On Mon, Nov 7, 2011 at 12:32 PM, Jacob VanderPlas
<[email protected]> wrote:
> I think, based on this, that KernelPCA is correct as written, except
> that the arpack method should use which='LA' rather than which='LM'
> (thus ignoring any negative eigenvalues). This would fix Alejandro's
> problem. I'll make the change in master.
Does this also affect Hessian LLE and Local Tangent Space Alignment? I
am observing some problems with these two that are solved by using
eigen_solver='dense'. The following code illustrates the problem with
Hessian LLE (I reported the problem with LTSA in a previous post):
##############################################
import numpy as np
from sklearn import manifold
n = 1000;
m = 50;
X = np.random.rand(n,m)
out_dim = 2
n_neighbors = 10
Y = manifold.LocallyLinearEmbedding(n_neighbors, out_dim,
eigen_solver='dense',
method='hessian').fit_transform(X)
print "Just computed HLLE using eigen_solver='dense'"
Y = manifold.LocallyLinearEmbedding(n_neighbors, out_dim,
method='hessian').fit_transform(X)
##############################################
And this is the output
Just computed HLLE using eigen_solver='dense'
Traceback (most recent call last):
File "hlle_test.py", line 15, in <module>
method='hessian').fit_transform(X)
File
"/usr/local/lib/python2.6/dist-packages/sklearn/manifold/locally_linear.py",
line 575, in fit_transform
self._fit_transform(X)
File
"/usr/local/lib/python2.6/dist-packages/sklearn/manifold/locally_linear.py",
line 546, in _fit_transform
hessian_tol=self.hessian_tol, modified_tol=self.modified_tol)
File
"/usr/local/lib/python2.6/dist-packages/sklearn/manifold/locally_linear.py",
line 459, in locally_linear_embedding
tol=tol, max_iter=max_iter)
File
"/usr/local/lib/python2.6/dist-packages/sklearn/manifold/locally_linear.py",
line 141, in null_space
tol=tol, maxiter=max_iter)
File "/usr/local/lib/python2.6/dist-packages/sklearn/utils/arpack.py",
line 1488, in eigsh
symmetric=True, tol=tol)
File "/usr/local/lib/python2.6/dist-packages/sklearn/utils/arpack.py",
line 1010, in get_OPinv_matvec
return get_inv_matvec(A, symmetric=symmetric, tol=tol)
File "/usr/local/lib/python2.6/dist-packages/sklearn/utils/arpack.py",
line 1003, in get_inv_matvec
return SpLuInv(M).matvec
File "/usr/local/lib/python2.6/dist-packages/sklearn/utils/arpack.py",
line 896, in __init__
self.M_lu = splu(M)
File
"/usr/local/lib/python2.6/dist-packages/scipy/sparse/linalg/dsolve/linsolve.py",
line 173, in splu
ilu=False, options=_options)
RuntimeError: Factor is exactly singular
Alejandro
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