CSCI-495 Artificial Intelligence

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19 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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CSCI
-
495

Artificial Intelligence


Lecture





29

Neural Networks

Biology


The brain uses massively parallel computation



10
11

neurons in the brain



10
4

connections per neuron

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Single
-
Input Neuron

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Single
-
Input Neuron








w

= 3,
p

= 2,
b

=
-
1.5, what is
a
?


Note that both
w

and
b

are adjustable scalar parameters
of the neuron. Typically the transfer function is chosen
by the designer and the parameters are adjusted by
some learning rule so that the input/output of the neuron
meets some specific goal


Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Multiple
-
Input Neuron

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Abbreviated Notation

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Linear Classifiers


Linear classifier


single linear decision boundary
(for 2
-
class case)


We can always represent a linear decision boundary by a
linear equation:


w
1
p
1

+
w
1
p
2

+ … +
w
1
p
R

+
b
=

S

w
i

p
i

+
b
=
Wp

+
b
= 0




In R dimensions, this defines a (R
-
1) dimensional
hyperplane


R=3, we get a plane; R=2, we get a line


For prediction we simply see if
S

w
i

p
i

+
b
> 0


The
w
i

are the weights (parameters)


Learning consists of searching in the R
-
dimensional weight space
for the set of weights (the linear boundary) that minimizes an error
measure


(DIAGRAM DONE IN CLASS)


Perceptron

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Two
-
Input Case First

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Decision Boundary

Apple/Banana Sorter

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Apple/Banana Sorter

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Prototype Banana

Prototype Apple

Shape
: {1 : round ;
-
1 : elliptical}

Texture
: {1 : smooth ;
-
1 : rough}

Weight
: {1 : > 1 lb. ;
-
1 : < 1 lb.}

Measurement Vector

The decision boundary should separate the prototype vectors

The

weight

vector

should

be

orthogonal

to

the

decision

boundary,

and

should

point

in

the

direction

of

the

vector

which

should

produce

an

output

of

1
.

The

bias

determines

the

position

of

the

boundary


(
DONE

IN

CLASS
)

Testing the Network

Slide Adapted from
:

M. Hagan, H. Demuth, M. Beale,
Neural Network Design


Banana:

Apple:

“Rough” Banana: