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DOC Fix dropdown content indentation (scikit-learn#30116)
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abhi-jha authored Oct 21, 2024
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26 changes: 13 additions & 13 deletions doc/modules/manifold.rst
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Expand Up @@ -293,24 +293,24 @@ It requires ``n_neighbors > n_components * (n_components + 3) / 2``.

.. dropdown:: Complexity

The HLLE algorithm comprises three stages:
The HLLE algorithm comprises three stages:

1. **Nearest Neighbors Search**. Same as standard LLE
1. **Nearest Neighbors Search**. Same as standard LLE

2. **Weight Matrix Construction**. Approximately
:math:`O[D N k^3] + O[N d^6]`. The first term reflects a similar
cost to that of standard LLE. The second term comes from a QR
decomposition of the local hessian estimator.
2. **Weight Matrix Construction**. Approximately
:math:`O[D N k^3] + O[N d^6]`. The first term reflects a similar
cost to that of standard LLE. The second term comes from a QR
decomposition of the local hessian estimator.

3. **Partial Eigenvalue Decomposition**. Same as standard LLE.
3. **Partial Eigenvalue Decomposition**. Same as standard LLE.

The overall complexity of standard HLLE is
:math:`O[D \log(k) N \log(N)] + O[D N k^3] + O[N d^6] + O[d N^2]`.
The overall complexity of standard HLLE is
:math:`O[D \log(k) N \log(N)] + O[D N k^3] + O[N d^6] + O[d N^2]`.

* :math:`N` : number of training data points
* :math:`D` : input dimension
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension
* :math:`N` : number of training data points
* :math:`D` : input dimension
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

.. rubric:: References

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2 changes: 1 addition & 1 deletion sklearn/manifold/tests/test_spectral_embedding.py
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Expand Up @@ -54,7 +54,7 @@

def _assert_equal_with_sign_flipping(A, B, tol=0.0):
"""Check array A and B are equal with possible sign flipping on
each columns"""
each column"""
tol_squared = tol**2
for A_col, B_col in zip(A.T, B.T):
assert (
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