All Questions
Tagged with eigenvector st.statistics
8 questions
4
votes
1
answer
172
views
Least squares problem with left and right unknowns
For $i=1,...,n$, let $b_i$ be a scalar and $A_i$ be an $k\times l$ matrix. Is there a closed form solution for the following problem assuming $n>k+l$?
$$\min_{x\in \mathbb{R}^k ,y\in \mathbb{R}^l} \...
- 230
2
votes
1
answer
294
views
Find a way to apply the MLE on Fisher or Covariance matrix to make cross-correlations
I have 2 Fisher matrixes which represent information for the same variables (I mean columns/rows represent the same parameters in the 2 matrixes).
Now I would like to make the cross-correlations ...
5
votes
1
answer
473
views
Statistical independence of eigenvectors of real symmetric Gaussian random matrices
What is known about the statistical independence of the eigenvectors of a real symmetric matrix with independent Gaussian entries with zero mean, and finite variance? The matrix elements are not ...
- 75
3
votes
1
answer
561
views
Reducing eigenvalues of symmetric PSD matrix towards 0: effect on ratios of original matrix elements?
Let $\boldsymbol{S}$ be $k \times k$ positive semi-definite real symmetric matrix with eigen decomposition $\boldsymbol{S} = \boldsymbol{X} \boldsymbol{\Lambda} \boldsymbol{X}'$ ($\boldsymbol{\Lambda}$...
- 33
3
votes
2
answers
4k
views
Singular Value Decomposition of Noisy Matrices
I am an engineer who makes measurements of a variable over a grid
of, say, $m\times n$. Since these are actual measurements, the true
values are always corrupted by noise, and what I measure is a ...
0
votes
1
answer
30k
views
Difference between Principal Component Analysis(PCA) and Singular Value Decomposition(SVD)? [closed]
I am confused between PCA and SVD.
The wikipedia page for PCA has this line. "PCA can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, ...
- 141
2
votes
1
answer
205
views
Statistical estimation of singular values and vectors
My question is about the well known and well studied singular value decomposition (SVD). What I am working on right now requires performing an SVD repeatedly on a slowly varying matrix. Since I don't ...
- 111
7
votes
1
answer
6k
views
The difference between Principal Components Analysis (PCA) and Factor Analysis (FA)
I am trying to understand the difference between PCA and FA. Through google research, I have come to understand that PCA accounts for all variance, while FA accounts for only common variance and ...
- 73