similar to: Confidence intervals for PCA scores/eigenvalues

Good day all. This is to thank all those who have helped in fixing this problem. Starting with a text book was indeed a problem, however, that gave me a clue of what I was looking for. This, with your contributions added to other materials I got on the net, put me on the right track. Thank you so much. Warmest regards Ogbos On 31 January 2010 14:07, S Ellison <S.Ellison@lgc.co.uk> wrote:

After doing a PCA using princomp, how do you view how much each component contributes to variance in the dataset. I'm still quite new to the theory of PCA - I have a little idea about eigenvectors and eigenvalues (these determine the variance explained?). Are the eigenvalues related to loadings in R? Thanks, Paul -- View this message in context:

Inicio del mensaje reenviado: > De: Arnau Mir <arnau.mir@uib.es> > Fecha: 14 de noviembre de 2011 13:24:31 GMT+01:00 > Para: Martin Maechler <maechler@stat.math.ethz.ch> > Asunto: Re: [R] How to compute eigenvectors and eigenvalues? > > Sorry, but I can't explain very well. > > > The matrix 4*mp is: > > 4*mp > [,1] [,2] [,3] > [1,]

Dear all, I've used the 'prcomp' command to calculate the eigenvalues and eigenvectors of a matrix(gg). Using the command 'principal' from the 'psych' package  I've performed the same exercise. I got the same eigenvalues but different eigenvectors. Is there any reason for that difference? Below are the steps I've followed: 1. PRCOMP #defining the matrix

Hello. Consider the following matrix: mp <- matrix(c(0,1/4,1/4,3/4,0,1/4,1/4,3/4,1/2),3,3,byrow=T) > mp [,1] [,2] [,3] [1,] 0.00 0.25 0.25 [2,] 0.75 0.00 0.25 [3,] 0.25 0.75 0.50 The eigenvectors of the previous matrix are 1, 0.25 and 0.25 and it is not a diagonalizable matrix. When you try to find the eigenvalues and eigenvectors with R, R responses: > eigen(mp) $values [1]

Hi all, As a molecular biologist by training, I'm fairly new to R (and statistics!), and was hoping for some advice. First of all, I'd like to apologise if my question is more methodological rather than relating to a specific R function. I've done my best to search both in the forum and elsewhere but can't seem to find an answer which works in practice. I am carrying out

Dear All, I want to know if there is some easy and reliable way to estimate the number of dominant eigenvalues when applying PCA on sample covariance matrix. Assume x-axis is the number of eigenvalues (1, 2, ....,n), and y-axis is the corresponding eigenvalues (a1,a2,..., an) arranged in desceding order. So this x-y plot will be a decreasing curve. Someone mentioned using the elbow (knee)

DeaR list, I happily use eigen() to compute the eigenvalues and eigenvectors of a fairly large matrix (200x200, say), but it seems over-killed as its rank is limited to typically 2 or 3. I sort of remember being taught that numerical techniques can find iteratively decreasing eigenvalues and corresponding orthogonal eigenvectors, which would provide a nice alternative (once I have the

I thought that the function eigen(A) will return a matrix with eigenvectors that are independent of each other (thus forming a base and the matrix being invertible). This seems not to be the case in the following example A=matrix(c(1,2,0,1),nrow=2,byrow=T) eigen(A) ->ev solve(ev$vectors) note that I try to get the upper triangular form with eigenvalues on the diagonal and (possibly) 1 just

Let's say I had a matrix like this: library(Ryacas) x<-Sym("x") m<-matrix(c(cos (x), sin(x), -sin(x), cos(x)), ncol=2) How can I use R to obtain the eigenvalues and eigenvectors? Thanks, John [[alternative HTML version deleted]]

Hello everyone. In my last post I did not explained my problem quite well. I made a principal component analysis and took the 2 first principal components. I made ​​a chart of my points based on the score of the 2 PC. I would like to add on this graph a 95% confidence region. To do this I used the ellipse function as follows: pcsref=PC$score[data[,1]==ref,1:2] #matrix containing the scores

x=rmvnorm(2000, rep(0, 6), diag(c(5, rep(1,5)))) x=scale(x, center=T, scale=F) pc <- princomp(x) biplot(pc) There are a bunch of red arrows plotted, what do they mean? I knew that the first arrow labelled with "Var1" should be pointing the most varying direction of the data-set (if we think them as 2000 data points, each being a vector of size 6). I also read from

Hi, I have the following problem. It has two parts. 1. I need to calculate the stationary probabilities of a Markov chain, eg if the transition matrix is P, I need x such that xP = x in other words, the left eigenvectors of P which have an eigenvalue of one. Currently I am using eigen(t(P)) and then pick out the vectors I need. However, this seems to be an overkill (I only need a single

Dear all, I am looking for some interactive study materials on Principal component analysis. Basically I would like to know what we are actually doing with PCA? What is happening within the dataset at the time of doing PCA. Probably a 3-dimensional interactive explanation would be best for me. I have gone through some online materials specially Wikipedia etc, however what I need a "movable

Hello, I am trying to run a PCA in R and I cannot get the PC scores for each of the values. Using pcX <- princomp(X) then loadings(pcX) I can get a listing of the eigenvectors but not the actual PC scores for each value in the dataset. I greatly appreciate any help anyone can offer Thanks Ken

After making E <- eigen( something ) I would like to extract those eigenvectors which have an eigenvalue of 1. If I had an isone() function, I would simply say E$vectors[,which(isone(E))] but the problem is that I have no such thing. I found all.equal, so I could test for all.equal(x, 1), but for complex numbers, I need to use something like all.equal(x, 1+0i), don't I? I tried

Hello, I have a short question about the prcomp function. First I cite the associated help page (help(prcomp)): "Value: ... SDEV the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix). ROTATION the matrix of variable loadings

Hi ... Please could you help with probably a very simple problem I have. I'm completely new to R and am trying to follow a tutorial using R for Force Distribution Analysis that I got from ... http://projects.eml.org/mbm/website/fda_gromacs.htm. Basically, the MDS I preform outputs a force matrix (.fm) from the force simulation I perform. Then, this matrix is read into R and prcomp is

Dear all I'm unable to find an example of extracting the rotated scores of a principal components analysis. I can do this easily for the un-rotated version. data(mtcars) .PC <- princomp(~am+carb+cyl+disp+drat+gear+hp+mpg, cor=TRUE, data=mtcars) unclass(loadings(.PC)) # component loadings summary(.PC) # proportions of variance mtcars$PC1 <- .PC$scores[,1] # extract un-rotated scores of

Apologies for the obvious, but just to clarify: there is no reason to "justify" a PCA -- it's just an eigen decomposition of a matrix and is therefore "justified" by linear algebra. If one wants to determine whether some subset of the eigenvectors = principal components suffice to "represent" the data in some sense, then that is where distributional