Add prominent mention of Laplacian Eigenmaps being the algorithm that Spectral Embedding implements

samsontmr · samsontmr · commit 5c9a6c4052e7 · 2017-01-12T13:44:19.000+08:00
diff --git a/doc/modules/manifold.rst b/doc/modules/manifold.rst
@@ -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
@@ -319,7 +319,7 @@ function :func:`spectral_embedding` or its object-oriented counterpart
 Complexity
 ----------
 
-The Spectral Embedding algorithm comprises three stages:
+The Laplacian Eigenmaps algorithm comprises three stages:
 
 1. **Weighted Graph Construction**. Transform the raw input data into
    graph representation using affinity (adjacency) matrix representation.
@@ -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.
-
diff --git a/sklearn/manifold/spectral_embedding_.py b/sklearn/manifold/spectral_embedding_.py
@@ -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
@@ -189,7 +191,7 @@ def spectral_embedding(adjacency, n_components=8, eigen_solver=None,
 
     Notes
     -----
-    Spectral embedding is most useful when the graph has one connected
+    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.
 
@@ -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
