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FIX: spectral_embedding.py initial eigenvector approximations for LOBPCG and AMG solvers should be randn not rand #21565

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Merged
merged 5 commits into from
Dec 14, 2021
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FIX: spectral_embedding.py initial eigenvector approximations for LOBPCG and AMG solvers should be randn not rand #21565

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77f7af1
Update _spectral_embedding.py
lobpcg Nov 5, 2021
b8b3140
Update v1.1.rst
lobpcg Nov 5, 2021
1c7e325
Update v1.1.rst
lobpcg Dec 3, 2021
67c3afd
Merge branch 'main' into patch-1
lobpcg Dec 3, 2021
37ac937
Update v1.1.rst
lobpcg Dec 4, 2021
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9 changes: 9 additions & 0 deletions doc/whats_new/v1.1.rst
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Expand Up @@ -34,6 +34,10 @@ random sampling procedures.
same solution, up to numerical rounding errors, but in general Lloyd's
algorithm uses much less memory, and it is often faster.

- |Fix| The eigenvectors initialization for :class:`cluster.SpectralClustering`
and :class:`manifold.SpectralEmbedding` now samples from a Gaussian when
using the `'amg'` or `'lobpcg'` solver. This change improves numerical
stability of the solver, but may result in a different model.

Changelog
---------
Expand Down Expand Up @@ -240,6 +244,11 @@ Changelog
preserve this dtype.
:pr:`21534` by :user:`Andrew Knyazev <lobpcg>`.

- |Fix| :func:`manifold.spectral_embedding` now uses Gaussian instead of
the previous uniform on [0, 1] random initial approximations to eigenvectors
in eigen_solvers `lobpcg` and `amg` to improve their numerical stability.
:pr:`21565` by :user:`Andrew Knyazev <lobpcg>`.

:mod:`sklearn.model_selection`
..............................

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4 changes: 2 additions & 2 deletions sklearn/manifold/_spectral_embedding.py
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Expand Up @@ -336,7 +336,7 @@ def spectral_embedding(

M = ml.aspreconditioner()
# Create initial approximation X to eigenvectors
X = random_state.rand(laplacian.shape[0], n_components + 1)
X = random_state.randn(laplacian.shape[0], n_components + 1)
X[:, 0] = dd.ravel()
X = X.astype(laplacian.dtype)
_, diffusion_map = lobpcg(laplacian, X, M=M, tol=1.0e-5, largest=False)
Expand Down Expand Up @@ -367,7 +367,7 @@ def spectral_embedding(
# We increase the number of eigenvectors requested, as lobpcg
# doesn't behave well in low dimension and create initial
# approximation X to eigenvectors
X = random_state.rand(laplacian.shape[0], n_components + 1)
X = random_state.randn(laplacian.shape[0], n_components + 1)
X[:, 0] = dd.ravel()
X = X.astype(laplacian.dtype)
_, diffusion_map = lobpcg(
Expand Down