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resubPredict

Clase: ClassificationECOC

Predict resubstitution responses for multiclass, error-correcting output codes model

Sintaxis

label = resubPredict(Mdl)
label = resubPredict(Mdl,Name,Value)
[label,NegLoss,PBScore] = resubPredict(___)
[label,NegLoss,PBScore,Posterior] = resubPredict(___)

Description

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label = resubPredict(Mdl) returns a vector of predicted class labels for the predictor data (stored in Mdl.X) based on the trained, multiclass, error-correcting output codes model Mdl.

The software predicts the classification of an observation by assigning the observation to the class yielding the largest negated average binary loss (or, equivalently, the smallest average binary loss).

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label = resubPredict(Mdl,Name,Value) returns predicted class labels with additional options specified by one or more Name,Value pair arguments.

For example, specify the posterior probability estimation method, decoding scheme, or verbosity level.

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[label,NegLoss,PBScore] = resubPredict(___) additionally returns negated average binary loss per class (NegLoss) for observations, and positive-class scores (PBScore) for the observations classified by each binary learner.

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[label,NegLoss,PBScore,Posterior] = resubPredict(___) additionally returns posterior class probability estimates for observations (Posterior).

To obtain posterior class probabilities, you must set 'FitPosterior',1 when training the ECOC model using fitcecoc. Otherwise, resubPredict throws an error.

Argumentos de entrada

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Multiclass ECOC model, specified as a ClassificationECOC model returned by fitcecoc.

Argumentos de par nombre-valor

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.

Binary learner loss function, specified as the comma-separated pair consisting of 'BinaryLoss' and a built-in loss function name or function handle.

  • This table contains names and descriptions of the built-in functions, where yj is a 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 such that the loss is 0.5 when yj = 0. Also, the software calculates the mean binary loss for each class.

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

    customFunction has this form:

    bLoss = customFunction(M,s)
    where:

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

    • s is the 1-by-L 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.

    • L is the number of binary learners.

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

By default, if all binary learners are:

  • SVMs or either linear or kernel classification models of SVM learners, then BinaryLoss is 'hinge'

  • Ensembles trained by AdaboostM1 or GentleBoost, then BinaryLoss is 'exponential'

  • Ensembles trained by LogitBoost, then BinaryLoss is 'binodeviance'

  • Linear or kernel classification models of logistic regression learners, or you specify to predict class posterior probabilities (that is, set 'FitPosterior',1 in fitcecoc), then BinaryLoss is 'quadratic'

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

Ejemplo: 'BinaryLoss','binodeviance'

Tipos de datos: char | string | function_handle

Decoding scheme that aggregates the binary losses, specified as the comma-separated pair consisting of 'Decoding' and 'lossweighted' or 'lossbased'. For more information, see Binary Loss.

Ejemplo: 'Decoding','lossbased'

Number of random initial values for fitting posterior probabilities by Kullback-Leibler divergence minimization, specified as the comma-separated pair consisting of 'NumKLInitializations' and a nonnegative integer scalar.

If you do not request the fourth output argument (Posterior) and set 'PosteriorMethod','kl' (the default), then the software ignores the value of NumKLInitializations.

For more details, see Posterior Estimation Using Kullback-Leibler Divergence.

Ejemplo: 'NumKLInitializations',5

Tipos de datos: single | double

Estimation options, specified as the comma-separated pair consisting of 'Options' and a structure array returned by statset.

To invoke parallel computing:

  • You need a Parallel Computing Toolbox™ license.

  • Specify 'Options',statset('UseParallel',1).

Posterior probability estimation method, specified as the comma-separated pair consisting of 'PosteriorMethod' and 'kl' or 'qp'.

  • If PosteriorMethod is 'kl', then the software estimates multiclass posterior probabilities by minimizing the Kullback-Leibler divergence between the predicted and expected posterior probabilities returned by binary learners. For details, see Posterior Estimation Using Kullback-Leibler Divergence.

  • If PosteriorMethod is 'qp', then the software estimates multiclass posterior probabilities by solving a least-squares problem using quadratic programming. You need an Optimization Toolbox™ license to use this option. For details, see Posterior Estimation Using Quadratic Programming.

  • If you do not request the fourth output argument (Posterior), then the software ignores the value of PosteriorMethod.

Ejemplo: 'PosteriorMethod','qp'

Verbosity level, specified as the comma-separated pair consisting of 'Verbose' and 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.

Ejemplo: 'Verbose',1

Tipos de datos: single | double

Output Arguments

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Predicted class labels, returned as a categorical or character array, logical or numeric vector, or cell array of character vectors.

label is the same data type as the Mdl.ClassNames, and has length equal to the number of rows of Mdl.X.

The software predicts the classification of an observation by assigning the observation to the class yielding the largest negated average binary loss (or, equivalently, the smallest average binary loss).

Negated, average binary losses, returned as a numeric matrix. NegLoss is an n-by-K matrix, where n is the number of observations (size(Mdl.X,1)) and K is the number of unique classes (size(Mdl.ClassNames,1)).

Positive-class scores for each binary learner, returned as a numeric matrix. PBScore is an n-by-L matrix, where n is the number of observations (size(Mdl.X,1)) and L is the number of binary learners (size(Mdl.CodingMatrix,2)).

Posterior class probabilities, returned as a numeric matrix. Posterior is an n-by-K matrix, where n is the number of observations (size(Mdl.X,1)) and K is the number of unique classes (size(Mdl.ClassNames,1)).

You must set 'FitPosterior',1 when training the ECOC model using fitcecoc to request Posterior. Otherwise, the software throws an error.

Ejemplos

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Load Fisher's iris data set.

load fisheriris
X = meas;
Y = categorical(species);
n = numel(Y); % Sample size
classOrder = unique(Y);

Train an ECOC model using SVM binary classifiers. It is good practice to standardize the predictors and define the class order. Specify to standardize the predictors using an SVM template.

t = templateSVM('Standardize',1);
Mdl = fitcecoc(X,Y,'Learners',t,'ClassNames',classOrder);

t is an SVM template object. The software uses default values for empty options in t during training. Mdl is a ClassificationECOC model.

Predict the labels of the training data. Print a random subset of true and predicted labels.

labels = resubPredict(Mdl);
rng(1);
idx = randsample(n,10);
table(Y(idx),labels(idx),'VariableNames',{'TrueLabels','PredictedLabels'})
ans =

  10x2 table

    TrueLabels    PredictedLabels
    __________    _______________

    setosa          setosa       
    versicolor      versicolor   
    virginica       virginica    
    setosa          setosa       
    versicolor      versicolor   
    setosa          setosa       
    versicolor      versicolor   
    versicolor      versicolor   
    setosa          setosa       
    setosa          setosa       

Mdl correctly labeled the observations with indices idx.

Load Fisher's iris data set.

load fisheriris
X = meas;
Y = categorical(species);
n = numel(Y);           % Sample size
classOrder = unique(Y); % Class order
K = numel(classOrder);  % Number of classes

Train an ECOC model using SVM binary classifiers. It is good practice to standardize the predictors and define the class order. Specify to standardize the predictors using an SVM template.

t = templateSVM('Standardize',1);
Mdl = fitcecoc(X,Y,'Learners',t,'ClassNames',classOrder);

t is an SVM template object. The software uses default values for empty options in t during training. Mdl is a ClassificationECOC model.

SVM scores are signed distances from the observation to the decision boundary. Therefore, the domain is . Create a custom binary loss function that:

  • Maps the coding design matrix (M) and positive-class classification scores (s) for each learner to the binary loss for each observation

  • Uses linear loss

  • Aggregates the binary learner loss using the median

You can create a separate function for the binary loss function, and then save it on the MATLAB® path. Or, you can specify an anonymous binary loss function.

customBL = @(M,s)nanmedian(1 - bsxfun(@times,M,s),2)/2;

Predict resubstitution labels and estimate the median binary loss per class. Print the median negative binary losses per class for a random set of 10 observations.

[label,NegLoss] = resubPredict(Mdl,'BinaryLoss',customBL);

rng(1); % For reproducibility
idx = randsample(n,10);
classOrder
table(Y(idx),label(idx),NegLoss(idx,:),'VariableNames',...
    {'TrueLabel','PredictedLabel','NegLoss'})
classOrder = 

  3x1 categorical array

     setosa 
     versicolor 
     virginica 


ans =

  10x3 table

    TrueLabel     PredictedLabel                NegLoss            
    __________    ______________    _______________________________

    setosa          versicolor      0.12376      1.9575     -3.5812
    versicolor      versicolor      -1.0171     0.62948     -1.1123
    virginica       virginica       -1.9088    -0.21759     0.62641
    setosa          versicolor      0.43846      2.2448     -4.1833
    versicolor      versicolor      -1.0735      0.3965    -0.82299
    setosa          versicolor      0.26658       2.201     -3.9675
    versicolor      versicolor      -1.1237     0.69927     -1.0756
    versicolor      versicolor      -1.2716     0.51847    -0.74687
    setosa          versicolor      0.35211      2.0683     -3.9204
    setosa          versicolor      0.23342      2.1892     -3.9226

The column order corresponds to the elements of classOrder. The software predicts the label based on the maximum negated loss. The results seem to indicate that the median of the linear losses might not perform as well as other losses.

Load Fisher's iris data set. Train the classifier using the petal dimensions as predictors.

load fisheriris
X = meas(:,3:4);
Y = species;
rng(1); % For reproducibility

Create an SVM template, and specify the Gaussian kernel. It is good practice to standardize the predictors.

t = templateSVM('Standardize',1,'KernelFunction','gaussian');

t is an SVM template. Most of its properties are empty. When the software trains the ECOC classifier, it sets the applicable properties to their default values.

Train the ECOC classifier using the SVM template. Transform classification scores to class posterior probabilities (which are returned by predict or resubPredict) using the 'FitPosterior' name-value pair argument. Display diagnostic messages during the training using the 'Verbose' name-value pair argument. It is good practice to specify the class order.

Mdl = fitcecoc(X,Y,'Learners',t,'FitPosterior',1,...
    'ClassNames',{'setosa','versicolor','virginica'},...
    'Verbose',2);
Training binary learner 1 (SVM) out of 3 with 50 negative and 50 positive observations.
Negative class indices: 2
Positive class indices: 1

Fitting posterior probabilities for learner 1 (SVM).
Training binary learner 2 (SVM) out of 3 with 50 negative and 50 positive observations.
Negative class indices: 3
Positive class indices: 1

Fitting posterior probabilities for learner 2 (SVM).
Training binary learner 3 (SVM) out of 3 with 50 negative and 50 positive observations.
Negative class indices: 3
Positive class indices: 2

Fitting posterior probabilities for learner 3 (SVM).

Mdl is a ClassificationECOC model. The same SVM template applies to each binary learner, but you can adjust options for each binary learner by passing in a cell vector of templates.

Predict the in-sample labels and class posterior probabilities. Display diagnostic messages during the computation of labels and class posterior probabilities using the 'Verbose' name-value pair argument.

[label,~,~,Posterior] = resubPredict(Mdl,'Verbose',1);
Mdl.BinaryLoss
Predictions from all learners have been computed.
Loss for all observations has been computed.
Computing posterior probabilities...

ans =

    'quadratic'

The software assigns an observation to the class that yields the smallest average binary loss. Since all binary learners are computing posterior probabilities, the binary loss function is quadratic.

Display a random set of results.

idx = randsample(size(X,1),10,1);
Mdl.ClassNames
table(Y(idx),label(idx),Posterior(idx,:),...
    'VariableNames',{'TrueLabel','PredLabel','Posterior'})
ans =

  3x1 cell array

    {'setosa'    }
    {'versicolor'}
    {'virginica' }


ans =

  10x3 table

     TrueLabel       PredLabel                    Posterior               
    ____________    ____________    ______________________________________

    'virginica'     'virginica'      0.0039321     0.0039869       0.99208
    'virginica'     'virginica'       0.017067      0.018263       0.96467
    'virginica'     'virginica'       0.014948      0.015856        0.9692
    'versicolor'    'versicolor'    2.2197e-14       0.87317       0.12683
    'setosa'        'setosa'             0.999    0.00025091    0.00074639
    'versicolor'    'virginica'     2.2195e-14      0.059429       0.94057
    'versicolor'    'versicolor'    2.2194e-14       0.97001      0.029986
    'setosa'        'setosa'             0.999     0.0002499    0.00074741
    'versicolor'    'versicolor'     0.0085646       0.98259      0.008849
    'setosa'        'setosa'             0.999    0.00025013    0.00074718

The columns of Posterior correspond to the class order of Mdl.ClassNames.

Define a grid of values in the observed predictor space. Predict the posterior probabilities for each instance in the grid.

xMax = max(X);
xMin = min(X);

x1Pts = linspace(xMin(1),xMax(1));
x2Pts = linspace(xMin(2),xMax(2));
[x1Grid,x2Grid] = meshgrid(x1Pts,x2Pts);

[~,~,~,PosteriorRegion] = predict(Mdl,[x1Grid(:),x2Grid(:)]);

For each coordinate on the grid, plot the maximum class posterior probability among all classes.

figure;
contourf(x1Grid,x2Grid,...
        reshape(max(PosteriorRegion,[],2),size(x1Grid,1),size(x1Grid,2)));
h = colorbar;
h.YLabel.String = 'Maximum posterior';
h.YLabel.FontSize = 15;
hold on
gh = gscatter(X(:,1),X(:,2),Y,'krk','*xd',8);
gh(2).LineWidth = 2;
gh(3).LineWidth = 2;

title 'Iris Petal Measurements and Maximum Posterior';
xlabel 'Petal length (cm)';
ylabel 'Petal width (cm)';
axis tight
legend(gh,'Location','NorthWest')
hold off

Train an error-correcting output codes, multiclass model and estimate posterior probabilities using parallel computing.

Load the arrhythmia data set.

load arrhythmia
Y = categorical(Y);
tabulate(Y)
n = numel(Y);
K = numel(unique(Y));
  Value    Count   Percent
      1      245     54.20%
      2       44      9.73%
      3       15      3.32%
      4       15      3.32%
      5       13      2.88%
      6       25      5.53%
      7        3      0.66%
      8        2      0.44%
      9        9      1.99%
     10       50     11.06%
     14        4      0.88%
     15        5      1.11%
     16       22      4.87%

Several classes are not represented in the data, and many other classes have low relative frequencies.

Specify an ensemble learning template that uses the GentleBoost method and 50 weak, classification tree learners.

t = templateEnsemble('GentleBoost',50,'Tree');

t is a template object. Most of the options are empty ([]). The software uses default values for all empty options during training.

Since there are many classes, specify a sparse random coding design.

rng(1); % For reproducibility
Coding = designecoc(K,'sparserandom');

Train an ECOC model using parallel computing. Specify to fit posterior probabilities.

pool = parpool;                      % Invokes workers
options = statset('UseParallel',1);
Mdl = fitcecoc(X,Y,'Learner',t,'Options',options,'Coding',Coding,...
    'FitPosterior',1);
Starting parallel pool (parpool) using the 'local' profile ... connected to 4 workers.

Mdl is a ClassificationECOC model. You can access its properties using dot notation. The pool invokes four workers. The number of workers might vary among systems.

Estimate posterior probabilities, and display the posterior probability of being classified as not having arrythmia (class 1) given the data.

[~,~,~,posterior] = resubPredict(Mdl);
idx = randsample(n,10,1);
table(idx,Y(idx),posterior(idx,1),...
    'VariableNames',{'ObservationIndex','TrueLabel','PosteriorNoArrythmia'})
ans = 

    ObservationIndex    TrueLabel    PosteriorNoArrythmia
    ________________    _________    ____________________

     79                 1             0.91522            
    248                 1             0.95376            
    398                 10           0.032369            
    207                 1             0.97965            
    340                 1             0.93628            
    206                 1             0.97795            
    345                 10           0.015643            
    296                 2             0.14796            
    391                 1             0.96494            
    406                 1             0.94867            

Más acerca de

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Algoritmos

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  • The software can estimate class posterior probabilities by minimizing the Kullback-Leibler divergence or by using quadratic programming. For the following descriptions of the posterior estimation algorithms, assume that:

    • mkj is the element (k,j) of the coding design matrix M.

    • I is the indicator function.

    • p^k is the class posterior probability estimate for class k of an observation, k = 1,...,K.

    • rj is the positive-class posterior probability for binary learner j. That is, rj is the probability that binary learner j classifies an observation into the positive class, given the training data.

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] Dietterich, T., and G. Bakiri. “Solving Multiclass Learning Problems Via Error-Correcting Output Codes.” Journal of Artificial Intelligence Research. Vol. 2, 1995, pp. 263–286.

[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.

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

[5] Hastie, T., and R. Tibshirani. “Classification by Pairwise Coupling.” Annals of Statistics. Vol. 26, Issue 2, 1998, pp. 451–471.

[6] Wu, T. F., C. J. Lin, and R. Weng. “Probability Estimates for Multi-Class Classification by Pairwise Coupling.” Journal of Machine Learning Research. Vol. 5, 2004, pp. 975–1005.

[7] Zadrozny, B. “Reducing Multiclass to Binary by Coupling Probability Estimates.” NIPS 2001: Proceedings of Advances in Neural Information Processing Systems 14, 2001, pp. 1041–1048.

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