Knowledge-Based Systems

198 Chapter 7 ConneCtionist Models

Definition

Two sets of points A and B in an n-dimensional space are linearly separable

if n + 1 real numbers W

1

,…,W

n+1

exist such that every point (X

1

, X

2

,…, X

n

)

∈ A satisfies ∑W

i

X

i

>= W

n+1

and every point (X

1

, X

2

,…, X

n

) ∈ B satisfies

∑W

i

X

i

< W

n+1

.

7.4.4 Perceptron Learning Rule

Perceptron output (assuming a single output unit) is determined by separat-

ing a hyperplane defined by W

1

*X

1

+ W

2

*X

2

+ … + W

n

*X

n

= t; hence, a

perceptron can only learn functions that are linearly separable. A perceptron

learns by using the update-weights function given by the formula:

W

i

= W

i

+ d W

i

Where d W

i

= a (T – O) X

i

Xi is the input associated with the ith input unit. T is the desired output.

α is a constant between 0 and 1 ...