In spectral clustering, it's standard practice to solve the eigenvector problem

$$L v = \lambda v$$

where $L$ is the graph Laplacian, $v$ is the eigenvector related to eigenvalue $\lambda$.

My question: why bother taking the graph Laplacian? Couldn't I just solve the eigenvector problem for the graph (affinity matrix) itself, like the guy did in this video?

  • $\begingroup$ How would you use PCA on a graph?!? $\endgroup$ – Anony-Mousse Nov 28 '15 at 12:55
  • $\begingroup$ I meant PCA on the affinity matrix (a square matrix with pairwise affinities) representing a graph, just like that video shows. $\endgroup$ – felipeduque Nov 28 '15 at 13:51
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    $\begingroup$ You mean singular value decomposition then? PCA is computing the covariance matrix, then decomposing it. $\endgroup$ – Anony-Mousse Nov 28 '15 at 16:33
  • $\begingroup$ You're completely right. My bad. Just edited. $\endgroup$ – felipeduque Nov 28 '15 at 16:47

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