LFD Book Forum Question 9 with triangles
 User Name Remember Me? Password
 FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
04-18-2013, 02:41 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Question 9 with triangles

I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions.

One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside -1 and three points surrounding it +1 and it won't work.

Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
#2
04-18-2013, 02:54 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: *ANSWER* Question 9 with triangles

Quote:
 Originally Posted by Michael Reach I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions. One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside -1 and three points surrounding it +1 and it won't work. Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
Take a look at this thread:

http://book.caltech.edu/bookforum/showthread.php?t=2606

and we can discuss this further.
__________________
Where everyone thinks alike, no one thinks very much
#3
04-18-2013, 03:59 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: *ANSWER* Question 9 with triangles

Well, I see that an N-gon (won't say which) is easy to shatter, and the (N+2)-gon is easy to see that it can't be shattered. So I know which of the answers to choose, but I'm still not clear on the (N+1)-gon in between.
#4
04-18-2013, 04:28 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Question 9 with triangles

I took out the *ANSWER* warning since the discussion seems safe so far.
__________________
Where everyone thinks alike, no one thinks very much
#5
04-18-2013, 04:48 PM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: Question 9 with triangles

Ah, well, I guess an (N+1)-gon works too - brute force check on all triangles. Not very elegant, but it works.
#6
04-19-2013, 08:02 AM
 Michael Reach Senior Member Join Date: Apr 2013 Location: Baltimore, Maryland, USA Posts: 71
Re: Question 9 with triangles

I was having about the same troubles figuring out the perceptron problem, but I think looking in the book (*ANSWER*) helps a lot.

 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 07:30 PM.

 Contact Us - LFD Book - Top

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, 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.