LFD Book Forum  

Go Back   LFD Book Forum > Course Discussions > Online LFD course > Homework 6

Reply
 
Thread Tools Display Modes
  #1  
Old 06-11-2013, 08:29 AM
skwong skwong is offline
Member
 
Join Date: Apr 2013
Location: Hong Kong
Posts: 13
Default Related to Legendre polynomials

In lect 12, we learn the regularization for a nonlinear transformation which is
composed of Legendre polynomials. But then in hw6, Q2 to Q6,
The nonlinear transform doesn't talk anything about Legendre polynomials.

Does it mean, Legendre polynomials is used in deriving the theory,
and any function, including the \phi in hw6, can actually be
expressed in terms of Legendre polynomials ? Further, does it only hold true
for the range -1 to 1 ?
Reply With Quote
  #2  
Old 06-11-2013, 01:20 PM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,474
Default Re: Related to Legendre polynomials

Quote:
Originally Posted by skwong View Post
In lect 12, we learn the regularization for a nonlinear transformation which is
composed of Legendre polynomials. But then in hw6, Q2 to Q6,
The nonlinear transform doesn't talk anything about Legendre polynomials.

Does it mean, Legendre polynomials is used in deriving the theory,
and any function, including the \phi in hw6, can actually be
expressed in terms of Legendre polynomials ? Further, does it only hold true
for the range -1 to 1 ?
Any polynomial, including the one in HW 6, can be expressed in terms Legendre polynomials. The polynomial can be defined outside the range [-1,+1] but the orthognality of Legendre polynomials is within [-1,+1].
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote
  #3  
Old 06-11-2013, 07:58 PM
skwong skwong is offline
Member
 
Join Date: Apr 2013
Location: Hong Kong
Posts: 13
Default Re: Related to Legendre polynomials

Thank you very much for the prompt reply. Does it mean that if we want to use
this regulariser, then we need to normalise the input data to range -1 to 1 ?
Reply With Quote
  #4  
Old 06-11-2013, 08:36 PM
yaser's Avatar
yaser yaser is offline
Caltech
 
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,474
Default Re: Related to Legendre polynomials

Quote:
Originally Posted by skwong View Post
Thank you very much for the prompt reply. Does it mean that if we want to use
this regulariser, then we need to normalise the input data to range -1 to 1 ?
The regularizer can be used for any domain. It just has a nice interpretation in the [-1,+1] domain because of the properties of Legendre polynomials in that domain.
__________________
Where everyone thinks alike, no one thinks very much
Reply With Quote
Reply

Thread Tools
Display Modes

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 Jump


All times are GMT -7. The time now is 03:44 AM.


Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2018, 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.