I am strucked to implement the diffusionmap algorithm for non linear reduction because of this eigenvalue and eigenvector representation.


like above link,

1. I have a x1,x2,x3,x4,x5,x6 points and considerede these as a nodes and then found the adjacency matrix which "W" with 6x6 matrix.
2. Finding the markov transation matrix P= W(i,j)/Di where Di is the degree of each node by summing all the rows in a adjacency matrix.
3. diagonalize the matrix P = (D^-0.5 * P * D^-0.5)
4. Now by using the svd command in matlab found the singular vector and singular values...ofcourse [u,s,v]=svd(P)...here considered approximately U as a eigenvector and s as a eigen value(even it is square root of singular values)..here i got 6x6 eigenvectors and eigenvalues
5. In Matlab the eigenvectors are reordered according eigenvalues in descending order. Now, How can I Identify eigen vector corresponding to X1,X2,....X6.(see the above link P representation with eigenvectors and eigenvalues) I am not able to identify corresponding eigenvector with respect to nodes..x1...x6. Please help me regarding this. How can I solve this.

I used SVD to find eigenvectors and eigen values because the matrix p is a singular matrix.