1 Artificial Neural Networks Sanun Srisuk 42973003 [email protected] EECP0720 Expert Systems – Artificial Neural Networks.

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Artificial Neural Networks

Sanun Srisuk 42973003

[email protected]

EECP0720 Expert Systems – Artificial Neural Networks

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Introduction

Artificial neural networks (ANNs) provide a general, practical method for learning real-valued, discrete-valued, and vector-valued functions from examples. Algorithms such as BACKPROPAGATION use gradient descent to tune network parameters to best fit a training set of input-output pairs. ANN learning is robust to errors in the training data and has been successfully applied to problems such as face recognition/detection, speech recognition, and learning robot control strategies.


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Autonomous Vehicle SteeringEECP0720 Expert Systems – Artificial Neural Networks

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Characteristics of ANNs

Instances are represented by many attribute-value pairs.

The target function output may be discrete-valued, real-valued, or a vector of several real- or discrete-valued attributes.

The training examples may contain errors.

Long training times are acceptable.

Fast evaluation of the learned target function may be required.

The ability of humans to understand the learned target function is not important.


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One type of ANN system is based on a unit called a perceptron.

The perceptron function can sometimes be written as

The space H of candidate hypotheses considered in perceptron learning is the set of all possible real-valued weight vectors.

PerceptronsEECP0720 Expert Systems – Artificial Neural Networks

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Representational Power of Perceptrons


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Decision surfaceEECP0720 Expert Systems – Artificial Neural Networks

linear decision surface nonlinear decision surface

Programming Example of Decision Surface

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The Perceptron Training RuleOne way to learn an acceptable weight vector is to begin with random weights, then iteratively apply the perceptron to each training example, modifying the perceptron weights whenever it misclassifies an example. This process is repeated, iterating through the training examples as many times as needed until the perceptron classifies all training examples correctly. Weights are modified at each step according to the perceptron training rule, which revises the weight associated with input according to the rule


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Gradient Descent and Delta Rule

The delta training rule is best understood by considering the task of training an unthresholded perceptron; that is, a linear unit for which the output o is given by

In order to derive a weight learning rule for linear units, let us begin by specifying a measure for the training error of a hypothesis (weight vector), relative to the training examples.


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Visualizing the Hypothesis SpaceEECP0720 Expert Systems – Artificial Neural Networks

minimum error

initial weight vector by random

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Derivation of the Gradient Descent Rule

The vector derivative is called the gradient of E with respect to , written

The gradient specifies the direction that produces the steepest increase in E. The negative of this vector therefore gives the direction of steepest decrease. The training rule for gradient descent is


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Derivation of the Gradient Descent Rule (cont.)

The negative sign is presented because we want to move the weight vector in the direction that decreases E. This training rule can also written in its component form

which makes it clear that steepest descent is achieved by altering each component of in proportion to .


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The vector of derivatives that form the gradient can be obtained by differentiating E


Derivation of the Gradient Descent Rule (cont.)

The weight update rule for standard gradient descent can be summarized as

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Stochastic Approximation to Gradient DescentEECP0720 Expert Systems – Artificial Neural Networks

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Summary of Perceptron

Perceptron training rule guaranteed to succeed if

training examples are linearly separable

sufficiently small learning rate

Linear unit training rule uses gradient descent

guaranteed to converge to hypothesis with minimum squared error

given sufficiently small learning rate

even when training data contains noise


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BACKPROPAGATION Algorithm


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Error Function

The Backpropagation algorithm learns the weights for a multilayer network, given a network with a fixed set of units and interconnections. It employs gradient descent to attempt to minimize the squared error between the network output values and the target values for those outputs. We begin by redefining E to sum the errors over all of the network output units

where outputs is the set of output units in the network, and tkd and okd are the target and output values associated with the kth output unit and training example d.


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Architecture of Backpropagation EECP0720 Expert Systems – Artificial Neural Networks

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Backpropagation Learning Algorithm


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Backpropagation Learning Algorithm (cont.)


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Face Detection using Neural NetworksEECP0720 Expert Systems – Artificial Neural Networks

Neural

Network

Face Database

Non-Face Database

Training ProcessOutput=1, for face database

Output=0, for non-face database

Face

orNon-

Face?

Test

ing P

roc e

ss

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End of Presentation


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Derivation of Backpropagation


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Derivation of Backpropagation (cont.)


1 Artificial Neural Networks Sanun Srisuk 42973003 [email protected] EECP0720 Expert Systems – Artificial Neural Networks.

Documents

training examples

training error

training data

perceptron learning

perceptron function

training set of input

perceptron weights

long training times