leigs.m

toolbox_dimreduc - a toolbox for dimension reduction methods This toolbox is an educational and rec

function [E,V] = leigs(X, NE, PARAM, TYPE)

% Laplacian Eigenmaps Algorithm
%
% please refer to University of Chicago
% Computer Science Technical Report TR-2002-01
% Mikhail Belkin, Partha Niyogi
% Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
% Note that Laplacian, not normalized Laplacian is used here
% http://www.cs.uchicago.edu/research/publications/techreports/TR-2002-1
%
%
% Calculate the graph laplacian of the adjacency graph of data set X.
%
% [E,V] = leigs(X, NE, PARAM, TYPE)
%
%   X - (dimension x nbr_points) matrix.
%   NE - number of eigenvectors
%   TYPE - string 'nn' or string 'epsballs'
%   PARAM - integer if TYPE='nn', real number if TYPE='epsballs'
%
% Returns:
%   E - (NE x nbr_points) matrix with eigenfunctions,
%   V is (NE x NE) matrix with eigenvalues on the diagonal
%
% Author:
%
%   Mikhail Belkin
%   [e-mail]
%
% Modified by Gabriel Peyr