8000 [MRG+1] Add prominent mention of Laplacian Eigenmaps by samsontmr · Pull Request #8155 · scikit-learn/scikit-learn · GitHub
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[MRG+1] Add prominent mention of Laplacian Eigenmaps #8155

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Jan 18, 2017
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[MRG+1] Add prominent mention of Laplacian Eigenmaps #8155

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Add prominent mention of Laplacian Eigenmaps being the algorithm that…
samsontmr Jan 5, 2017
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jnothman Jan 18, 2017
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8000 13 changes: 6 additions & 7 deletions doc/modules/manifold.rst
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Expand Up @@ -305,11 +305,11 @@ The overall complexity of standard HLLE is
Spectral Embedding
====================

Spectral Embedding (also known as Laplacian Eigenmaps) is one method
to calculate non-linear embedding. It finds a low dimensional representation
of the data using a spectral decomposition of the graph Laplacian.
The graph generated can be considered as a discrete approximation of the
low dimensional manifold in the high dimensional space. Minimization of a
Spectral Embedding is an approach to calculating a non-linear embedding.
Scikit-learn implements Laplacian Eigenmaps, which finds a low dimensional
representation of the data using a spectral decomposition of the graph
Laplacian. The graph generated can be considered as a discrete approximation of
the low dimensional manifold in the high dimensional space. Minimization of a
cost function based on the graph ensures that points close to each other on
the manifold are mapped close to each other in the low dimensional space,
preserving local distances. Spectral embedding can be performed with the
Expand All @@ -319,7 +319,7 @@ function :func:`spectral_embedding` or its object-oriented counterpart
Complexity
----------

The Spectral Embedding algorithm comprises three stages:
The Spectral Embedding (Laplacian Eigenmaps) algorithm comprises three stages:

1. **Weighted Graph Construction**. Transform the raw input data into
graph representation using affinity (adjacency) matrix representation.
Expand Down Expand Up @@ -640,4 +640,3 @@ Tips on practical use
:ref:`random_trees_embedding` can also be useful to derive non-linear
representations of feature space, also it does not perform
dimensionality reduction.

10 changes: 7 additions & 3 deletions sklearn/manifold/spectral_embedding_.py
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Expand Up @@ -149,6 +149,8 @@ def spectral_embedding(adjacency, n_components=8, eigen_solver=None,
However care must taken to always make the affinity matrix symmetric
so that the eigenvector decomposition works as expected.

Note : Laplacian Eigenmaps is the actual algorithm implemented here.

Read more in the :ref:`User Guide <spectral_embedding>`.

Parameters
Expand Down Expand Up @@ -189,9 +191,9 @@ def spectral_embedding(adjacency, n_components=8, eigen_solver=None,

Notes
-----
Spectral embedding is most useful when the graph has one connected
component. If there graph has many components, the first few eigenvectors
732E will simply uncover the connected components of the graph.
Spectral Embedding (Laplacian Eigenmaps) is most useful when the graph
has one connected component. If there graph has many components, the first
few eigenvectors will simply uncover the connected components of the graph.

References
----------
Expand Down Expand Up @@ -329,6 +331,8 @@ class SpectralEmbedding(BaseEstimator):
The resulting transformation is given by the value of the
eigenvectors for each data point.

Note : Laplacian Eigenmaps is the actual algorithm implemented here.

Read more in the :ref:`User Guide <spectral_embedding>`.

Parameters
Expand Down
0