.. _example_plot_kernel_approximation.py:


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Explicit feature map approximation for RBF kernels
==================================================

.. currentmodule:: sklearn.kernel_approximation

An example shows how to use :class:`RBFSampler` to appoximate the feature map
of an RBF kernel for classification with an SVM on the digits dataset.  Results
using a linear SVM in the original space, a linear SVM using the approximate
mapping and using a kernelized SVM are compared.  Timings and accuracy for
varying amounts of Monte Carlo samplings for the approximate mapping are shown.

Sampling more dimensions clearly leads to better classification results, but
comes at a greater cost. This means there is a tradeoff between runtime and
accuracy, given by the parameter n_components.  Note that solving the Linear
SVM and also the approximate kernel SVM could be greatly accelerated by using
stochastic gradient descent via :class:`sklearn.linear_model.SGDClassifier`.
This is not easily possible for the case of the kernelized SVM.

The second plot visualized the decision surfaces of the RBF kernel SVM and
the linear SVM with approximate kernel map.
The plot shows decision surfaces of the classifiers projected onto
the first two principal components of the data. This visualization should
be taken with a grain of salt since it is just an interesting slice through
the decision surface in 64 dimensions. In particular note that
a datapoint (represented as a dot) does not necessarily be classified
into the region it is lying in, since it will not lie on the plane
that the first two principal components span.

The usage of :class:`RBFSampler` is described in detail in
:ref:`kernel_approximation`.




.. rst-class:: horizontal


    *

      .. image:: images/plot_kernel_approximation_2.png
            :scale: 47

    *

      .. image:: images/plot_kernel_approximation_1.png
            :scale: 47




**Python source code:** :download:`plot_kernel_approximation.py <plot_kernel_approximation.py>`

.. literalinclude:: plot_kernel_approximation.py
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