LFD Book Forum Positive rays, Positive Intervals, Convex sets and the growth function
 User Name Remember Me? Password
 FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
04-21-2013, 08:38 PM
 jlaurentum Member Join Date: Apr 2013 Location: Venezuela Posts: 41
Positive rays, Positive Intervals, Convex sets and the growth function

Hello,

From what I understood in lecture 5 as the discussion progresses from positive rays to positive intervals to convex sets, the idea is to put an upper bound on all possible dichotomies. As convex sets, with an upper bound of on the growth function, are the most general scenario possible, then this is the upperbound on the growth function for perceptrons, which fall somewhere in between the positive ray- positive interval-convex sets continuum. Is my understanding correct?

Due to the political unrest in my country (Venezuela), I've not been able to get started with lecture 6 at this time, so I don't know if what I'm about to ask is addressed later on.

I imagine rotating a perceptron to the point where the boundary line is horizontal and all points fall above or bellow this boundary line:

If this is possible (the rotation), then wouldn't the growth function for linearly separable data with perceptrons be limited to , as in the case of positive rays?
#2
04-21-2013, 09:33 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Positive rays, Positive Intervals, Convex sets and the growth function

Quote:
 Originally Posted by jlaurentum Hello, From what I understood in lecture 5 as the discussion progresses from positive rays to positive intervals to convex sets, the idea is to put an upper bound on all possible dichotomies. As convex sets, with an upper bound of on the growth function, are the most general scenario possible, then this is the upperbound on the growth function for perceptrons, which fall somewhere in between the positive ray- positive interval-convex sets continuum. Is my understanding correct? Due to the political unrest in my country (Venezuela), I've not been able to get started with lecture 6 at this time, so I don't know if what I'm about to ask is addressed later on. I imagine rotating a perceptron to the point where the boundary line is horizontal and all points fall above or bellow this boundary line: If this is possible (the rotation), then wouldn't the growth function for linearly separable data with perceptrons be limited to , as in the case of positive rays?
The points on which to generate dichotomies are arbitrary but fixed. When you rotate the plane, the points are no longer fixed, but move with every new hypothesis, so it is not the same notion.

Stay safe.
__________________
Where everyone thinks alike, no one thinks very much

 Thread Tools Display Modes Hybrid 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 03:53 PM.

 Contact Us - LFD Book - Top

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.