6.5 Computer Science - Pattern Recognition THIS is the books DL content - http:/

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6.5 Computer Science - Pattern Recognition

THIS is the books DL content - http://extras.springer.com/2013/978-1-4614-5322-2

Follow the signals through the network, and find the required values of the three thresholds.

(What are the thresholds? How did you solve it? Prove that it works).

Question 6.5

Follow the signals through the network, and find the required values of the three thresholds.

(a. What are the thresholds? b. How did you solve it? c. Prove that it works).

5. Example 6.2 in the text considers a two-layer network (Fig. 6.17b) to implement the XOR function, with w11 W 12 -1; w21 W22 1: b 0.5 and b2 0.5. We could also make w 1, Wo 1 and b 0. Follow the signals through the network, and find the required values of the three thresholds. (See spreadsheet, Q6.5.xls, downloadable from http://extras.springer.com)

Explanation / Answer

I have designed and developed the thresholds values for the given signals throghout the network. I have added the comments for each section and attached the final output of the thresholds value.

Let me explain you in step-by-step manner:-

A) Step-1:

The initial step is to know the threshold function which basically determines the neural network based on the Number of input values which it receives by calculating the sum and by weighting the inputs which are together holds a data coming in the network.

The thresholds are Input X = [x1, x2] and the Weight are W = [ w1, w2,w11,w22, w12, w21 ]

B) Step-2:

The threshold value can be calculated based on the input and the weight parameters:-

Example:-

=> x1.w1 + x2.w2 + x1.w11 + x2.w22 + x1.w12 + x2.w21 = Threshold Value (THV) ;

C) Step-3:

The inputs X and the weight W is being multiplied with each input and weight parameter to achieve the threshold value of the given signal network.

Proof:-

Finally, the threshold value is being changed to the normal weight,

=> x1.w1 + x2.w2 + x1.w11 + x2.w22 + x1.w12 + x2.w21 -1. THV = 0;

=> x1.w1 + x2.w2 + x1.w11 + x2.w22 + x1.w12 + x2.w21 -1. w0= 0;

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