sklearn.qda.QDA¶

class sklearn.qda.QDA(priors=None, reg_param=0.0)¶

Quadratic Discriminant Analysis (QDA)

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.

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)

See also

sklearn.lda.LDA: Linear discriminant analysis

Examples

>>> from sklearn.qda import QDA
>>> 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 = QDA()
>>> clf.fit(X, y)
QDA(priors=None, reg_param=0.0)
>>> print(clf.predict([[-0.8, -1]]))
[1]

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 an array of shape [n_samples, n_samples], the rotation of the Gaussian distribution, i.e. its principal axis.
scalings_	array-like, shape = [n_classes, n_features]	Contains the scaling of the Gaussian distributions along the principal axes for each class, i.e. the variance in the rotated coordinate system.

Methods

`decision_function`(X)	Apply decision function to an array of samples.
`fit`(X, y[, store_covariances, tol])	Fit the QDA 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)	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)¶

decision_function(X)¶

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=False, tol=0.0001)¶

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

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)

store_covariances : boolean

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

get_params(deep=True)¶

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)¶

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)¶

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)¶

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)¶

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

Parameters :

X : array-like, shape = (n_samples, n_features)

Test samples.

y : array-like, shape = (n_samples,)

True labels for X.

Returns :

score : float

Mean accuracy of self.predict(X) wrt. y.

set_params(**params)¶

Set the parameters of this estimator.

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

Returns :	self :