resubEdge

Resubstitution classification edge

Syntax

e = resubEdge(Mdl)

e = resubEdge(Mdl,'IncludeInteractions',includeInteractions)

Description

e = resubEdge(Mdl) returns the weighted resubstitution Classification Edge (e) for the trained classification model Mdl using the predictor data stored in Mdl.X, the corresponding true class labels stored in Mdl.Y, and the observation weights stored in Mdl.W.

e = resubEdge(Mdl,'IncludeInteractions',includeInteractions) specifies whether to include interaction terms in computations. This syntax applies only to generalized additive models.

Examples

Estimate Resubstitution Edge of SVM Classifiers

Load the ionosphere data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

load ionosphere

Train a support vector machine (SVM) classifier. Standardize the data and specify that 'g' is the positive class.

SVMModel = fitcsvm(X,Y,'Standardize',true,'ClassNames',{'b','g'});

SVMModel is a trained ClassificationSVM classifier.

Estimate the resubstitution edge, which is the mean of the training sample margins.

e = resubEdge(SVMModel)

e = 
5.0997

Select Naive Bayes Classifier Features by Comparing In-Sample Edges

The classifier edge measures the average of the classifier margins. One way to perform feature selection is to compare training sample edges from multiple models. Based solely on this criterion, the classifier with the highest edge is the best classifier.

Load the ionosphere data set. Remove the first two predictors for stability.

load ionosphere
X = X(:,3:end);

Define these two data sets:

• fullX contains all predictors.

• partX contains the 10 most important predictors.

fullX = X;
idx = fscmrmr(X,Y);
partX = X(:,idx(1:10));

Train a naive Bayes classifier for each predictor set.

FullMdl = fitcnb(fullX,Y);
PartMdl = fitcnb(partX,Y);

FullMdl and PartMdl are trained ClassificationNaiveBayes classifiers.

Estimate the training sample edge for each classifier.

fullEdge = resubEdge(FullMdl)

fullEdge = 
0.6554

partEdge = resubEdge(PartMdl)

partEdge = 
0.7796

The edge of the classifier trained on the 10 most important predictors is larger. This result suggests that the classifier trained using only those predictors has a better in-sample fit.

Compare GAMs by Examining Training Sample Margins and Edge

Compare a generalized additive model (GAM) with linear terms to a GAM with both linear and interaction terms by examining the training sample margins and edge. Based solely on this comparison, the classifier with the highest margins and edge is the best model.

Load the 1994 census data stored in census1994.mat. The data set consists of demographic data from the US Census Bureau to predict whether an individual makes over $50,000 per year. The classification task is to fit a model that predicts the salary category of people given their age, working class, education level, marital status, race, and so on.

load census1994

census1994 contains the training data set adultdata and the test data set adulttest. To reduce the running time for this example, subsample 500 training observations from adultdata by using the datasample function.

rng('default') % For reproducibility
NumSamples = 5e2;
adultdata = datasample(adultdata,NumSamples,'Replace',false);

Train a GAM that contains both linear and interaction terms for predictors. Specify to include all available interaction terms whose p-values are not greater than 0.05.

Mdl = fitcgam(adultdata,'salary','Interactions','all','MaxPValue',0.05)

Mdl = 
  ClassificationGAM
           PredictorNames: {'age'  'workClass'  'fnlwgt'  'education'  'education_num'  'marital_status'  'occupation'  'relationship'  'race'  'sex'  'capital_gain'  'capital_loss'  'hours_per_week'  'native_country'}
             ResponseName: 'salary'
    CategoricalPredictors: [2 4 6 7 8 9 10 14]
               ClassNames: [<=50K    >50K]
           ScoreTransform: 'logit'
                Intercept: -28.5594
             Interactions: [82×2 double]
          NumObservations: 500


  Properties, Methods

Mdl is a ClassificationGAM model object. Mdl includes 82 interaction terms.

Estimate the training sample margins and edge for Mdl.

M = resubMargin(Mdl);
E = resubEdge(Mdl)

E = 
1.0000

Estimate the training sample margins and edge for Mdl without including interaction terms.

M_nointeractions = resubMargin(Mdl,'IncludeInteractions',false);
E_nointeractions = resubEdge(Mdl,'IncludeInteractions',false)

E_nointeractions = 
0.9516

Display the distributions of the margins using box plots.

boxplot([M M_nointeractions],'Labels',{'Linear and Interaction Terms','Linear Terms Only'})
title('Box Plots of Training Sample Margins')

When you include the interaction terms in the computation, all the resubstitution margin values for Mdl are 1, and the resubstitution edge value (average of the margins) is 1. The margins and edge decrease when you do not include the interaction terms in Mdl.

Input Arguments

Mdl — Classification machine learning model

full classification model object

Classification machine learning model, specified as a full classification model object, as given in the following table of supported models.

Model	Classification Model Object
Generalized additive model	ClassificationGAM
k-nearest neighbor model	ClassificationKNN
Naive Bayes model	ClassificationNaiveBayes
Neural network model	ClassificationNeuralNetwork
Support vector machine for one-class and binary classification	ClassificationSVM

includeInteractions — Flag to include interaction terms

true | false

Flag to include interaction terms of the model, specified as true or false. This argument is valid only for a generalized additive model (GAM). That is, you can specify this argument only when Mdl is ClassificationGAM.

The default value is true if Mdl contains interaction terms. The value must be false if the model does not contain interaction terms.

Data Types: logical

More About

Classification Edge

The classification edge is the weighted mean of the classification margins.

One way to choose among multiple classifiers, for example to perform feature selection, is to choose the classifier that yields the greatest edge.

Classification Margin

The classification margin for binary classification is, for each observation, the difference between the classification score for the true class and the classification score for the false class. The classification margin for multiclass classification is the difference between the classification score for the true class and the maximal classification score for the false classes.

If the margins are on the same scale (that is, the score values are based on the same score transformation), then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.

Algorithms

resubEdge computes the classification edge according to the corresponding edge function of the object (Mdl). For a model-specific description, see the edge function reference pages in the following table.

Model	Classification Model Object (Mdl)	edge Object Function
Generalized additive model	ClassificationGAM	edge
k-nearest neighbor model	ClassificationKNN	edge
Naive Bayes model	ClassificationNaiveBayes	edge
Neural network model	ClassificationNeuralNetwork	edge
Support vector machine for one-class and binary classification	ClassificationSVM	edge

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• This function fully supports GPU arrays for a trained classification model specified as a ClassificationKNN, ClassificationNeuralNetwork, or ClassificationSVM object.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a

R2024b: Specify GPU arrays for neural network models (requires Parallel Computing Toolbox)

resubEdge fully supports GPU arrays for ClassificationNeuralNetwork.

R2023b: Observations with missing predictor values are used in resubstitution and cross-validation computations

Starting in R2023b, the following classification model object functions use observations with missing predictor values as part of resubstitution ("resub") and cross-validation ("kfold") computations for classification edges, losses, margins, and predictions.

Model Type	Model Objects	Object Functions
Discriminant analysis classification model	ClassificationDiscriminant	resubEdge, resubLoss, resubMargin, resubPredict
	ClassificationPartitionedModel	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
Ensemble of discriminant analysis learners for classification	ClassificationEnsemble	resubEdge, resubLoss, resubMargin, resubPredict
	ClassificationPartitionedEnsemble	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
Gaussian kernel classification model	ClassificationPartitionedKernel	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
	ClassificationPartitionedKernelECOC	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
Linear classification model	ClassificationPartitionedLinear	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
	ClassificationPartitionedLinearECOC	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
Neural network classification model	ClassificationNeuralNetwork	resubEdge, resubLoss, resubMargin, resubPredict
	ClassificationPartitionedModel	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict
Support vector machine (SVM) classification model	ClassificationSVM	resubEdge, resubLoss, resubMargin, resubPredict
	ClassificationPartitionedModel	kfoldEdge, kfoldLoss, kfoldMargin, kfoldPredict

In previous releases, the software omitted observations with missing predictor values from the resubstitution and cross-validation computations.

R2022a: resubEdge returns a different value for a ClassificationSVM model with a nondefault cost matrix

If you specify a nondefault cost matrix when you train the input model object for an SVM model, the resubEdge function returns a different value compared to previous releases.

The resubEdge function uses the observation weights stored in the W property. The way the function uses the W property value has not changed. However, the property value stored in the input model object has changed for a ClassificationSVM model object with a nondefault cost matrix, so the function can return a different value.

For details about the property value change, see Cost property stores the user-specified cost matrix.

If you want the software to handle the cost matrix, prior probabilities, and observation weights in the same way as in previous releases, adjust the prior probabilities and observation weights for the nondefault cost matrix, as described in Adjust Prior Probabilities and Observation Weights for Misclassification Cost Matrix. Then, when you train a classification model, specify the adjusted prior probabilities and observation weights by using the Prior and Weights name-value arguments, respectively, and use the default cost matrix.