# resubEdge

Resubstitution classification edge

## Description

returns the weighted resubstitution Classification Edge (`e`

= resubEdge(`Mdl`

)`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`

.

specifies whether to include interaction terms in computations. This syntax applies only to
generalized additive models.`e`

= resubEdge(`Mdl`

,'IncludeInteractions',`includeInteractions`

)

## 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 = 5.0999

### 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: [82x2 double] NumObservations: 500

`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`

or`ClassificationSVM`

object.

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

## Version History

**Introduced in R2012a**

### 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.

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.

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