Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spectra of the Laplacian (Matrix)

  1. Mar 6, 2013 #1
    Hi all

    I was reading this paper about spectral clustering:
    Ng et all. (Nips 2001) http://ai.stanford.edu/~ang/papers/nips01-spectral.pdf

    Short question:
    What is the connection between the eigenvalues of a Laplacian?

    Long question:

    I got stuck on why the process makes sense.
    Substantially the idea is that some data cannot be simply represented by distribution, but rather as vertices of a graph, where something simpler than graph-cut can be employed.

    The "something simpler" is to construct a Laplacian matrix from the graph and then use
    the eigenvectors of this matrix as new data and then perform a traditional clustering
    algorithm. In this way the data are more "manegeable".

    The part where I got stuck is why the eigenvectors are more manegeable?
    In a survey about methods for spectral clustering (von Luxburg 2007), when they talk about this paper they say something like: "hence the graph laplacian measures the variation of
    a function along a graph: the eingenvalue is low if close points have close function value".
    this anyway does not explain why a classification using eigenvectors is easier?

    In other words, does the eigenvalues capture the local "shape variation"?
    This is what I gather from
    http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
    and reading other stuff about the eigenvalues of the laplace-beltrami
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Spectra of the Laplacian (Matrix)
  1. Laplacian's theorem (Replies: 5)

Loading...