8000 DOC Adding dropdown for module 2.2 Manifold Learning by punndcoder28 · Pull Request #26720 · scikit-learn/scikit-learn · GitHub
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DOC Adding dropdown for module 2.2 Manifold Learning #26720

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DOC Adding dropdown for module 2.2 Manifold Learning #26720

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70 changes: 50 additions & 20 deletions doc/modules/manifold.rst
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Expand Up @@ -130,8 +130,10 @@ distances between all points. Isomap can be performed with the object
:align: center
:scale: 50

Complexity
----------
|details-start|
**Complexity**
|details-split|

The Isomap algorithm comprises three stages:

1. **Nearest neighbor search.** Isomap uses
Expand Down Expand Up @@ -162,6 +164,8 @@ The overall complexity of Isomap is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* `"A global geometric framework for nonlinear dimensionality reduction"
Expand All @@ -187,8 +191,9 @@ Locally linear embedding can be performed with function
:align: center
:scale: 50

Complexity
----------
|details-start|
**Complexity**
|details-split|

The standard LLE algorithm comprises three stages:

Expand All @@ -209,6 +214,8 @@ The overall complexity of standard LLE is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* `"Nonlinear dimensionality reduction by locally linear embedding"
Expand Down Expand Up @@ -241,8 +248,9 @@ It requires ``n_neighbors > n_components``.
:align: center
:scale: 50

Complexity
----------
|details-start|
**Complexity**
|details-split|

The MLLE algorithm comprises three stages:

Expand All @@ -265,6 +273,8 @@ The overall complexity of MLLE is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* `"MLLE: Modified Locally Linear Embedding Using Multiple Weights"
Expand All @@ -291,8 +301,9 @@ It requires ``n_neighbors > n_components * (n_components + 3) / 2``.
:align: center
:scale: 50

Complexity
----------
|details-start|
**Complexity**
|details-split|

The HLLE algorithm comprises three stages:

Expand All @@ -313,6 +324,8 @@ The overall complexity of standard HLLE is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* `"Hessian Eigenmaps: Locally linear embedding techniques for
Expand All @@ -335,8 +348,9 @@ preserving local distances. Spectral embedding can be performed with the
function :func:`spectral_embedding` or its object-oriented counterpart
:class:`SpectralEmbedding`.

Complexity
----------
|details-start|
**Complexity**
|details-split|

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

Expand All @@ -358,6 +372,8 @@ The overall complexity of spectral embedding is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* `"Laplacian Eigenmaps for Dimensionality Reduction
Expand All @@ -383,8 +399,9 @@ tangent spaces to learn the embedding. LTSA can be performed with function
:align: center
:scale: 50

Complexity
----------
|details-start|
**Complexity**
|details-split|

The LTSA algorithm comprises three stages:

Expand All @@ -404,6 +421,8 @@ The overall complexity of standard LTSA is
* :math:`k` : number of nearest neighbors
* :math:`d` : output dimension

|details-end|

.. topic:: References:

* :arxiv:`"Principal manifolds and nonlinear dimensionality reduction via
Expand Down Expand Up @@ -448,8 +467,9 @@ the similarities chosen in some optimal ways. The objective, called the
stress, is then defined by :math:`\sum_{i < j} d_{ij}(X) - \hat{d}_{ij}(X)`


Metric MDS
----------
|details-start|
**Metric MDS**
|details-split|

The simplest metric :class:`MDS` model, called *absolute MDS*, disparities are defined by
:math:`\hat{d}_{ij} = S_{ij}`. With absolute MDS, the value :math:`S_{ij}`
Expand All @@ -458,8 +478,11 @@ should then correspond exactly to the distance between point :math:`i` and

Most commonly, disparities are set to :math:`\hat{d}_{ij} = b S_{ij}`.

Nonmetric MDS
-------------
|details-end|

|details-start|
**Nonmetric MDS**
|details-split|

Non metric :class:`MDS` focuses on the ordination of the data. If
:math:`S_{ij} > S_{jk}`, then the embedding should enforce :math:`d_{ij} <
Expand Down Expand Up @@ -490,6 +513,7 @@ in the metric case.
:align: center
:scale: 60

|details-end|

.. topic:: References:

Expand Down Expand Up @@ -551,8 +575,10 @@ The disadvantages to using t-SNE are roughly:
:align: center
:scale: 50

Optimizing t-SNE
----------------
|details-start|
**Optimizing t-SNE**
|details-split|

The main purpose of t-SNE is visualization of high-dimensional data. Hence,
it works best when the data will be embedded on two or three dimensions.

Expand Down Expand Up @@ -601,8 +627,11 @@ but less accurate results.
provides a good discussion of the effects of the various parameters, as well
as interactive plots to explore the effects of different parameters.

Barnes-Hut t-SNE
----------------
|details-end|

|details-start|
**Barnes-Hut t-SNE**
|details-split|

The Barnes-Hut t-SNE that has been implemented here is usually much slower than
other manifold learning algorithms. The optimization is quite difficult
Expand Down Expand Up @@ -638,6 +667,7 @@ imply that the data cannot be correctly classified by a supervised model. It
might be the case that 2 dimensions are not high enough to accurately represent
the internal structure of the data.

|details-end|

.. topic:: References:

Expand Down
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