometric interpretation of TLU action

  8. Training of TLU w’i = wi + ∆wi repeat for each training vector pair (v, t) evaluate the output y when v is input to the TLU if y ≠ t then form a new weight vector w ’according to formulas above else do nothing end if end for until y = t for all vectors

  9. Perceptron of Rosenblatt The A-units can be assigned any arbitrary Boolean functionality but are fixed - they do not learn.

  10. Classification

  11. 1. The four classes may separated by 2-hyperplanes 2. (A,B) was linearly separable from (C,D) and (A,D) was linearly separable from (B,C).

  12. wij(t+1)=wij(t)+xj(di-yi) Task of minimization of function: Rule of training of Widrow-Hoff It was implemented in ADALINE (Adaptive Linear Elements)

  13. Classification of models of neural networks • Tutoring • Supervised learning • Unsupervised learning • Reinforcement learning • Structure • Forward or recurrent networks • With regular or not links • Describes by full-links graph or no • Static or dynamic (constructive learning) • Signals (inputs or outputs, hidden) • Binary • Analog • Time • Discrete • Continuous • Kind of giving of inputs and getting of outputs • State of synapses • State of neurons • Weights of synapses

  14. Tasks solved by neural networks • Classification • In diagnostic systems • In monitoring systems • In recognition systems of robots • In speech recognition • In security systems for authentication • Clusterization • In Data Mining for extracting of knowledge • In search systems for indexing of documents • Prediction • In financial analyzing • In control systems of mobile robots • Approximation • In control systems of technological processes

  15. Comparison of Computing Approaches

  16. Comparisons of Expert Systems and Neural Networks

  17. Advantages of neural computing • Clearly the style of processing is completely dierent - it is more akin to signal processing than symbol processing. The combining of signals and producing new ones is to be contrasted with the execution of instructions stored in a memory. • Information is stored in a set of weights rather than a program. The weights are supposed to adapt when the net is shown examples from a training set. • Nets are robust in the presence of noise: small changes in an input signal will not drastically aect a node's output. • Nets are robust in the presence of hardware failure: a change in a weight may only aect the output for a few of the possible input patterns. • High level concepts will be represented as a pattern of activity across many nodes rather than as the contents of a small portion of computer memory. • The net can deal with `unseen' patterns and generalise from the training set. • Nets are good at `perceptual' tasks and associative recall. These are just the tasks that the symbolic approach has diculties with.