.. _`Quadratic Discriminant Analysis`:

.. _`com.sympathyfordata.advancedmachinelearning.quadratic_discriminant_analysis`:

Quadratic Discriminant Analysis
```````````````````````````````

.. image:: QDA.svg
   :width: 48


Constructs a quadratic classifier that separates two or more classes.




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

Attributes
==========

    **covariance_**
        For each class, gives the covariance matrix estimated using the
        samples of that class. The estimations are unbiased. Only present if
        `store_covariance` is True.


    **means_**
        Class-wise means.


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


    **rotations_**
        For each class k an array of shape (n_features, n_k), where
        ``n_k = min(n_features, number of elements in class k)``
        It is the rotation of the Gaussian distribution, i.e. its
        principal axis. It corresponds to `V`, the matrix of eigenvectors
        coming from the SVD of `Xk = U S Vt` where `Xk` is the centered
        matrix of samples from class k.


    **scalings_**
        For each class, contains the scaling of
        the Gaussian distributions along its principal axes, i.e. the
        variance in the rotated coordinate system. It corresponds to `S^2 /
        (n_samples - 1)`, where `S` is the diagonal matrix of singular values
        from the SVD of `Xk`, where `Xk` is the centered matrix of samples
        from class k.


Definition
::::::::::


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

    **model**  model
        Model




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

    **Covariance regularization parameter** (reg_param)
        Regularizes the per-class covariance estimates by transforming S2 as
        ``S2 = (1 - reg_param) * S2 + reg_param * np.eye(n_features)``,
        where S2 corresponds to the `scaling_` attribute of a given class.
    **Store covariance** (store_covariance)
        If True, the class covariance matrices are explicitly computed and
        stored in the `self.covariance_` attribute.

        .. versionadded:: 0.17
    **Tolerance** (tol)
        Absolute threshold for the covariance matrix to be considered rank
        deficient after applying some regularization (see `reg_param`) to each
        `Sk` where `Sk` represents covariance matrix for k-th class. This
        parameter does not affect the predictions. It controls when a warning
        is raised if the covariance matrix is not full rank.

        .. versionadded:: 0.17







Examples
========

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




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

.. automodule:: node_discriminant_analysis
    :noindex:

.. class:: QuadraticDiscriminantAnalysis
    :noindex: