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-   -   Does the perceptron algorithm allow w to obtain non-integer values? (http://book.caltech.edu/bookforum/showthread.php?t=3852)

 carpdiem 01-14-2013 10:21 PM

Does the perceptron algorithm allow w to obtain non-integer values?

Since the perceptron algorithm updates each of the weights with y_n * x_n, then it updates w with

w <- w + y_n * x_n

and y_n is +/- 1, and we have defined x_n = 1.

Then, it seems that w may only ever attain values that differ from its initial value by an integer. For example, if we initialized w = 0, then w could never attain a value of 1/2.

This seems like an odd limitation to the perceptron algorithm. Am I interpreting it correctly that this limitation exists, and does this limitation have any other side effects?

 yaser 01-14-2013 10:28 PM

Re: Does the perceptron algorithm allow w to obtain non-integer values?

Quote:
 Originally Posted by carpdiem (Post 8675) Since the perceptron algorithm updates each of the weights with y_n * x_n, then it updates w with w <- w + y_n * x_n and y_n is +/- 1, and we have defined x_n = 1. Then, it seems that w may only ever attain values that differ from its initial value by an integer. For example, if we initialized w = 0, then w could never attain a value of 1/2. This seems like an odd limitation to the perceptron algorithm. Am I interpreting it correctly that this limitation exists, and does this limitation have any other side effects?
You are right, but this is not really a limitation since scaling the weight vector up or down leads to an equivalent perceptron, so an integer value of is equivalent to a non-integer value in a properly scaled version.

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