Sometimes this sort of error can happen when not enough neighbors are 
used, so that your data is split into two unconnected regions.  
Increasing the number of neighbors could help
  Jake

Timmy Wilson wrote:
> I get the following error when running Hessian-based LLE::
>
>
> /home/timmyt/projects/smarttypes/smarttypes/scripts/reduce_twitter_graph.py
> in <module>()
>      32         print "Passed our little test: following %s users!" %
> len(tmp_followies)
>      33
> ---> 34     results = reduce_graph(adjacency_matrix, follower_ids,
> out_dim=2, n_neighbors=30, method='hessian')
>      35
>      36
>
> /home/timmyt/projects/graphreduce/graphreduce.py in
> reduce_graph(input_graph, sample_ids, out_dim, n_neighbors, method)
>       7 def reduce_graph(input_graph, sample_ids, out_dim=2,
> n_neighbors=30, method='modified'):
>       8     clf = manifold.LocallyLinearEmbedding(n_neighbors,
> out_dim=out_dim, method=method)
> ----> 9     results = clf.fit_transform(input_graph)
>      10     print "Done. Reconstruction error: %g" % clf.reconstruction_error_
>      11     return results
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/manifold/locally_linear.pyc
> in fit_transform(self, X, y)
>     573         X_new: array-like, shape (n_samples, out_dim)
>     574         """
> --> 575         self._fit_transform(X)
>     576         return self.embedding_
>     577
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/manifold/locally_linear.pyc
> in _fit_transform(self, X)
>     544                 eigen_solver=self.eigen_solver, tol=self.tol,
>     545                 max_iter=self.max_iter, method=self.method,
> --> 546                 hessian_tol=self.hessian_tol,
> modified_tol=self.modified_tol)
>     547
>     548     def fit(self, X, y=None):
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/manifold/locally_linear.pyc
> in locally_linear_embedding(X, n_neighbors, out_dim, reg,
> eigen_solver, tol, max_iter, method, hessian_tol, modified_tol)
>     457
>     458     return null_space(M, out_dim, k_skip=1, eigen_solver=eigen_solver,
> --> 459                       tol=tol, max_iter=max_iter)
>     460
>     461
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/manifold/locally_linear.pyc
> in null_space(M, k, k_skip, eigen_solver, tol, max_iter)
>     139     if eigen_solver == 'arpack':
>     140         eigen_values, eigen_vectors = eigsh(M, k + k_skip, sigma=0.0,
> --> 141                                             tol=tol, maxiter=max_iter)
>     142
>     143         return eigen_vectors[:, k_skip:], 
> np.sum(eigen_values[k_skip:])
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/utils/arpack.pyc
> in eigsh(A, k, M, sigma, which, v0, ncv, maxiter, tol,
> return_eigenvectors, Minv, OPinv, mode)
>    1486             if OPinv is None:
>    1487                 Minv_matvec = get_OPinv_matvec(A, M, sigma,
> -> 1488                                                symmetric=True, 
> tol=tol)
>    1489             else:
>    1490                 OPinv = _aslinearoperator_with_dtype(OPinv)
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/utils/arpack.pyc
> in get_OPinv_matvec(A, M, sigma, symmetric, tol)
>    1008 def get_OPinv_matvec(A, M, sigma, symmetric=False, tol=0):
>    1009     if sigma == 0:
> -> 1010         return get_inv_matvec(A, symmetric=symmetric, tol=tol)
>    1011
>    1012     if M is None:
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/utils/arpack.pyc
> in get_inv_matvec(M, symmetric, tol)
>    1001         if isspmatrix_csr(M) and symmetric:
>    1002             M = M.T
> -> 1003         return SpLuInv(M).matvec
>    1004     else:
>    1005         return IterInv(M, tol=tol).matvec
>
> /home/timmyt/.virtualenvs/smarttypes/lib/python2.6/site-packages/sklearn/utils/arpack.pyc
> in __init__(self, M)
>     894     """
>     895     def __init__(self, M):
> --> 896         self.M_lu = splu(M)
>     897         LinearOperator.__init__(self, M.shape, self._matvec,
> dtype=M.dtype)
>     898         self.isreal = not np.issubdtype(self.dtype, 
> np.complexfloating)
>
> /usr/lib/python2.6/dist-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
>
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> This white paper is intended to serve as a reference, checklist and point of 
> discussion for anyone considering optimizing the pricing and packaging model 
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Cloud Services Checklist: Pricing and Packaging Optimization
This white paper is intended to serve as a reference, checklist and point of 
discussion for anyone considering optimizing the pricing and packaging model 
of a cloud services business. Read Now!
http://www.accelacomm.com/jaw/sfnl/114/51491232/
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