eigenvector

Given a set of points, how do I approximate the major axis of its shape?

Given a "shape" drawn by the user, I would like to "normalize" it so they all have similar size and orientation. What we have is a set of points. I can approximate the size using bounding box or circle, but the orientation is a bit more tricky. The right way to do it, I think, is to calculate the majoraxis of its bounding ellipse. To do...

Issue with Jama's Eigen value decomposition fuction

I am getting a wrong eigen-vector (also checked by running multiple times to be sure) when i am using matrix.eig(). The matrix is: 1.2290 1.2168 2.8760 2.6370 2.2949 2.6402 1.2168 0.9476 2.5179 2.1737 1.9795 2.2828 2.8760 2.5179 8.8114 8.6530 7.3910 8.1058 2.6370 2.1737 8.6530 7.6366 6.9503 7.6743 2.2949 1.9795 7.3910 6.9503 6.2722 7.3...

Singular Value Decomposition (SVD) in PHP

Hello! I would like to implement Singular Value Decomposition (SVD) in PHP. I know that there are several external libraries which could do this for me. But I have two questions concerning PHP, though: 1) Do you think it's possible and/or reasonable to code the SVD in PHP? 2) If (1) is yes: Can you help me to code it in PHP? I've alrea...

Eigenvector computation using OpenCV

Hi I have this matrix A, representing similarities of pixel intensities of an image. For example: Consider a 10 x 10 image. Matrix A in this case would be of dimension 100 x 100, and element A(i,j) would have a value in the range 0 to 1, representing the similarity of pixel i to j in terms of intensity. I am using OpenCV for image proc...

Eigenvalues and Eigenvectors Computation in Intel Math Kernel

Does any know what is the algorithm used for eigenvalues and eigenvectors computation in Intel Math Kernel library? From the link I can find is that it seems to use pdsyev algorithm, which uses QR algorithm, that would deteriorate in the face of large matrix. If this were true, then the mkl isn't a suitable library for computing large ...

Sorting eigenvectors by their eigenvalues (associated sorting)

I have an unsorted vector of eigenvalues and a related matrix of eigenvectors. I'd like to sort the columns of the matrix with respect to the sorted set of eigenvalues. (e.g., if eigenvalue[3] moves to eigenvalue[2], I want column 3 of the eigenvector matrix to move over to column 2.) I know I can sort the eigenvalues in O(N log N) via ...

Eigenvector centrality

Hi, I am new to programming and I am trying to calculate the eigenvector centrality of an directed graph mapping onto a social network. These are large matrices. I know how to calculate eigenvectors and the adjacency matrix associated with the graph. I am just unsure how to combine those two parts to calculate eigenvector centrality. Th...

Java package for eigenvector/eigenvalues computation?

Hi all, which java package do you recommend for computing eigenvectors/eigenvalues? I know about JMathTools and JAMA; do you have some pro/cons for these packages? Other suggestions? ...

Eigenvector (Spectral) Decomposition

I am trying to find a program in C code that will allow me to compute a eigenvalue (spectral) decomposition for a square matrix. I am specifically trying to find code where the highest eigenvalue (and therefore its associated eigenvalue) are located int the first column. The reason I need the output to be in this order is because I am t...

Eigenvalues in MATLAB

In MATLAB when I run the command [V,D] = eig(a) for a symmetric matrix the largest eigenvalue (and its associated vector) is located in last column. However, when I run it with a non-symmetric matrix however the largest eigenvalue is in the first column. I am trying to calculate eigenvector centrality which requires that I take the compu...

Eigenvector (Spectral) Decomposition (w/ordered eigenvalues and eigenvectors)

Possible Duplicate: Eigenvector (Spectral) Decomposition I am trying to find a program in C code that will allow me to compute a eigenvalue (spectral) decomposition for a square matrix. I am specifically trying to find code where the highest eigenvalue (and therefore its associated eigenvalue) are located int the first column....

Can I use Lapack for calculating the eigenvalues and eigenvectors of large sparse matrices?

If I had a square matrix that is 1,000 by 1,000 could Lapack calculate the eigenvectors and eigenvalues for this matrix? And if it can how long would it take? Also what about for a 10,000 by 10,000 matrix or even a 1,000,000 by 1,000,000 matrix? Please note these are going to be sparse matrices primarily populated by 0s (the matrices w...

How to improve accuracy rate on Eigenface Algorithm

I use EmguCV library(openCV wrapper) on C# to implemented face detection and facial recognition using Eigenface algorithm I found many mistakes of accuracy rate such as minimum distance is not a same person in Training Set, person who doesn't exist in Training Set but match with person in Training set with good distance, etc. please he...

Finding eigenvectors of covariance matrix to create 3D bounding sphere

I'm currently in the process of writing a function to find an "exact" bounding-sphere for a set of points in 3D space. I think I have a decent understanding of the process so far, but I've gotten stuck. Here's what I'm working with: A) Points in 3D space B) 3x3 covariance matrix stored in a 4x4 matrix class (referenced by cells m0,m1,m2...