CGAL users discussion list

[Pierre Alliez <>]

hi,

for PCA in CGAL it is the default orthogonal projection.

pierre

Pierre Alliez
INRIA Sophia Antipolis - Mediterranee 
Project-team GEOMETRICA 
http://www-sop.inria.fr/members/Pierre.Alliez/
Tel: +33 4 92 38 76 77
Fax: +33 4 97 15 53 95

ganders a écrit :

Hi Pierre,

thanks for your reply, but I read this manual and it confuses me a bit and
thus I had - and still have - this question. Looking at figure 1 on page 3

I. Markovsky and S. Van Huffel, Overview of total least squares methods,
Signal Processing, Volume 87, pages 2283-2302, 2007.
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/markovsky/reports/05-34.pdf

the difference between LS and TLS is clearly described and obvious. The
right TLS picture has a orthogonal projection, the left LS one does not.
This CGAL manual is mentioning a LS - but not explicitely a TLS - with
orthogonal projection. Interpreting your answer, I guess it is a TLS, right?
Thanks in advance.

Cheers,
Gerd


Pierre Alliez wrote:
  

hi Gerd,

the documentation of the PCA component (user manual 
<http://www.cgal.org/Manual/last/doc_html/cgal_manual/Principal_component_analysis/Chapter_main.html>) 
says:
Given a set of objects, /linear least squares fitting/ amounts to 
finding the linear sub-space which minimizes the sum of squared 
distances from all points composing the objects of the set, to their 
projection onto this linear sub-space. Such linear sub-space is obtained 
by so-called principal component analysis (PCA). PCA is defined as a 
transformation that transforms the objects to a new coordinate system 
such that the greatest variance by orthogonal projection of the objects 
comes to lie on the first coordinate (called the first principal 
component), the second greatest variance on the second coordinate, and 
so on.

pierre

Pierre Alliez
INRIA Sophia Antipolis - Mediterranee 
Project-team GEOMETRICA 
http://www-sop.inria.fr/members/Pierre.Alliez/
Tel: +33 4 92 38 76 77
Fax: +33 4 97 15 53 95



ganders a écrit :
    

Dear CGAL-team,

I am searching for a method that calculates a fitting line in terms of a
total-least-squares (TLS) approach for 3D points. As input I would like
to
provide a matrix with the x/y/z coordinates and as output I would like to
receive two points describing the straight line. It looks that
linear_least_squares_fitting_3 is exactly that what I am looking for. But
I
am not sure if it really calculates the TLS or the different
linear-least-squares (LLS) solution. May I ask you to tell me what
approach
is implemented (TLS or LLS)? Thanks a lot in advance.

Cheers,
Gerd 
  
      

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