Quadratic Discriminant Analysis

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.

Added in version 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.

Added in version 0.17.

Examples

• Fisher_faces.syx

Implementation

Some of the docstrings for this module have been automatically extracted from the scikit-learn library and are covered by their respective licenses.

class node_discriminant_analysis.QuadraticDiscriminantAnalysis