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resubEdge

Resubstitution classification edge for multiclass error-correcting output codes (ECOC) model

Description

e = resubEdge(Mdl) returns the resubstitution classification edge (e) for the multiclass error-correcting output codes (ECOC) model Mdl using the training data stored in Mdl.X and the corresponding class labels stored in Mdl.Y.

The classification edge is a scalar value that represents the weighted mean of the classification margins.

example

e = resubEdge(Mdl,Name,Value) computes the resubstitution classification edge with additional options specified by one or more name-value pair arguments. For example, you can specify a decoding scheme, binary learner loss function, and verbosity level.

example

Examples

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Compute the resubstitution edge for an ECOC model with SVM binary learners.

Load Fisher's iris data set. Specify the predictor data X and the response data Y.

load fisheriris
X = meas;
Y = species;

Train an ECOC model using SVM binary classifiers. Standardize the predictors using an SVM template, and specify the class order.

t = templateSVM('Standardize',true);
classOrder = unique(Y)
classOrder = 3×1 cell
    {'setosa'    }
    {'versicolor'}
    {'virginica' }

Mdl = fitcecoc(X,Y,'Learners',t,'ClassNames',classOrder);

t is an SVM template object. During training, the software uses default values for empty properties in t. Mdl is a ClassificationECOC model.

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

e = resubEdge(Mdl)
e = 
0.7440

Perform feature selection by comparing training-sample edges from multiple models. Based solely on this comparison, the classifier with the greatest edge is the best classifier.

Load Fisher's iris data set. Define two data sets:

  • fullX contains all four predictors.

  • partX contains the sepal measurements only.

load fisheriris
X = meas;
fullX = X; 
partX = X(:,1:2);
Y = species;

Train an ECOC model using SVM binary learners for each predictor set. Standardize the predictors using an SVM template, specify the class order, and compute the posterior probabilities.

t = templateSVM('Standardize',true);
classOrder = unique(Y)
classOrder = 3×1 cell
    {'setosa'    }
    {'versicolor'}
    {'virginica' }

FullMdl = fitcecoc(fullX,Y,'Learners',t,'ClassNames',classOrder,... 
    'FitPosterior',true);
PartMdl = fitcecoc(partX,Y,'Learners',t,'ClassNames',classOrder,...
    'FitPosterior',true);

The default SVM score is the distance from the decision boundary. If you specify to compute posterior probabilities, then the software uses posterior probabilities as scores.

Compute the resubstitution edge for each classifier. The quadratic loss function operates on scores in the domain [0,1]. Specify to use quadratic loss when aggregating the binary learners for both models.

fullEdge = resubEdge(FullMdl,'BinaryLoss','quadratic')
fullEdge = 
0.9896
partEdge = resubEdge(PartMdl,'BinaryLoss','quadratic')
partEdge = 
0.5059

The edge for the classifier trained on the complete data set is greater, suggesting that the classifier trained with all the predictors has a better training-sample fit.

Input Arguments

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Full, trained multiclass ECOC model, specified as a ClassificationECOC model trained with fitcecoc.

Name-Value Arguments

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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: resubEdge(Mdl,'BinaryLoss','quadratic') specifies a quadratic binary learner loss function.

Binary learner loss function, specified as a built-in loss function name or function handle.

  • This table describes the built-in functions, where yj is the class label for a particular binary learner (in the set {–1,1,0}), sj is the score for observation j, and g(yj,sj) is the binary loss formula.

    ValueDescriptionScore Domaing(yj,sj)
    "binodeviance"Binomial deviance(–∞,∞)log[1 + exp(–2yjsj)]/[2log(2)]
    "exponential"Exponential(–∞,∞)exp(–yjsj)/2
    "hamming"Hamming[0,1] or (–∞,∞)[1 – sign(yjsj)]/2
    "hinge"Hinge(–∞,∞)max(0,1 – yjsj)/2
    "linear"Linear(–∞,∞)(1 – yjsj)/2
    "logit"Logistic(–∞,∞)log[1 + exp(–yjsj)]/[2log(2)]
    "quadratic"Quadratic[0,1][1 – yj(2sj – 1)]2/2

    The software normalizes binary losses so that the loss is 0.5 when yj = 0. Also, the software calculates the mean binary loss for each class [1].

  • For a custom binary loss function, for example customFunction, specify its function handle BinaryLoss=@customFunction.

    customFunction has this form:

    bLoss = customFunction(M,s)

    • M is the K-by-B coding matrix stored in Mdl.CodingMatrix.

    • s is the 1-by-B row vector of classification scores.

    • bLoss is the classification loss. This scalar aggregates the binary losses for every learner in a particular class. For example, you can use the mean binary loss to aggregate the loss over the learners for each class.

    • K is the number of classes.

    • B is the number of binary learners.

    For an example of passing a custom binary loss function, see Predict Test-Sample Labels of ECOC Model Using Custom Binary Loss Function.

This table identifies the default BinaryLoss value, which depends on the score ranges returned by the binary learners.

AssumptionDefault Value

All binary learners are any of the following:

  • Classification decision trees

  • Discriminant analysis models

  • k-nearest neighbor models

  • Linear or kernel classification models of logistic regression learners

  • Naive Bayes models

"quadratic"
All binary learners are SVMs or linear or kernel classification models of SVM learners."hinge"
All binary learners are ensembles trained by AdaboostM1 or GentleBoost."exponential"
All binary learners are ensembles trained by LogitBoost."binodeviance"
You specify to predict class posterior probabilities by setting FitPosterior=true in fitcecoc."quadratic"
Binary learners are heterogeneous and use different loss functions."hamming"

To check the default value, use dot notation to display the BinaryLoss property of the trained model at the command line.

Example: BinaryLoss="binodeviance"

Data Types: char | string | function_handle

Decoding scheme that aggregates the binary losses, specified as "lossweighted" or "lossbased". For more information, see Binary Loss.

Example: Decoding="lossbased"

Data Types: char | string

Estimation options, specified as a structure array as returned by statset.

To invoke parallel computing you need a Parallel Computing Toolbox™ license.

Example: Options=statset(UseParallel=true)

Data Types: struct

Verbosity level, specified as 0 or 1. Verbose controls the number of diagnostic messages that the software displays in the Command Window.

If Verbose is 0, then the software does not display diagnostic messages. Otherwise, the software displays diagnostic messages.

Example: Verbose=1

Data Types: single | double

More About

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Tips

  • To compare the margins or edges of several ECOC classifiers, use template objects to specify a common score transform function among the classifiers during training.

References

[1] Allwein, E., R. Schapire, and Y. Singer. “Reducing multiclass to binary: A unifying approach for margin classifiers.” Journal of Machine Learning Research. Vol. 1, 2000, pp. 113–141.

[2] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of error-correcting output codes.” Pattern Recog. Lett. Vol. 30, Issue 3, 2009, pp. 285–297.

[3] Escalera, S., O. Pujol, and P. Radeva. “On the decoding process in ternary error-correcting output codes.” IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 32, Issue 7, 2010, pp. 120–134.

Extended Capabilities

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Version History

Introduced in R2014b