.. _`Partial Least Squares cross-decomposition (PLS regression)`:

.. _`org.sysess.sympathy.machinelearning.pls`:

Partial Least Squares cross-decomposition (PLS regression)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. image:: PCA.svg
   :width: 48


Finds the fundamental relations between two matrices X and Y, ie. it finds the (multidimensional) direction in X that best explains maximum multidimensional direction in Y. See also PCA-analysis



**Documentation**

Finds the fundamental relations between two matrices X and Y, ie. it finds the (multidimensional) direction in X that best explains maximum multidimensional direction in Y. See also PCA-analysis

*Configuration*:


  - *n_components*

    Number of components to keep. Should be in `[1, min(n_samples,
    n_features, n_targets)]`.


  - *scale*

    Whether to scale `X` and `Y`.


  - *max_iter*

    The maximum number of iterations of the power method when
    `algorithm='nipals'`. Ignored otherwise.


  - *tol*

    The tolerance used as convergence criteria in the power method: the
    algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
    than `tol`, where `u` corresponds to the left singular vector.




*Attributes*:


  - *x_weights_*

    The left singular vectors of the cross-covariance matrices of each
    iteration.


  - *y_weights_*

    The right singular vectors of the cross-covariance matrices of each
    iteration.


  - *x_loadings_*

    The loadings of `X`.


  - *y_loadings_*

    The loadings of `Y`.


  - *x_scores_*

    The transformed training samples.


  - *y_scores_*

    The transformed training targets.


  - *x_rotations_*

    The projection matrix used to transform `X`.


  - *y_rotations_*

    The projection matrix used to transform `Y`.


  - *coef_*

    The coefficients of the linear model such that `Y` is approximated as
    `Y = X @ coef_`.


  - *n_iter_*

    Number of iterations of the power method, for each
    component. Empty if `algorithm='svd'`.




*Input ports*:


*Output ports*:
    **model** : model
        Model


**Definition**


*Input ports*


*Output ports*

    :model:  model

        Model





.. automodule:: node_decomposition
    :noindex:

.. class:: PLSRegressionCrossDecomposition
    :noindex: