Timmy,
I'm taking a closer look at your problem now. There's something very
strange in your adjacency matrix: a small set of points are the nearest
neighbors of virtually every other point. I think this is leading to
the singular weight matrices which cause the error. I visualized it
like this:
import pylab as pl
from sklearn.neighbors import BallTree
test_adjancey_matrix = np.load('test_adjacency_matrix.npy')
N = test_adjancey_matrix.shape[0]
dist, ind =
BallTree(test_adjancey_matrix).query(test_adjancey_matrix, 30)
M = np.zeros((N, N))
M[np.arange(N)[:, None], ind] = 1
pl.imshow(M, origin='lower', interpolation='nearest')
pl.show()
Taking a look at this matrix, it's not surprising that the weights end
up being singular.
I'm fixing the source code now - essentially, I'm going to have it raise
a more intuitive error when the weight matrix is singular. Thanks for
the bug report - we appreciate it
Jake
Timmy Wilson wrote:
> 'standard' + 'modified' both work fine
>
> 'hessian' + 'ltsa' both have issues
>
> ltsa is printing:
>
> RuntimeWarning: Diagonal number 2 is exactly zero. Singular matrix.
>
> and then setting everything to -nan
>
> i tried adding random noise and increasing n_neighbors -- but no dice
>
> Fabian's suggestion is still under review --
> https://github.com/scikit-learn/scikit-learn/pull/457
>
>
>
> On Thu, Dec 8, 2011 at 11:39 AM, Fabian Pedregosa
> <[email protected]> wrote:
>
>> I reduced the problem to a difference of results with eigsh when
>> working in shift-invert mode and when not. Notice that the following
>> works with sigma=None but not with sigma=0. , thus seems to me that we
>> should fall back to non invert-mode for singular matrices (see
>> asociated pull request).
>>
>> ```
>> In [8]: M = sparse.csr_matrix([[1, 1, 1], [1, 1, 1], [1, 1, 1.]])
>>
>> In [9]: linalg.eigsh(M, 1)
>> Out[9]:
>> (array([ 3.]),
>> array([[-0.57735027],
>> [-0.57735027],
>> [-0.57735027]]))
>>
>> In [10]: linalg.eigsh(M, 1, sigma=0.)
>> ---------------------------------------------------------------------------
>> RuntimeError Traceback (most recent call last)
>> /home/fabian/dev/sandbox/<ipython-input-10-f646f5be93ec> in <module>()
>> ----> 1 linalg.eigsh(M, 1, sigma=0.)
>>
>> /home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
>> in eigsh(A, k, M, sigma, which, v0, ncv, maxiter, tol,
>> return_eigenvectors, Minv, OPinv, mode)
>> 1484 if OPinv is None:
>> 1485 Minv_matvec = get_OPinv_matvec(A, M, sigma,
>> -> 1486 symmetric=True,
>> tol=tol)
>> 1487 else:
>> 1488 OPinv = _aslinearoperator_with_dtype(OPinv)
>>
>> /home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
>> in get_OPinv_matvec(A, M, sigma, symmetric, tol)
>> 1004 def get_OPinv_matvec(A, M, sigma, symmetric=False, tol=0):
>> 1005 if sigma == 0:
>> -> 1006 return get_inv_matvec(A, symmetric=symmetric, tol=tol)
>> 1007
>> 1008 if M is None:
>>
>> /home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
>> in get_inv_matvec(M, symmetric, tol)
>> 997 if isspmatrix_csr(M) and symmetric:
>> 998 M = M.T
>> --> 999 return SpLuInv(M).matvec
>> 1000 else:
>> 1001 return IterInv(M, tol=tol).matvec
>>
>> /home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/eigen/arpack/arpack.pyc
>> in __init__(self, M)
>> 890 """
>> 891 def __init__(self, M):
>> --> 892 self.M_lu = splu(M)
>> 893 LinearOperator.__init__(self, M.shape, self._matvec,
>> dtype=M.dtype)
>> 894 self.isreal = not np.issubdtype(self.dtype,
>> np.complexfloating)
>>
>> /home/fabian/envs/p26/lib/python2.6/site-packages/scipy/sparse/linalg/dsolve/linsolve.pyc
>> in splu(A, permc_spec, diag_pivot_thresh, drop_tol, relax, panel_size,
>> options)
>> 171 _options.update(options)
>> 172 return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
>> --> 173 ilu=False, options=_options)
>> 174
>> 175 def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None,
>> permc_spec=None,
>>
>> RuntimeError: Factor is exactly singular
>>
>> In [11]:
>> ```
>>
>> ------------------------------------------------------------------------------
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>
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