LFD Book Forum

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Homework 1 (http://book.caltech.edu/bookforum/forumdisplay.php?f=130)
-   -   Does the perceptron algorithm allow w[0] 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[0] to obtain non-integer values?
 
Since the perceptron algorithm updates each of the weights with y_n * x_n, then it updates w[0] with

w[0] <- w[0] + y_n * x_n[0]

and y_n is +/- 1, and we have defined x_n[0] = 1.

Then, it seems that w[0] may only ever attain values that differ from its initial value by an integer. For example, if we initialized w[0] = 0, then w[0] 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[0] 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[0] with

w[0] <- w[0] + y_n * x_n[0]

and y_n is +/- 1, and we have defined x_n[0] = 1.

Then, it seems that w[0] may only ever attain values that differ from its initial value by an integer. For example, if we initialized w[0] = 0, then w[0] 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 w_0 is equivalent to a non-integer value in a properly scaled version.


All times are GMT -7. The time now is 02:40 AM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.