Linked Questions

2 votes
1 answer
3k views

Difference between Principal Component Analysis(PCA) and Singular Value Decomposition(SVD)? [duplicate]

Possible Duplicate: What is the intuitive relationship between SVD and PCA I am confused between PCA and SVD. The wikipedia page for the PCA has this line: "PCA can be done by eigenvalue ...
athena's user avatar
  • 121
63 votes
2 answers
27k views

What do eigenvalues have to do with pictures?

I am trying to write a program that will perform OCR on a mobile phone, and I recently encountered this article : Can someone explain this to me ?
Patryk's user avatar
  • 751
57 votes
5 answers
132k views

Best Fitting Plane given a Set of Points

Nothing more to explain. I just don't know how to find the best fitting plane given a set of $N$ points in a $3D$ space. I then have to write the corresponding algorithm. Thank you ;)
G4bri3l's user avatar
  • 703
12 votes
1 answer
4k views

Why is SVD on $X$ preferred to eigendecomposition of $XX^\top$ in PCA?

In this post J.M. has mentioned that ... In fact, using the SVD to perform PCA makes much better sense numerically than forming the covariance matrix to begin with, since the formation of $XX^\top$ ...
S. P's user avatar
  • 303
7 votes
2 answers
3k views

Relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). A radical result(?)

I was wondering if I could get a mathematical description of the relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). To be more specific I have some ...
Sergio Sarmiento's user avatar
5 votes
1 answer
4k views

compute pca with this useful trick

A is matrix (m rows, n cols), each row is an object, and each cols is a feature (a dimension). Typically, I compute the pca ...
avocado's user avatar
  • 1,259
2 votes
2 answers
2k views

Decomposing a matrix into lower dimension sub-components

Given a matrix $M^{n \times n}$, I would like to decompose it into two smaller matrices $A^{n \times m}$ and $B^{m \times n}$, with $m < n$ so that the multiplication of both $AB = M'$ ...
dagnelies's user avatar
  • 193
1 vote
0 answers
2k views

Best-fitting plane

I need to implement the algorithm described below. Everything is fine until the eigenvalues computation. I'm completely new to them and I found a lot of very complicated paper on the net. Is it ...
abenci's user avatar
  • 185
1 vote
2 answers
992 views

What does singular value decomposition of covariance matrix represent?

I am reading the paper "Understanding dimensional collapse in contrastive self-supervised learning." The authors identified a dimensional collapse phenomenon: i.e. some dimension of ...
Noel's user avatar
  • 11
1 vote
1 answer
728 views

Principal Component Analysis - Eigen value decomposition or Singular value decomposition?

I have been reading various articles/papers on PCA and some of the authors mention it as a Eigen values whereas others go by singular values. From whetever remnants of Bachelor's algebra in my memory, ...
user295338's user avatar
0 votes
0 answers
402 views

Why is SVD stable when eigendecomposition is not?

In this post, it is stated that In fact, using the SVD to perform PCA makes much better sense numerically than forming the covariance matrix to begin with, since the formation of $XX^\top$ can cause ...
user avatar
1 vote
0 answers
232 views

Equivalence of maximizing variance and sum-of-squares for a projection.

(The following is motivated by the singular value decomposition:) Say we have an N x D matrix $A$. The first principal component $v_1$ is the unit-length vector of dimension D which maximizes the ...
Jake Grimes's user avatar
2 votes
0 answers
224 views

Computational stability of calculating EV-decomposition vs SVD with the Läuchli matrix.

In a lecture on PCA the lecturer claimed that (and I've also found it in this answer but it had 17 comments and I didn't want to make them 17 more) instead of calculating the eigenvalue ...
ViktorStein's user avatar
  • 4,858