sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis

class sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis(priors=None, reg_param=0.0, store_covariance=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)

store_covariance : boolean

If True the covariance matrices are computed and stored in the self.covariance_ attribute.

New in version 0.17.

tol : float, optional, default 1.0e-4

Threshold used for rank estimation.

New in version 0.17.
Attributes:
covariance_ : 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.

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_covariance=False, tol=0.0001)
>>> print(clf.predict([[-0.8, -1]]))
[1]

Methods

decision_function(self, X) Apply decision function to an array of samples.
fit(self, X, y) Fit the model according to the given training data and parameters.
get_params(self[, deep]) Get parameters for this estimator.
predict(self, X) Perform classification on an array of test vectors X.
predict_log_proba(self, X) Return posterior probabilities of classification.
predict_proba(self, X) Return posterior probabilities of classification.
score(self, X, y[, sample_weight]) Returns the mean accuracy on the given test data and labels.
set_params(self, \*\*params) Set the parameters of this estimator.
__init__(self, priors=None, reg_param=0.0, store_covariance=False, tol=0.0001)[source]
decision_function(self, 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(self, X, y)[source]

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

Changed in version 0.19: store_covariances has been moved to main constructor as store_covariance

Changed in version 0.19: tol has been moved to main constructor.

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

Training vector, where n_samples is the number of samples and n_features is the number of features.

y : array, shape = [n_samples]

Target values (integers)
get_params(self, 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(self, 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(self, 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(self, 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(self, 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(self, **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