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.
Added in version 0.17.
For a comparison between
QuadraticDiscriminantAnalysis
andLinearDiscriminantAnalysis
, see Linear and Quadratic Discriminant Analysis with covariance ellipsoid.Read more in the User Guide.
- Parameters:
- priorsarray-like of shape (n_classes,), default=None
Class priors. By default, the class proportions are inferred from the training data.
- reg_paramfloat, default=0.0
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 thescaling_
attribute of a given class.- store_covariancebool, default=False
If True, the class covariance matrices are explicitly computed and stored in the
self.covariance_
attribute.Added in version 0.17.
- tolfloat, default=1.0e-4
Absolute threshold for the covariance matrix to be considered rank deficient after applying some regularization (see
reg_param
) to eachSk
whereSk
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.
- Attributes:
- covariance_list of len n_classes of ndarray of shape (n_features, n_features)
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_array-like of shape (n_classes, n_features)
Class-wise means.
- priors_array-like of shape (n_classes,)
Class priors (sum to 1).
- rotations_list of len n_classes of ndarray of shape (n_features, n_k)
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 toV
, the matrix of eigenvectors coming from the SVD ofXk = U S Vt
whereXk
is the centered matrix of samples from class k.- scalings_list of len n_classes of ndarray of shape (n_k,)
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)
, whereS
is the diagonal matrix of singular values from the SVD ofXk
, whereXk
is the centered matrix of samples from class k.- classes_ndarray of shape (n_classes,)
Unique class labels.
- n_features_in_int
Number of features seen during fit.
Added in version 0.24.
- feature_names_in_ndarray of shape (
n_features_in_
,) Names of features seen during fit. Defined only when
X
has feature names that are all strings.Added in version 1.0.
See also
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() >>> print(clf.predict([[-0.8, -1]])) [1]
- decision_function(X)[source]#
Apply decision function to an array of samples.
The decision function is equal (up to a constant factor) to the log-posterior of the model, i.e.
log p(y = k | x)
. In a binary classification setting this instead corresponds to the differencelog p(y = 1 | x) - log p(y = 0 | x)
. See Mathematical formulation of the LDA and QDA classifiers.- Parameters:
- Xarray-like of shape (n_samples, n_features)
Array of samples (test vectors).
- Returns:
- Cndarray of shape (n_samples,) or (n_samples, n_classes)
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)[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 asstore_covariance
.Changed in version 0.19:
tol
has been moved to main constructor.- Parameters:
- Xarray-like of shape (n_samples, n_features)
Training vector, where
n_samples
is the number of samples andn_features
is the number of features.- yarray-like of shape (n_samples,)
Target values (integers).
- Returns:
- selfobject
Fitted estimator.
- get_metadata_routing()[source]#
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
- Returns:
- routingMetadataRequest
A
MetadataRequest
encapsulating routing information.
- get_params(deep=True)[source]#
Get parameters for this estimator.
- Parameters:
- deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns:
- paramsdict
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:
- Xarray-like of shape (n_samples, n_features)
Vector to be scored, where
n_samples
is the number of samples andn_features
is the number of features.
- Returns:
- Cndarray of shape (n_samples,)
Estimated probabilities.
- predict_log_proba(X)[source]#
Return log of posterior probabilities of classification.
- Parameters:
- Xarray-like of shape (n_samples, n_features)
Array of samples/test vectors.
- Returns:
- Cndarray of shape (n_samples, n_classes)
Posterior log-probabilities of classification per class.
- predict_proba(X)[source]#
Return posterior probabilities of classification.
- Parameters:
- Xarray-like of shape (n_samples, n_features)
Array of samples/test vectors.
- Returns:
- Cndarray of shape (n_samples, n_classes)
Posterior probabilities of classification per class.
- score(X, y, sample_weight=None)[source]#
Return accuracy on provided 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:
- Xarray-like of shape (n_samples, n_features)
Test samples.
- yarray-like of shape (n_samples,) or (n_samples, n_outputs)
True labels for
X
.- sample_weightarray-like of shape (n_samples,), default=None
Sample weights.
- Returns:
- scorefloat
Mean accuracy of
self.predict(X)
w.r.t.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
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object.- Parameters:
- **paramsdict
Estimator parameters.
- Returns:
- selfestimator instance
Estimator instance.
- set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') QuadraticDiscriminantAnalysis [source]#
Configure whether metadata should be requested to be passed to the
score
method.Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with
enable_metadata_routing=True
(seesklearn.set_config
). Please check the User Guide on how the routing mechanism works.The options for each parameter are:
True
: metadata is requested, and passed toscore
if provided. The request is ignored if metadata is not provided.False
: metadata is not requested and the meta-estimator will not pass it toscore
.None
: metadata is not requested, and the meta-estimator will raise an error if the user provides it.str
: metadata should be passed to the meta-estimator with this given alias instead of the original name.
The default (
sklearn.utils.metadata_routing.UNCHANGED
) retains the existing request. This allows you to change the request for some parameters and not others.Added in version 1.3.
- Parameters:
- sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for
sample_weight
parameter inscore
.
- Returns:
- selfobject
The updated object.
Gallery examples#

Linear and Quadratic Discriminant Analysis with covariance ellipsoid