Retinal Prosthesis Dissertation - Student Home Pages

This is also the Cartesian co-ordinate system method of computing the dot product of
the input vector and the weight vector.
Conclusion: the weighted sum most commonly used in the transfer functions of
neural networks is the same as computing the dot product of the input pattern vector
with the receiving neurons weight vector.
Alternatively x ● w = |x| x |w| Cos Ø where Ø is the angle between the input vector
and the weight vector. N.B: From trigonometry cos is +ve if the angle is < ± 90° and
–ve otherwise.”
w x w x w x 0
(7)
0 0 1 1 2 2
This can be rearranged to give:
w
2x2
w1
x1
w0
x0
(8)
w w
x
(9)
1 0
2
x1
x0
w2
w2
Comparing equation (9) with equation (5) i.e. x 2 – 5.875x 1 – 2.35 = 0 and putting
x 1gives
w1
w0
0
m , and c
w2
w2
There is no unique solution to these two equations. Just as an example, let us start by
assuming that w 1 0 then equation (5) is obtained from the values:
2
.
w
0
2.35 and w1
5.875
With these weights the unit can discriminate between the two classes of objects. A
single unit with these weights classifies objects A and B in the preceding figure 13.
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