.. _sphx_glr_auto_examples_plot_ovk_regression_cf.py:


===================================================
Vector-field Learning with structured output kernel
===================================================

An example to illustrate structured learning with operator-valued kernels.

We compare Operator-valued kernel (OVK) with scikit-learn multi-output ridge
regression.




.. image:: /auto_examples/images/sphx_glr_plot_ovk_regression_cf_001.png
    :align: center


.. rst-class:: sphx-glr-script-out

 Out::

    R2 curl-free ridge: 0.76959
    R2 independent ridge: 0.63015




|


.. code-block:: python

    # Author: Romain Brault <ro.brault@gmail.com>
    # License: MIT

    # -*- coding: utf-8 -*-
    import operalib as ovk

    import matplotlib.pyplot as plt

    import numpy as np
    from numpy.random import RandomState

    from sklearn.model_selection import train_test_split
    from sklearn.kernel_ridge import KernelRidge


    def main():
        """Example of vector-field learning."""

        # Fix a seed
        random_state = RandomState(0)

        # Generate data
        inputs, targets = ovk.toy_data_curl_free_field(n_samples=2000)
        inputs_mesh = ovk.array2mesh(inputs)

        inputs_train, inputs_test, targets_train, targets_test = train_test_split(
            inputs, targets, train_size=(inputs.shape[0] - 40 ** 2),
            random_state=random_state)
        # Add some noise
        targets_train = (targets_train +
                         .175 * random_state.randn(targets_train.shape[0],
                                                   targets_train.shape[1]))

        regressor = {'CF':
                     ovk.OVKRidge(ovkernel=ovk.RBFCurlFreeKernel(gamma=2.),
                                  lbda=1e-4),
                     'Indep':
                     KernelRidge(kernel='rbf', gamma=.5, alpha=1e-4)}

        # Learning with curl-free
        regressor['CF'].fit(inputs_train, targets_train)
        score_cf = regressor['CF'].score(inputs_test, targets_test)
        print('R2 curl-free ridge: %.5f' % score_cf)
        targets_mesh_cf = ovk.array2mesh(regressor['CF'].predict(inputs))

        # Learning with sklearn ridge
        regressor['Indep'].fit(inputs_train, targets_train)
        scode_id = regressor['Indep'].score(inputs_test, targets_test)
        print('R2 independent ridge: %.5f' % scode_id)
        targets_mesh_id = ovk.array2mesh(regressor['Indep'].predict(inputs))

        # Plotting
        # pylint: disable=E1101
        fig, axarr = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(14, 7))
        axarr[0].streamplot(inputs_mesh[0], inputs_mesh[1],
                            targets_mesh_cf[0], targets_mesh_cf[1],
                            color=np.sqrt(targets_mesh_cf[0]**2 +
                                          targets_mesh_cf[1]**2),
                            linewidth=.5, cmap=plt.cm.jet, density=2,
                            arrowstyle=u'->')
        axarr[1].streamplot(inputs_mesh[0], inputs_mesh[1],
                            targets_mesh_id[0], targets_mesh_id[1],
                            color=np.sqrt(targets_mesh_id[0]**2 +
                                          targets_mesh_id[1]**2),
                            linewidth=.5, cmap=plt.cm.jet, density=2,
                            arrowstyle=u'->')
        axarr[0].set_ylim([-1, 1])
        axarr[0].set_xlim([-1, 1])
        axarr[0].set_title('Curl-Free Ridge, R2: %.5f' % score_cf)
        axarr[1].set_ylim([-1, 1])
        axarr[1].set_xlim([-1, 1])
        axarr[1].set_title('Independent Ridge, R2: %.5f' % scode_id)

        fig.suptitle('Vectorfield learning')
        plt.show()


    if __name__ == '__main__':
        main()

**Total running time of the script:** ( 0 minutes  17.491 seconds)



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     :download:`Download Python source code: plot_ovk_regression_cf.py <plot_ovk_regression_cf.py>`



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