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## PowerPoint Slideshow about ' Neural Networks' - ashlyn

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Introduction

- Neural networks and their use to classification and other tasks
- ICS AS CR
- Theoretical computer science
- Neural networks, genetic alg. and nonlinear methods
- Numeric algorithms ..1 mil. eq.
- Fuzzy sets, approximate reasoning, possibility th.
- Applications: Nuclear science, Ecology, Meteorology, Reliability in machinery, Medical informatics …

Institute of Computer Science, Prague

Structure of talk

- NN classification
- Some theory
- Interesting paradigms
- NN and statistics
- NN and optimization and genetic algorithms
- About application of NN
- Conlusions

Institute of Computer Science, Prague

Associative memories

General

Predictors

Auto-associative

Hetero-associative

Classifiers

Teacher

MLP-BP

RBF

GMDH

NNSU

Marks

Klán

Hopfield

Perceptron(*)

Hamming

No teacher

Kohonen

CarpentierGrossberg

(SOM)

NE

Kohonen

(NE)

Signals

Continuous, real-valued

Binary, multi-valued (continuous)

NN classificationNE – not existing. Associated response can be arbitrary and then must be given - by teacher

Feed-forward, recurrent

Fixed structure - growing

Institute of Computer Science, Prague

Some theory

Kolmogorov theorem

Kůrková – Theorem

Sigmoid transfer function

Institute of Computer Science, Prague

MLP - BP

Three layer - Single hidden layer MLP – 4 layer – 2 hidden

Other paradigms have its own theory – another

Institute of Computer Science, Prague

Interesting paradigms

Paradigm – general notion on structure, functions and algorithms of NN

- MLP - BP
- RBF
- GMDH
- NNSU

All: approximators

Approximator + thresholding = Classifier

Institute of Computer Science, Prague

MLP - BP

MLP – error Back Propagation

coefficients , (0,1)

- Lavenberg-Marquart

- Optimization tools

MLP with jump transfer function

- Optimization

Feed – forward (in recall)

Matlab, NeuralWorks, …

Good when default is sufficient or when network is well tuned: Layers, neurons, ,

Institute of Computer Science, Prague

RBF

- Structure same as in MLP
- Bell-shaped transfer function (Gauss)
- Number and positions of centers: random – cluster analysis
- “broadness” of that bell
- Size of individual bells
- Learning methods
- Theory similar to MLP
- Matlab, NeuralWorks, …

Good when default is sufficient or when network is well tuned : Layers mostly one hidden, # neurons, transfer function, proper cluster analysis (fixed No. of clusters, variable? Near – Far metric or criteria)

Institute of Computer Science, Prague

GMDH 1 (…5)

Group Method Data Handling

- Group – initially a pair of signals only
- “per partes” or successive polynomial approximator
- Growing network
- “parameterless” – parameter-barren
- No. of new neurons in each layer only (processing time)
- (output limits, stopping rule parameters)
- Overtraining – learning set is split to
- Adjusting set
- Evaluation set

GMDH 2-5: neuron, growing network, learning strategy, variants

Institute of Computer Science, Prague

GMDH 2 – neuron

- Two inputs x1, x2 only
- True inputs
- Outputs from neurons of the preceding layer
- Full second order polynomial

y = a x12 + b x1 x2 + c x22 + d x1 + e x2 + f

y = neuron’s output

- n inputs => n(n-1)/2 neurons in the first layer
- Number of neurons grows exponentially
- Order of resulting polynomial grows exponentially: 2, 4, 8, 16, 32, …
- Ivakhnenko polynomials … some elements are missing

Institute of Computer Science, Prague

GMDH 3 – learning a neuron

- Matrix of data: inputs and desired value

u1, u2 , u3, …, un,y sample 1

u1, u2 , u3, …, un,y sample 1

…. sample m

- A pair of two u’s are neuron’s inputs x1, x2
- m approximating equations, one for each sample

a x12 + b x1 x2 + c x22 + d x1 + e x2 + f = y

- Matrix X = Y= (a, b, c, d, e, f)t
- Each row of X is x12+x1x2+x22+x1+x2+1
- LMS solution = (XtX)-1XtY
- If XtX is singular, we omit this neuron

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GMDH 5 learn. strategy

Problem: Number of neurons grows exponentially

NN=n(n-1)2

- Let the first layer of neurons grow unlimited
- In next rows:
- [learning set split to adjusting set and evaluating set]
- Compute parameters a,…f using adjusting set
- Evaluate error using evaluating set and sort
- Select some n best neurons and delete the others
- Build the next layer OR
- Stop learning if stopping condition is met.

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GMDH 6 learn. Strategy 2

Select some n best neurons and delete the others

Control parameter of GMDH network

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GMDH 7 - variants

- Basic – full quadratic polynomial – Ivakh. poly
- Cubic, Fourth order simplified …
- Reach higher order in less layers and less params
- Different stopping rules
- Different ratio of sizes of adjusting set and evaluating set

Institute of Computer Science, Prague

NNSU GA

Neural Network with Switching Units

learned by the use of Genetic Algorithm

- Approximator by lot of local hyper-planes; today also by local more general hyper-surfaces
- Feed-forward network
- Originally derived from MLP for optical implementation
- Structure looks like columns above individual inputs
- More … František

Institute of Computer Science, Prague

Learning and testing set

- Learning set
- Adjusting (tuning) set
- Evaluation set
- Testing set

One data set – the splitting influences results

- Fair evaluation problem

Institute of Computer Science, Prague

NN and statistics

- MLP-BP mean squared error minimization
- Sum of errors squared … MSE criterion
- Hamming distance for (pure) classifiers
- No other statistical criteria or tests are in NN:
- NN transforms data, generates mapping
- statistical criteria or tests are outside NN (2, K-S, C-vM,…)

Is NN good for K-S test? … is y=sin(x) good for 2 test?

- Bayes classifiers, k-th nearest neighbor, kernel methods …

Institute of Computer Science, Prague

NN and optimization and genetic algorithms

Learning is an optimization procedure

- Specific to given NN
- General optimization systems or methods
- Whole NN
- Parts – GMDH and NNSU - linear regression
- Genetic algorithm
- Not only parameters, the structure, too
- May be faster than iterations

Institute of Computer Science, Prague

About application of NN

- Soft problems
- Nonlinear
- Lot of noise
- Problematic variables
- Mutual dependence of variables
- Application areas
- Economy
- Pattern recognition
- Robotics
- Particle physics
- …

Institute of Computer Science, Prague

Strategy when using NN

- For “soft problems” only
- NOT for
- Exact function generation
- periodic signals etc.
- First subtract all “systematics”
- Nearly noise remains
- Approximate this nearly noise
- Add back all systematics
- Understand your paradigm
- Tune it patiently or
- Use “parameterless” paradigm

Institute of Computer Science, Prague

Conlusions

- Powerfull tool
- Good when well used
- Simple paradigm, complex behavior
- Special tool
- Approximator
- Classifier
- Universal tool
- Very different problems
- Soft problems

Institute of Computer Science, Prague

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