# CSCI-495 Artificial Intelligence

Τεχνίτη Νοημοσύνη και Ρομποτική

19 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

84 εμφανίσεις

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

:

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

Single
-
Input Neuron

:

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

:

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

Multiple
-
Input Neuron

:

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

Abbreviated Notation

:

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

:

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

Two
-
Input Case First

:

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

Decision Boundary

Apple/Banana Sorter

:

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

Apple/Banana Sorter

:

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