Description Usage Arguments Details Value References See Also Examples
Given the diffusion map coordinates of a training data set, estimates the diffusion map coordinates of a new set of data using the pairwise distance matrix from the new data to the original data.
a '"dmap"' object from the original data set, computed by diffuse()
distance matrix between each new data point and every point in the training data set. Matrix is m-by-n, where m is the number of data points in the new set and n is the number of training data points
scalar giving the size of the Nystrom extension kernel. Default uses the tuning parameter of the original diffusion map
Often, it is computationally infeasible to compute the exact diffusion map coordinates for large data sets. In this case, one may use the exact diffusion coordinates of a training data set to extend to a new data set using the Nystrom approximation.
A Gaussian kernel is used: exp(-D(x,y)^2/sigma). The default value of sigma is the epsilon value used in the construction of the original diffusion map. Other methods to select sigma, such as Algorithm 2 in Lafon, Keller, and Coifman (2006) have been proposed.
The dimensionality of the diffusion map representation of the new data set will be the same as the dimensionality of the diffusion map constructed on the original data.
The estimated diffusion coordinates for the new data, a matrix of dimensions m by p, where p is the dimensionality of the input diffusion map
Freeman, P. E., Newman, J. A., Lee, A. B., Richards, J. W., and Schafer, C. M. (2009), MNRAS, Volume 398, Issue 4, pp. 2012-2021
Lafon, S., Keller, Y., and Coifman, R. R. (2006), IEEE Trans. Pattern Anal. and Mach. Intel., 28, 1784
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
library(stats) Norig = 1000 Next = 4000 t=runif(Norig+Next)^.7*10 al=.15;bet=.5; x1=bet*exp(al*t)*cos(t)+rnorm(length(t),0,.1) y1=bet*exp(al*t)*sin(t)+rnorm(length(t),0,.1) D = as.matrix(dist(cbind(x1,y1))) Dorig = D[1:Norig,1:Norig] # training distance matrix DExt = D[(Norig+1):(Norig+Next),1:Norig] # new data distance matrix # compute original diffusion map dmap = diffuse(Dorig,neigen=2) # use Nystrom extension dmapExt = nystrom(dmap,DExt) plot(dmapExt[,1:2],pch=8,col=2, main="Diffusion map, black = original, red = new data", xlab="1st diffusion coefficient",ylab="2nd diffusion coefficient") points(dmap$X[,1:2],pch=19,cex=.5)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.