Linear Discriminant Analysis

Constructs linear combinations of features that separates two or more classes. Can used either as a linear classifier or, more commonly, as a dimensionality reduction technique. For dimensionality reduction it requires a Y input to the fit_transform node

Documentation

Attributes

classes_

Unique class labels.

coef_

Weight vector(s).

covariance_

Weighted within-class covariance matrix. It corresponds to sum_k prior_k * C_k where C_k is the covariance matrix of the samples in class k. The C_k are estimated using the (potentially shrunk) biased estimator of covariance. If solver is ‘svd’, only exists when store_covariance is True.

explained_variance_ratio_

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.

intercept_

Intercept term.

means_

Class-wise means.

priors_

Class priors (sum to 1).

scalings_

Scaling of the features in the space spanned by the class centroids. Only available for ‘svd’ and ‘eigen’ solvers.

xbar_

Overall mean. Only present if solver is ‘svd’.

Definition

Output ports

model model

Model

Configuration

N. of components for dimensionality reduction (n_components)

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.

For a usage example, see sphx_glr_auto_examples_decomposition_plot_pca_vs_lda.py.

Shrinkage parameter (shrinkage)

Shrinkage parameter, possible values:

• None: no shrinkage (default).

• ‘auto’: automatic shrinkage using the Ledoit-Wolf 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.

For a usage example, see sphx_glr_auto_examples_classification_plot_lda.py.

Solver to use (solver)

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.

Changed in version 1.2: solver=”svd” now has experimental Array API support. See the Array API User Guide <array_api> for more details.

Store covariance (store_covariance)

If True, explicitly compute the weighted within-class covariance matrix when solver is ‘svd’. The matrix is always computed and stored for the other solvers.

Added in version 0.17.

Tolerance (tol)

Absolute threshold for a singular value of X to be considered significant, used to estimate the rank of X. Dimensions whose singular values are non-significant are discarded. Only used if solver is ‘svd’.

Added in version 0.17.

Examples

• Fisher_faces.syx

Implementation

Some of the docstrings for this module have been automatically extracted from the scikit-learn library and are covered by their respective licenses.

class node_discriminant_analysis.LinearDiscriminantAnalysis