Matlab implementation of PCA on a graph

graph_pca.m

function X = graph_pca(A, k)
  % A: the adjacency matrix of a graph
  % k: the number of dimensions to reduce to
  %
  % Calculates the ECTD-preserving PCA of the graph given by A.
  % See http://outobox.cs.umn.edu/PCA_on_a_Graph.pdf for background.
  L = diag(sum(A)) - A;
  Lp = pinv(L);
  [U, E] = eigs(Lp, k);
  X = E.^(1/2) * U';
endfunction

So this is actually a very silly and inefficient way to do this, since inv(eigs(L)) == eigs(pinv(L)). Inverting L, which is mad expensive, is not actually necessary. See the python version for an improvement.