sklearn.discriminant_analysis
.LinearDiscriminantAnalysis¶

class
sklearn.discriminant_analysis.
LinearDiscriminantAnalysis
(solver='svd', shrinkage=None, priors=None, n_components=None, store_covariance=False, tol=0.0001, covariance_estimator=None)[source]¶ Linear Discriminant Analysis
A classifier with a linear decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule.
The model fits a Gaussian density to each class, assuming that all classes share the same covariance matrix.
The fitted model can also be used to reduce the dimensionality of the input by projecting it to the most discriminative directions, using the
transform
method.New in version 0.17: LinearDiscriminantAnalysis.
Read more in the User Guide.
 Parameters
 solver{‘svd’, ‘lsqr’, ‘eigen’}, default=’svd’
 Solver to use, possible values:
‘svd’: Singular value decomposition (default). Does not compute the covariance matrix, therefore this solver is recommended for data with a large number of features.
‘lsqr’: Least squares solution. Can be combined with shrinkage or custom covariance estimator.
‘eigen’: Eigenvalue decomposition. Can be combined with shrinkage or custom covariance estimator.
 shrinkage‘auto’ or float, default=None
 Shrinkage parameter, possible values:
None: no shrinkage (default).
‘auto’: automatic shrinkage using the LedoitWolf lemma.
float between 0 and 1: fixed shrinkage parameter.
This should be left to None if
covariance_estimator
is used. Note that shrinkage works only with ‘lsqr’ and ‘eigen’ solvers. priorsarraylike of shape (n_classes,), default=None
The class prior probabilities. By default, the class proportions are inferred from the training data.
 n_componentsint, default=None
Number of components (<= min(n_classes  1, n_features)) for dimensionality reduction. If None, will be set to min(n_classes  1, n_features). This parameter only affects the
transform
method. store_covariancebool, default=False
If True, explicitely compute the weighted withinclass covariance matrix when solver is ‘svd’. The matrix is always computed and stored for the other solvers.
New in version 0.17.
 tolfloat, default=1.0e4
Absolute threshold for a singular value of X to be considered significant, used to estimate the rank of X. Dimensions whose singular values are nonsignificant are discarded. Only used if solver is ‘svd’.
New in version 0.17.
 covariance_estimatorcovariance estimator, default=None
If not None,
covariance_estimator
is used to estimate the covariance matrices instead of relying on the empirical covariance estimator (with potential shrinkage). The object should have a fit method and acovariance_
attribute like the estimators insklearn.covariance
. if None the shrinkage parameter drives the estimate.This should be left to None if
shrinkage
is used. Note thatcovariance_estimator
works only with ‘lsqr’ and ‘eigen’ solvers.New in version 0.24.
 Attributes
 coef_ndarray of shape (n_features,) or (n_classes, n_features)
Weight vector(s).
 intercept_ndarray of shape (n_classes,)
Intercept term.
 covariance_arraylike of shape (n_features, n_features)
Weighted withinclass covariance matrix. It corresponds to
sum_k prior_k * C_k
whereC_k
is the covariance matrix of the samples in classk
. TheC_k
are estimated using the (potentially shrunk) biased estimator of covariance. If solver is ‘svd’, only exists whenstore_covariance
is True. explained_variance_ratio_ndarray of shape (n_components,)
Percentage of variance explained by each of the selected components. If
n_components
is not set then all components are stored and the sum of explained variances is equal to 1.0. Only available when eigen or svd solver is used. means_arraylike of shape (n_classes, n_features)
Classwise means.
 priors_arraylike of shape (n_classes,)
Class priors (sum to 1).
 scalings_arraylike of shape (rank, n_classes  1)
Scaling of the features in the space spanned by the class centroids. Only available for ‘svd’ and ‘eigen’ solvers.
 xbar_arraylike of shape (n_features,)
Overall mean. Only present if solver is ‘svd’.
 classes_arraylike of shape (n_classes,)
Unique class labels.
See also
QuadraticDiscriminantAnalysis
Quadratic Discriminant Analysis.
Examples
>>> import numpy as np >>> from sklearn.discriminant_analysis import LinearDiscriminantAnalysis >>> 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 = LinearDiscriminantAnalysis() >>> clf.fit(X, y) LinearDiscriminantAnalysis() >>> print(clf.predict([[0.8, 1]])) [1]
Methods
Apply decision function to an array of samples.
fit
(X, y)Fit LinearDiscriminantAnalysis model according to the given
fit_transform
(X[, y])Fit to data, then transform it.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict class labels for samples in X.
Estimate log probability.
Estimate probability.
score
(X, y[, sample_weight])Return the mean accuracy on the given test data and labels.
set_params
(**params)Set the parameters of this estimator.
transform
(X)Project data to maximize class separation.

decision_function
(X)[source]¶ Apply decision function to an array of samples.
The decision function is equal (up to a constant factor) to the logposterior 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
 Xarraylike 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 twoclass case, the shape is (n_samples,), giving the log likelihood ratio of the positive class.

fit
(X, y)[source]¶  Fit LinearDiscriminantAnalysis model according to the given
training data and parameters.
Changed in version 0.19: store_covariance has been moved to main constructor.
Changed in version 0.19: tol has been moved to main constructor.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training data.
 yarraylike of shape (n_samples,)
Target values.

fit_transform
(X, y=None, **fit_params)[source]¶ Fit to data, then transform it.
Fits transformer to
X
andy
with optional parametersfit_params
and returns a transformed version ofX
. Parameters
 Xarraylike of shape (n_samples, n_features)
Input samples.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs), default=None
Target values (None for unsupervised transformations).
 **fit_paramsdict
Additional fit parameters.
 Returns
 X_newndarray array of shape (n_samples, n_features_new)
Transformed array.

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]¶ Predict class labels for samples in X.
 Parameters
 Xarraylike or sparse matrix, shape (n_samples, n_features)
Samples.
 Returns
 Carray, shape [n_samples]
Predicted class label per sample.

predict_log_proba
(X)[source]¶ Estimate log probability.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Input data.
 Returns
 Cndarray of shape (n_samples, n_classes)
Estimated log probabilities.

predict_proba
(X)[source]¶ Estimate probability.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Input data.
 Returns
 Cndarray of shape (n_samples, n_classes)
Estimated probabilities.

score
(X, y, sample_weight=None)[source]¶ Return the mean accuracy on the given test data and labels.
In multilabel 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
 Xarraylike of shape (n_samples, n_features)
Test samples.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True labels for
X
. sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
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
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.