.. _`Linear Discriminant Analysis`:

.. _`com.sympathyfordata.advancedmachinelearning.linear_discriminant_analysis`:

Linear Discriminant Analysis
````````````````````````````

.. image:: LDA.svg
   :width: 48


Constructs linear combinations of features that separates two or more classes. Can used either as a linear classifier or, more commonly, as a dimensionality reduction technique. For dimensionality reduction it requires a Y input to the fit_transform node




Documentation
:::::::::::::

Attributes
==========

    **classes_**
        Unique class labels.


    **coef_**
        Weight vector(s).


    **covariance_**
        Weighted within-class covariance matrix. It corresponds to
        `sum_k prior_k * C_k` where `C_k` is the covariance matrix of the
        samples in class `k`. The `C_k` are estimated using the (potentially
        shrunk) biased estimator of covariance. If solver is 'svd', only
        exists when `store_covariance` is True.


    **explained_variance_ratio_**
        Percentage of variance explained by each of the selected components.
        If ``n_components`` is not set then all components are stored and the
        sum of explained variances is equal to 1.0. Only available when eigen
        or svd solver is used.


    **intercept_**
        Intercept term.


    **means_**
        Class-wise means.


    **priors_**
        Class priors (sum to 1).


    **scalings_**
        Scaling of the features in the space spanned by the class centroids.
        Only available for 'svd' and 'eigen' solvers.


    **xbar_**
        Overall mean. Only present if solver is 'svd'.


Definition
::::::::::


Output ports
============

    **model**  model
        Model




Configuration
=============

    **N. of components for dimensionality reduction** (n_components)
        Number of components (<= min(n_classes - 1, n_features)) for
        dimensionality reduction. If None, will be set to
        min(n_classes - 1, n_features). This parameter only affects the
        `transform` method.

        For a usage example, see
        sphx_glr_auto_examples_decomposition_plot_pca_vs_lda.py.
    **Shrinkage parameter** (shrinkage)
        Shrinkage parameter, possible values:
          - None: no shrinkage (default).
          - 'auto': automatic shrinkage using the Ledoit-Wolf lemma.
          - float between 0 and 1: fixed shrinkage parameter.

        This should be left to None if `covariance_estimator` is used.
        Note that shrinkage works only with 'lsqr' and 'eigen' solvers.

        For a usage example, see
        sphx_glr_auto_examples_classification_plot_lda.py.
    **Solver to use** (solver)
        Solver to use, possible values:
          - 'svd': Singular value decomposition (default).
            Does not compute the covariance matrix, therefore this solver is
            recommended for data with a large number of features.
          - 'lsqr': Least squares solution.
            Can be combined with shrinkage or custom covariance estimator.
          - 'eigen': Eigenvalue decomposition.
            Can be combined with shrinkage or custom covariance estimator.

        .. versionchanged:: 1.2
            `solver="svd"` now has experimental Array API support. See the
            Array API User Guide <array_api> for more details.
    **Store covariance** (store_covariance)
        If True, explicitly compute the weighted within-class covariance
        matrix when solver is 'svd'. The matrix is always computed
        and stored for the other solvers.

        .. versionadded:: 0.17
    **Tolerance** (tol)
        Absolute threshold for a singular value of X to be considered
        significant, used to estimate the rank of X. Dimensions whose
        singular values are non-significant are discarded. Only used if
        solver is 'svd'.

        .. versionadded:: 0.17







Examples
========

* :download:`Fisher_faces.syx </Examples/Advanced Machine Learning/Fisher_faces.syx>`




Implementation
==============

.. automodule:: node_discriminant_analysis
    :noindex:

.. class:: LinearDiscriminantAnalysis
    :noindex: