untitled.asv

关于高维数据降维的非线性方法ＬＬＥ代码

N=2000
K=12
d=2
angle = pi*(1.5*rand(1,N/2)-1); height = 5*rand(1,N)
X = [[cos(angle), -cos(angle)]; height;[ sin(angle), 2-sin(angle)]]
function [Y] = lle(X,K,d)

[D,N] = size(X)
fprintf(1,'LLE running on %d points in %d dimensions\n',N,D)


% STEP1: COMPUTE PAIRWISE DISTANCES & FIND NEIGHBORS 
fprintf(1,'-->Finding %d nearest neighbours.\n',K)

X2 = sum(X.^2,1)
distance = repmat(X2,N,1)+repmat(X2',1,N)-2*X'*X

[sorted,index] = sort(distance)
neighborhood = index(2:(1+K),:)



% STEP2: SOLVE FOR RECONSTRUCTION WEIGHTS
fprintf(1,'-->Solving for reconstruction weights.\n')

if(K>D) 
  fprintf(1,'   [note: K>D; regularization will be used]\n')
  tol=1e-3; % regularlizer in case constrained fits are ill conditioned
else
  tol=0
end

W = zeros(K,N)
for ii=1:N
   z = X(:,neighborhood(:,ii))-repmat(X(:,ii),1,K)
   C = z'*z
   C = C + eye(K,K)*tol*trace(C)
   W(:,ii) = C\ones(K,1)
   W(:,ii) = W(:,ii)/sum(W(:,ii))
end;


% STEP 3: COMPUTE EMBEDDING FROM EIGENVECTS OF COST MATRIX M=(I-W)'(I-W)
fprintf(1,'-->Computing embedding.\n')

% M=eye(N,N); % use a sparse matrix with storage for 4KN nonzero elements
M = sparse(1:N,1:N,ones(1,N),N,N,4*K*N)
for ii=1:N
   w = W(:,ii)
   jj = neighborhood(:,ii)
   M(ii,jj) = M(ii,jj) - w'
   M(jj,ii) = M(jj,ii) - w
   M(jj,jj) = M(jj,jj) + w*w'
end

% CALCULATION OF EMBEDDING
options.disp = 0; options.isreal = 1; options.issym = 1
[Y,eigenvals] = eigs(M,d+1,0,options);
Y = Y(:,2:d+1)'*sqrt(N); % bottom evect is [1,1,1,1...] with eval 0


fprintf(1,'Done.\n')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% other possible regularizers for K>D
%   C = C + tol*diag(diag(C));                       % regularlization
%   C = C + eye(K,K)*tol*trace(C)*K;                 % regularlization

Y=lle(X,K,d)