I think it may be important, but I am not sure. Actually I am trying to program the adaptive nearest neighbor method proposed by Hastie and Tibshirani. I am following the steps in the book 'The elements of statistical learning' by Hastie, Tibshirani and Friedman, in which the local metric is defined as W^(-1/2)[B*+I]W^(-1/2), where W is the pooled within-class covariance matrix. Cindy
On Mon, Aug 10, 2009 at 4:28 PM, Gabor Grothendieck <ggrothendi...@gmail.com > wrote: > If its not important which of many solutions you use then > the generalized inverse can be used, say. Just use 0 > for each small eigenvalue and 1/sqrt(x) for the others. > > On Mon, Aug 10, 2009 at 6:36 PM, cindy Guo<cindy.g...@gmail.com> wrote: > > Hi, Ted, > > > > Thanks for the sample code. It is exactly what I want. But can I ask > another > > question? The matrix for which I want the negative square root is a > > covariance matrix. I suppose it should be positive definite, so I can do > > 1/sqrt(V) as you wrote. But the covariance matrix I got in R using the > > function cov has a lot of negative eigenvalues, like -5.338634e-17, so > > 1/sqrt(V) generates NA's. Can you tell what's the problem here. > > > > Thanks, > > Cindy > > > > On Mon, Aug 10, 2009 at 2:53 PM, Ted Harding > > <ted.hard...@manchester.ac.uk>wrote: > > > >> On 10-Aug-09 21:31:30, cindy Guo wrote: > >> > Hi, All, > >> > If I have a symmetric matrix, how can I get the negative square root > >> > of the matrx, ie. X^(-1/2) ? > >> > > >> > Thanks, > >> > > >> > Cindy > >> > >> X <- matrix(c(2,1,1,2),nrow=2) > >> X > >> # [,1] [,2] > >> # [1,] 2 1 > >> # [2,] 1 2 > >> > >> E <- eigen(X) > >> V <- E$values > >> Q <- E$vectors > >> Y <- Q%*%diag(1/sqrt(V))%*%t(Q) > >> Y > >> # [,1] [,2] > >> # [1,] 0.7886751 -0.2113249 > >> # [2,] -0.2113249 0.7886751 > >> > >> solve(Y%*%Y) ## i.e. find its inverse > >> # [,1] [,2] > >> # [1,] 2 1 > >> # [2,] 1 2 > >> > >> Hence (Y%*%Y)^(-1) = X, or Y = X^(-1/2) > >> > >> Hopingb this helps, > >> Ted. > >> > >> -------------------------------------------------------------------- > >> E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> > >> Fax-to-email: +44 (0)870 094 0861 > >> Date: 10-Aug-09 Time: 22:53:25 > >> ------------------------------ XFMail ------------------------------ > >> > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html> > > and provide commented, minimal, self-contained, reproducible code. > > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
