thanks jake.
I believe the current implementation is equivalent to the first several
> equations in this document:
> http://www.math.ucsd.edu/~fan/research/cb/ch1.pdf
> It may be that there are several ways to define a laplacian; I'm not an
> expert on the subject. Gael might be able to weigh in - I think he
> contributed the current Laplacian implementation.
>
that's helpful. the difference was in the adjacency matrix. i was assuming
a system with a self loop on the nodes with arbitrary weights (i.e., a
general form of a undirected graph). the scikits implementation works on
the assumption that the diag of the adjacency matrix is 0 (no self loops).
also as i note in the updated comment on the issue, the
scikits-implementation corresponds to Lsym from the von Luxborg paper,
although he describes why L_{rw} might be a better matrix::
----
The reason is that the eigenvectors of Lrw are cluster indicator vectors 1Ai
, while the eigenvectors of Lsym are additionally multiplied with D1/2, which
might lead to undesired arti- facts. As using Lsym also does not have any
computational advantages, we thus advocate for using Lrw.
----
all sklearners: I'd like to propose allowing the different normalizations
and if necessary switching to Lrw as the default and allowing for any
adjacency matrix. any objections?
jake: would it be helpful to send the same request to your scipy PR?
FYI, I'm working on some related things in a current scipy PR:
> https://github.com/scipy/scipy/pull/119 (unfortunately it's been sitting
> idle for the last month or so - I hope to be able to finish and merge it
> some time soon).
>
from a scikits perspective, is this going to happen anytime soon? i.e. how
long should we maintain a version in scikits. i hate to see multiple places
where the same functionality is implemented.
i don't want to get into a long discussion about this, but is the plan to
recreate networkx in scipy? why not simply improve the efficiency in
networkx or merge networkx into scipy and improve efficiency?
cheers,
satra
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