I was reading $Von \ Luxburg's$ tutorial on $Spectral \ Clustering$, but got stuck into some technical details about Laplacians. THenotations is as usual.
1) I was told that D\W and I-D\W are iso-spectrum, but I thought that the relation between their eigenvalues is $1-\lambda,$ so I am missing something. Is this because of the normalization process somehow?
2) When we build the Laplacian Graph, we start from a similarity matrix, apply Gaussian Kernel and then use knhgood or $\epsilon$ nghood etc, after which we weight the edges and get the Laplacian. From here we compute the eigenvectors. Is it common practice to directly compute the eigenvalues of the similarity matrix , before applying any kernel or k-nghood?
3) After we finish Spectral Clustering, we apply k means to get the indicator vectors. But instead , we get some other k vectors which have the same Span as the indicator vectors. Is this correct? Is there any well known method/algorithm to retrieve the indicators vectors from that? Any help is appreciated. THank you.