Answered: Two layers neural networks consist of 3…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Two layers neural networks consist of 3 input neurons and one output neuron. The input vector is (x1, x2, x3) where x3 is always =1.0.

x1, x2 and the desired output d are given by the table below.

When using the initial weight vector w = (1.0, 1.0, -3.0) there was an error as shown in the figure. The equation for the decision boundary was: x1*1 + x2*1 - 1*3=0.

, (i.e. net = x1*w1+x2*w2+x3*w3), f(net) is the sign of net

What are the new values of the vector w after the first input (1,1,1), note that input x3 is always 1.0?
What are the new values of the vector w after the second input (9.4, 6.4, 1.0)?
Suggest a vector w such that the total error is ZERO for the 10 points.

Two layers neural networks consist of 3 input neurons and one output neuron. The input vector is
(x1, x2, x3) where x3 is always =1.0.
x1, x2 and the desired output d are given by the table below.
When using the initial weight vector w = (1.0, 1.0, -3.0) there was an error as shown in the
figure. The equation for the decision boundary was: x1*1 + x2*1 - 1*3=0.
net = Σx; w₁, (i.e. net = x1*wl+x2*w2+x3*w3), f(net) is the sign of net
W = W.1+ c(dt-1-sign (wt.1.xt.1)) xt.1
Use:
What are the new values of the vector w after the first input (1,1,1), note that input x3 is
always 1.0?
What are the new values of the vector w after the second input (9.4, 6.4, 1.0)?
Suggest a vector w such that the total error is ZERO for the 10 points.
X₁
1.0
9.4
2.5
8.0
0.5
7.9
7.0
2.8
1.2
7.8
x2
1.0
6.4
2.1
7.7
2.2
8.4
7.0
0.8
3.0
6.1
Output
1
-1
1
-1
1
-1
-1
1
1
-1
10.0
32 5.0-
where c is the traing factor c=0.2
0.0-
0.0
P
A
f(net)=0
5.0
10.0

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