8.14.1. sklearn.lda.LDA

class sklearn.lda.LDA(n_components=None, priors=None)

Linear Discriminant Analysis (LDA)

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.

Parameters :

n_components: int :

Number of components (< n_classes - 1) for dimensionality reduction

priors : array, optional, shape = [n_classes]

Priors on classes

See also

sklearn.qda.QDA

Quadratic discriminant analysis

Examples

>>> import numpy as np
>>> from sklearn.lda import LDA
>>> 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 = LDA()
>>> clf.fit(X, y)
LDA(n_components=None, priors=None)
>>> print clf.predict([[-0.8, -1]])
[1]

Attributes

means_	array-like, shape = [n_classes, n_features]	Class means
xbar_	float, shape = [n_features]	Over all mean
priors_	array-like, shape = [n_classes]	Class priors (sum to 1)
covariance_	array-like, shape = [n_features, n_features]	Covariance matrix (shared by all classes)

Methods

decision_function(X)	This function return the decision function values related to each
fit(X, y[, store_covariance, tol])	Fit the LDA model according to the given training data and parameters.
fit_transform(X[, y])	Fit to data, then transform it
get_params([deep])	Get parameters for the estimator
predict(X)	This function does classification on an array of test vectors X.
predict_log_proba(X)	This function return posterior log-probabilities of classification
predict_proba(X)	This function 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 the estimator.
transform(X)	Project the data so as to maximize class separation (large separation between projected class means and small variance within each class).

__init__(n_components=None, priors=None)

decision_function(X)

This function return the decision function values related to each class on an array of test vectors X.

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

fit(X, y, store_covariance=False, tol=0.0001)

Fit the LDA 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_covariance : boolean

If True the covariance matrix (shared by all classes) is computed and stored in self.covariance_ attribute.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters :

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns :

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

Notes

This method just calls fit and transform consecutively, i.e., it is not an optimized implementation of fit_transform, unlike other transformers such as PCA.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.

predict(X)

This function does 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)

This function return posterior log-probabilities of classification according to each class on an array of test vectors X.

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

predict_proba(X)

This function return posterior probabilities of classification according to each class on an array of test vectors X.

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

score(X, y)

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

Parameters :

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

Training set.

y : array-like, shape = [n_samples]

Labels for X.

Returns :

z : float

set_params(**params)

Set the parameters of the 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 :

transform(X)

Project the data so as to maximize class separation (large separation between projected class means and small variance within each class).

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