LFD Book Forum Does the perceptron algorithm allow w[0] to obtain non-integer values?
 User Name Remember Me? Password
 Register FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
01-14-2013, 10:21 PM
 carpdiem Member Join Date: Apr 2012 Posts: 16
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?
#2
01-14-2013, 10:28 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Does the perceptron algorithm allow w[0] to obtain non-integer values?

Quote:
 Originally Posted by carpdiem 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 is equivalent to a non-integer value in a properly scaled version.
__________________
Where everyone thinks alike, no one thinks very much

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General     General Discussion of Machine Learning     Free Additional Material         Dynamic e-Chapters         Dynamic e-Appendices Course Discussions     Online LFD course         General comments on the course         Homework 1         Homework 2         Homework 3         Homework 4         Homework 5         Homework 6         Homework 7         Homework 8         The Final         Create New Homework Problems Book Feedback - Learning From Data     General comments on the book     Chapter 1 - The Learning Problem     Chapter 2 - Training versus Testing     Chapter 3 - The Linear Model     Chapter 4 - Overfitting     Chapter 5 - Three Learning Principles     e-Chapter 6 - Similarity Based Methods     e-Chapter 7 - Neural Networks     e-Chapter 8 - Support Vector Machines     e-Chapter 9 - Learning Aides     Appendix and Notation     e-Appendices

All times are GMT -7. The time now is 07:10 AM.

 Contact Us - LFD Book - Top