kfoldEdge

Classification edge for cross-validated kernel classification model

Syntax

edge = kfoldEdge(CVMdl)

edge = kfoldEdge(CVMdl,Name,Value)

Description

edge = kfoldEdge(CVMdl) returns the classification edge obtained by the cross-validated, binary kernel model (ClassificationPartitionedKernel) CVMdl. For every fold, kfoldEdge computes the classification edge for validation-fold observations using a model trained on training-fold observations.

edge = kfoldEdge(CVMdl,Name,Value) returns the classification edge with additional options specified by one or more name-value pair arguments. For example, specify the number of folds or the aggregation level.

Examples

Estimate k-Fold Cross-Validation Edge

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

load ionosphere

Cross-validate a binary kernel classification model using the data.

CVMdl = fitckernel(X,Y,'Crossval','on')

CVMdl = 
  ClassificationPartitionedKernel
    CrossValidatedModel: 'Kernel'
           ResponseName: 'Y'
        NumObservations: 351
                  KFold: 10
              Partition: [1x1 cvpartition]
             ClassNames: {'b'  'g'}
         ScoreTransform: 'none'

CVMdl is a ClassificationPartitionedKernel model. By default, the software implements 10-fold cross-validation. To specify a different number of folds, use the 'KFold' name-value pair argument instead of 'Crossval'.

Estimate the cross-validated classification edge.

edge = kfoldEdge(CVMdl)

edge = 
1.5585

Alternatively, you can obtain the per-fold edges by specifying the name-value pair 'Mode','individual' in kfoldEdge.

Feature Selection Using k-Fold Edges

Perform feature selection by comparing k-fold edges from multiple models. Based solely on this criterion, the classifier with the greatest edge is the best classifier.

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

load ionosphere

Randomly choose half of the predictor variables.

rng(1); % For reproducibility
p = size(X,2); % Number of predictors
idxPart = randsample(p,ceil(0.5*p));

Cross-validate two binary kernel classification models: one that uses all of the predictors, and one that uses half of the predictors.

CVMdl = fitckernel(X,Y,'CrossVal','on');
PCVMdl = fitckernel(X(:,idxPart),Y,'CrossVal','on');

CVMdl and PCVMdl are ClassificationPartitionedKernel models. By default, the software implements 10-fold cross-validation. To specify a different number of folds, use the 'KFold' name-value pair argument instead of 'Crossval'.

Estimate the k-fold edge for each classifier.

fullEdge = kfoldEdge(CVMdl)

fullEdge = 
1.5142

partEdge = kfoldEdge(PCVMdl)

partEdge = 
1.8910

Based on the k-fold edges, the classifier that uses half of the predictors is the better model.

Input Arguments

CVMdl — Cross-validated, binary kernel classification model

ClassificationPartitionedKernel model object

Cross-validated, binary kernel classification model, specified as a ClassificationPartitionedKernel model object. You can create a ClassificationPartitionedKernel model by using fitckernel and specifying any one of the cross-validation name-value pair arguments.

To obtain estimates, kfoldEdge applies the same data used to cross-validate the kernel classification model (X and Y).

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: kfoldEdge(CVMdl,'Mode','individual') returns the classification edge for each fold.

Folds — Fold indices for prediction

1:CVMdl.KFold (default) | numeric vector of positive integers

Fold indices for prediction, specified as the comma-separated pair consisting of 'Folds' and a numeric vector of positive integers. The elements of Folds must be within the range from 1 to CVMdl.KFold.

The software uses only the folds specified in Folds for prediction.

Example: 'Folds',[1 4 10]

Data Types: single | double

Mode — Aggregation level for output

'average' (default) | 'individual'

Aggregation level for the output, specified as the comma-separated pair consisting of 'Mode' and 'average' or 'individual'.

This table describes the values.

Value	Description
'average'	The output is a scalar average over all folds.
'individual'	The output is a vector of length k containing one value per fold, where k is the number of folds.

Example: 'Mode','individual'

Output Arguments

edge — Classification edge

numeric scalar | numeric column vector

Classification edge, returned as a numeric scalar or numeric column vector.

If Mode is 'average', then edge is the average classification edge over all folds. Otherwise, edge is a k-by-1 numeric column vector containing the classification edge for each fold, where k is the number of folds.

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 software defines the classification margin for binary classification as

$$m=2yf\left(x\right).$$

x is an observation. If the true label of x is the positive class, then y is 1, and –1 otherwise. f(x) is the positive-class classification score for the observation x. The classification margin is commonly defined as m = yf(x).

If the margins are on the same scale, then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.

Classification Score

For kernel classification models, the raw classification score for classifying the observation x, a row vector, into the positive class is defined by

$$f\left(x\right)=T(x)\beta +b.$$

• $$T(·)$$ is a transformation of an observation for feature expansion.

• β is the estimated column vector of coefficients.

• b is the estimated scalar bias.

The raw classification score for classifying x into the negative class is −f(x). The software classifies observations into the class that yields a positive score.

If the kernel classification model consists of logistic regression learners, then the software applies the 'logit' score transformation to the raw classification scores (see ScoreTransform).

Version History

Introduced in R2018b

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: kfoldEdge returns a different value for a model with a nondefault cost matrix

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

The kfoldEdge 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 model with a nondefault cost matrix, so the function might 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.