hlle

Standard Hessian LLE implementation of Hessian Eigenmaps

Copyright: C. Grimes and D. Donoho, March 2003

Input Arguments:

• Data matrix X, which is p by n. NOTE that this is the transpose of how we usually have our data matrix.
• k is the number of nearest neighbor points to be used. If k is a scalar, then the same neighborhood size is used at all points. If k is a vector of length n, then the individual neighborhood k(i) will be assigned to the observations.
• d is the number of dimensions for the lower-dimensional representation of X.

Output Arguments:

• Y is the output data embedded in d dimensions
• mse is the sum (at each neighborhood used) of the eigenvalues(d+2:end) of the local coordinate representation. used for adaptive neighborhood restructuring

Synopsis

[Y, mse] = HLLE(X,k,d)

Example:

N=1000;
k=12;
d=2;
tt = (3*pi/2)*(1+2*rand(1,N));
height = 21*rand(1,N);
X = [tt.*cos(tt); height; tt.*sin(tt)];
[Y, mse] = HLLE(X,k,d);

References:

Donoho, D. L. and C. Grimes. 2003. “Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data,” Proceedings of the National Academy of Science, 100:5591-5596.

HLLE Webpage