discriminant_analysis.QuadraticDiscriminantAnalysis()

class sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis(priors=None, reg_param=0.0, store_covariances=False, tol=0.0001) [source]

Quadratic Discriminant Analysis

A classifier with a quadratic decision boundary, generated by fitting class conditional densities to the data and using Bayes? rule.

The model fits a Gaussian density to each class.

New in version 0.17: QuadraticDiscriminantAnalysis

Read more in the User Guide.

Parameters:

priors : array, optional, shape = [n_classes] Priors on classes reg_param : float, optional Regularizes the covariance estimate as (1-reg_param)*Sigma + reg_param*np.eye(n_features)

Attributes:

covariances_ : list of array-like, shape = [n_features, n_features] Covariance matrices of each class. means_ : array-like, shape = [n_classes, n_features] Class means. priors_ : array-like, shape = [n_classes] Class priors (sum to 1). rotations_ : list of arrays For each class k an array of shape [n_features, n_k], with n_k = min(n_features, number of elements in class k) It is the rotation of the Gaussian distribution, i.e. its principal axis. scalings_ : list of arrays For each class k an array of shape [n_k]. It contains the scaling of the Gaussian distributions along its principal axes, i.e. the variance in the rotated coordinate system. store_covariances : boolean If True the covariance matrices are computed and stored in the self.covariances_ attribute. New in version 0.17. tol : float, optional, default 1.0e-4 Threshold used for rank estimation. New in version 0.17.

See also

sklearn.discriminant_analysis.LinearDiscriminantAnalysis

Linear Discriminant Analysis

Examples

>>> from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> y = np.array([1, 1, 1, 2, 2, 2])
>>> clf = QuadraticDiscriminantAnalysis()
>>> clf.fit(X, y)
... 
QuadraticDiscriminantAnalysis(priors=None, reg_param=0.0,
                              store_covariances=False, tol=0.0001)
>>> print(clf.predict([[-0.8, -1]]))
[1]

Methods

decision_function(X)	Apply decision function to an array of samples.
fit(X, y[, store_covariances, tol])	Fit the model according to the given training data and parameters.
get_params([deep])	Get parameters for this estimator.
predict(X)	Perform classification on an array of test vectors X.
predict_log_proba(X)	Return posterior probabilities of classification.
predict_proba(X)	Return posterior probabilities of classification.
score(X, y[, sample_weight])	Returns the mean accuracy on the given test data and labels.
set_params(\*\*params)	Set the parameters of this estimator.

__init__(priors=None, reg_param=0.0, store_covariances=False, tol=0.0001) [source]

decision_function(X) [source]

Apply decision function to an array of samples.

Parameters:	X : array-like, shape = [n_samples, n_features] Array of samples (test vectors).
Returns:	C : array, shape = [n_samples, n_classes] or [n_samples,] Decision function values related to each class, per sample. In the two-class case, the shape is [n_samples,], giving the log likelihood ratio of the positive class.

fit(X, y, store_covariances=None, tol=None) [source]

Fit the model according to the given training data and parameters.

Changed in version 0.17: Deprecated store_covariance have been moved to main constructor.

Changed in version 0.17: Deprecated tol have been moved to main constructor.

Parameters:	X : array-like, shape = [n_samples, n_features] Training vector, where n_samples in the number of samples and n_features is the number of features. y : array, shape = [n_samples] Target values (integers)

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping of string to any Parameter names mapped to their values.

predict(X) [source]

Perform classification on an array of test vectors X.

The predicted class C for each sample in X is returned.

Parameters:	X : array-like, shape = [n_samples, n_features]
Returns:	C : array, shape = [n_samples]

predict_log_proba(X) [source]

Return posterior probabilities of classification.

Parameters:	X : array-like, shape = [n_samples, n_features] Array of samples/test vectors.
Returns:	C : array, shape = [n_samples, n_classes] Posterior log-probabilities of classification per class.

predict_proba(X) [source]

Return posterior probabilities of classification.

Parameters:	X : array-like, shape = [n_samples, n_features] Array of samples/test vectors.
Returns:	C : array, shape = [n_samples, n_classes] Posterior probabilities of classification per class.

score(X, y, sample_weight=None) [source]

Returns the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters:	X : array-like, shape = (n_samples, n_features) Test samples. y : array-like, shape = (n_samples) or (n_samples, n_outputs) True labels for X. sample_weight : array-like, shape = [n_samples], optional Sample weights.
Returns:	score : float Mean accuracy of self.predict(X) wrt. y.

set_params(**params) [source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it?s possible to update each component of a nested object.

Returns:	self :

Examples using sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis

Classifier comparison

Linear and Quadratic Discriminant Analysis with confidence ellipsoid