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merged 4 commits into from
Jun 21, 2023
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DOC Add dropdowns to module 1.4 SVM #26641

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3bb5146
Add html dropdown
Tech-Netiums Jun 20, 2023
2a58d04
Add dropdowns
Tech-Netiums Jun 20, 2023
93c2e2c
Merge remote-tracking branch 'upstream/main' into dropdown_svm
Tech-Netiums Jun 21, 2023
8c01535
Merge branch 'main' into dropdown_svm
GaelVaroquaux Jun 21, 2023
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33 changes: 24 additions & 9 deletions doc/modules/svm.rst
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Expand Up @@ -149,6 +149,10 @@ multi-class strategy, thus training `n_classes` models.
See :ref:`svm_mathematical_formulation` for a complete description of
the decision function.

|details-start|
**Details on multi-class strategies**
|details-split|

Note that the :class:`LinearSVC` also implements an alternative multi-class
strategy, the so-called multi-class SVM formulated by Crammer and Singer
[#8]_, by using the option ``multi_class='crammer_singer'``. In practice,
Expand Down Expand Up @@ -199,6 +203,8 @@ Then ``dual_coef_`` looks like this:
|for SVs of class 0 |for SVs of class 1 |for SVs of class 2 |
+--------------------------------------------------------------------------+-------------------------------------------------+-------------------------------------------------+

|details-end|

.. topic:: Examples:

* :ref:`sphx_glr_auto_examples_svm_plot_iris_svc.py`,
Expand Down Expand Up @@ -505,9 +511,9 @@ is advised to use :class:`~sklearn.model_selection.GridSearchCV` with
* :ref:`sphx_glr_auto_examples_svm_plot_rbf_parameters.py`
* :ref:`sphx_glr_auto_examples_svm_plot_svm_nonlinear.py`


Custom Kernels
--------------
|details-start|
**Custom Kernels**
|details-split|

You can define your own kernels by either giving the kernel as a
python function or by precomputing the Gram matrix.
Expand Down Expand Up @@ -571,6 +577,7 @@ test vectors must be provided:
>>> clf.predict(gram_test)
array([0, 1, 0])

|details-end|

.. _svm_mathematical_formulation:

Expand Down Expand Up @@ -667,8 +674,9 @@ term :math:`b`
estimator used is :class:`~sklearn.linear_model.Ridge` regression,
the relation between them is given as :math:`C = \frac{1}{alpha}`.

LinearSVC
---------
|details-start|
**LinearSVC**
|details-split|

The primal problem can be equivalently formulated as

Expand All @@ -683,10 +691,13 @@ does not involve inner products between samples, so the famous kernel trick
cannot be applied. This is why only the linear kernel is supported by
:class:`LinearSVC` (:math:`\phi` is the identity function).

|details-end|

.. _nu_svc:

NuSVC
-----
|details-start|
**NuSVC**
|details-split|

The :math:`\nu`-SVC formulation [#7]_ is a reparameterization of the
:math:`C`-SVC and therefore mathematically equivalent.
Expand All @@ -699,6 +710,7 @@ to a sample that lies on the wrong side of its margin boundary: it is either
misclassified, or it is correctly classified but does not lie beyond the
margin.

|details-end|

SVR
---
Expand Down Expand Up @@ -747,8 +759,9 @@ which holds the difference :math:`\alpha_i - \alpha_i^*`, ``support_vectors_`` w
holds the support vectors, and ``intercept_`` which holds the independent
term :math:`b`

LinearSVR
---------
|details-start|
**LinearSVR**
|details-split|

The primal problem can be equivalently formulated as

Expand All @@ -760,6 +773,8 @@ where we make use of the epsilon-insensitive loss, i.e. errors of less than
:math:`\varepsilon` are ignored. This is the form that is directly optimized
by :class:`LinearSVR`.

|details-end|

.. _svm_implementation_details:

Implementation details
Expand Down