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# sklearn.qda.QDA¶

class sklearn.qda.QDA(priors=None, reg_param=0.0)[source]

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) 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.

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]
```

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[, sample_weight]) Returns the mean accuracy on the given test data and labels. set_params(**params) Set the parameters of this estimator.
static __init__(priors=None, reg_param=0.0)[source]
static 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). 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.
static fit(X, y, store_covariances=False, tol=0.0001)[source]

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. tol : float, optional, default 1.0e-4 Threshold used for rank estimation.
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. params : mapping of string to any Parameter names mapped to their values.
static 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] C : array, shape = [n_samples]
static predict_log_proba(X)[source]

Return posterior probabilities of classification.

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

Return posterior probabilities of classification.

Parameters: X : array-like, shape = [n_samples, n_features] Array of samples/test vectors. 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. 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 former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns: self :