templateDiscriminant

Discriminant analysis classifier template

Syntax

t = templateDiscriminant()

t = templateDiscriminant(Name,Value)

Description

t = templateDiscriminant() returns a discriminant analysis learner template suitable for training ensembles or error-correcting output code (ECOC) multiclass models.

If you specify a default template, then the software uses default values for all input arguments during training.

Specify t as a learner in fitcensemble or fitcecoc.

t = templateDiscriminant(Name,Value) creates a template with additional options specified by one or more name-value pair arguments.

For example, you can specify the discriminant type or the regularization parameter.

If you display t in the Command Window, then all options appear empty ([]), except those that you specify using name-value pair arguments. During training, the software uses default values for empty options.

Examples

Create a Discriminant Analysis Template for Ensemble Learning

Create a nondefault discriminant analysis template for use in fitcensemble.

Load Fisher's iris data set.

load fisheriris

Create a template for pseudolinear discriminant analysis.

t = templateDiscriminant('DiscrimType','pseudoLinear')

t = 
Fit template for classification Discriminant.

    DiscrimType: 'pseudoLinear'
          Gamma: []
          Delta: []
     FillCoeffs: []
     SaveMemory: []
        Version: 1
         Method: 'Discriminant'
           Type: 'classification'

All properties of the template object are empty except for DiscrimType, Method, and Type. When trained on, the software fills in the empty properties with their respective default values.

Specify t as a weak learner for a classification ensemble.

Mdl = fitcensemble(meas,species,'Method','Subspace','Learners',t);

Display the in-sample (resubstitution) misclassification error.

L = resubLoss(Mdl)

L = 0.0400

Input Arguments

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'DiscrimType','pseudoLinear','SaveMemory','on' specifies a template for pseudolinear discriminant analysis that does not store the full covariance matrix.

'Delta' — Linear coefficient threshold

0 (default) | nonnegative scalar value

Linear coefficient threshold, specified as the comma-separated pair consisting of 'Delta' and a nonnegative scalar value. If a coefficient of Mdl has magnitude smaller than Delta, Mdl sets this coefficient to 0, and you can eliminate the corresponding predictor from the model. Set Delta to a higher value to eliminate more predictors.

Delta must be 0 for quadratic discriminant models.

Data Types: single | double

'DiscrimType' — Discriminant type

'linear' (default) | 'quadratic' | 'diaglinear' | 'diagquadratic' | 'pseudolinear' | 'pseudoquadratic'

Discriminant type, specified as the comma-separated pair consisting of 'DiscrimType' and a character vector or string scalar in this table.

Value	Description	Predictor Covariance Treatment
'linear'	Regularized linear discriminant analysis (LDA)	All classes have the same covariance matrix. $${\widehat{\Sigma }}_{\gamma }=\left(1-\gamma \right)\widehat{\Sigma }+\gamma \text{diag}\left(\widehat{\Sigma }\right).$$ $$\widehat{\Sigma }$$ is the empirical, pooled covariance matrix and γ is the amount of regularization.
'diaglinear'	LDA	All classes have the same, diagonal covariance matrix.
'pseudolinear'	LDA	All classes have the same covariance matrix. The software inverts the covariance matrix using the pseudo inverse.
'quadratic'	Quadratic discriminant analysis (QDA)	The covariance matrices can vary among classes.
'diagquadratic'	QDA	The covariance matrices are diagonal and can vary among classes.
'pseudoquadratic'	QDA	The covariance matrices can vary among classes. The software inverts the covariance matrix using the pseudo inverse.

Note

To use regularization, you must specify 'linear'. To specify the amount of regularization, use the Gamma name-value pair argument.

Example: 'DiscrimType','quadratic'

'FillCoeffs' — Coeffs property flag

'on' | 'off'

Coeffs property flag, specified as the comma-separated pair consisting of 'FillCoeffs' and 'on' or 'off'. Setting the flag to 'on' populates the Coeffs property in the classifier object. This can be computationally intensive, especially when cross-validating. The default is 'on', unless you specify a cross-validation name-value pair, in which case the flag is set to 'off' by default.

Example: 'FillCoeffs','off'

'Gamma' — Amount of regularization

scalar value in the interval [0,1]

Amount of regularization to apply when estimating the covariance matrix of the predictors, specified as the comma-separated pair consisting of 'Gamma' and a scalar value in the interval [0,1]. Gamma provides finer control over the covariance matrix structure than DiscrimType.

• If you specify 0, then the software does not use regularization to adjust the covariance matrix. That is, the software estimates and uses the unrestricted, empirical covariance matrix.

  • For linear discriminant analysis, if the empirical covariance matrix is singular, then the software automatically applies the minimal regularization required to invert the covariance matrix. You can display the chosen regularization amount by entering Mdl.Gamma at the command line.

  • For quadratic discriminant analysis, if at least one class has an empirical covariance matrix that is singular, then the software throws an error.

• If you specify a value in the interval (0,1), then you must implement linear discriminant analysis, otherwise the software throws an error. Consequently, the software sets DiscrimType to 'linear'.

• If you specify 1, then the software uses maximum regularization for covariance matrix estimation. That is, the software restricts the covariance matrix to be diagonal. Alternatively, you can set DiscrimType to 'diagLinear' or 'diagQuadratic' for diagonal covariance matrices.

Example: 'Gamma',1

Data Types: single | double

'SaveMemory' — Flag to save covariance matrix

'off' (default) | 'on'

Flag to save covariance matrix, specified as the comma-separated pair consisting of 'SaveMemory' and either 'on' or 'off'. If you specify 'on', then fitcdiscr does not store the full covariance matrix, but instead stores enough information to compute the matrix. The predict method computes the full covariance matrix for prediction, and does not store the matrix. If you specify 'off', then fitcdiscr computes and stores the full covariance matrix in Mdl.

Specify SaveMemory as 'on' when the input matrix contains thousands of predictors.

Example: 'SaveMemory','on'

Output Arguments

t — Discriminant analysis classification template

template object

Discriminant analysis classification template suitable for training ensembles or error-correcting output code (ECOC) multiclass models, returned as a template object. Pass t to fitcensemble or fitcecoc to specify how to create the discriminant analysis classifier for the ensemble or ECOC model, respectively.

If you display t to the Command Window, then all unspecified options appear empty ([]). However, the software replaces empty options with their corresponding default values during training.