fitcecoc
Fit multiclass models for support vector machines or other classifiers
Syntax
Description
returns
a full, trained, multiclass, errorcorrecting
output codes (ECOC) model using the predictors in table Mdl
= fitcecoc(Tbl
,ResponseVarName
)Tbl
and
the class labels in Tbl.ResponseVarName
. fitcecoc
uses K(K –
1)/2 binary support vector machine (SVM) models using the oneversusone coding design, where K is
the number of unique class labels (levels). Mdl
is
a ClassificationECOC
model.
returns
an ECOC model with additional options specified by one or more Mdl
= fitcecoc(___,Name,Value
)Name,Value
pair
arguments, using any of the previous syntaxes.
For example, specify different binary learners, a different
coding design, or to crossvalidate. It is good practice to crossvalidate
using the Kfold
Name,Value
pair
argument. The crossvalidation results determine how well the model
generalizes.
[
also returns hyperparameter optimization details when you specify the
Mdl
,HyperparameterOptimizationResults
]
= fitcecoc(___,Name,Value
)OptimizeHyperparameters
namevalue pair argument and
use linear or kernel binary learners. For other Learners
,
the HyperparameterOptimizationResults
property of
Mdl
contains the results.
Examples
Train Multiclass Model Using SVM Learners
Train a multiclass errorcorrecting output codes (ECOC) model using support vector machine (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 a multiclass ECOC model using the default options.
Mdl = fitcecoc(X,Y)
Mdl = ClassificationECOC ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' BinaryLearners: {3x1 cell} CodingName: 'onevsone'
Mdl
is a ClassificationECOC
model. By default, fitcecoc
uses SVM binary learners and a oneversusone coding design. You can access Mdl
properties using dot notation.
Display the class names and the coding design matrix.
Mdl.ClassNames
ans = 3x1 cell
{'setosa' }
{'versicolor'}
{'virginica' }
CodingMat = Mdl.CodingMatrix
CodingMat = 3×3
1 1 0
1 0 1
0 1 1
A oneversusone coding design for three classes yields three binary learners. The columns of CodingMat
correspond to the learners, and the rows correspond to the classes. The class order is the same as the order in Mdl.ClassNames
. For example, CodingMat(:,1)
is [1; –1; 0]
and indicates that the software trains the first SVM binary learner using all observations classified as 'setosa'
and 'versicolor'
. Because 'setosa'
corresponds to 1
, it is the positive class; 'versicolor'
corresponds to –1
, so it is the negative class.
You can access each binary learner using cell indexing and dot notation.
Mdl.BinaryLearners{1} % The first binary learner
ans = CompactClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [1 1] ScoreTransform: 'none' Beta: [4x1 double] Bias: 1.4505 KernelParameters: [1x1 struct]
Compute the resubstitution classification error.
error = resubLoss(Mdl)
error = 0.0067
The classification error on the training data is small, but the classifier might be an overfitted model. You can crossvalidate the classifier using crossval
and compute the crossvalidation classification error instead.
Train Multiclass Linear Classification Model
Create a default linear learner template, and then use it to train an ECOC model containing multiple binary linear classification models.
Load the NLP data set.
load nlpdata
X
is a sparse matrix of predictor data, and Y
is a categorical vector of class labels. The data contains 13 classes.
Create a default linear learner template.
t = templateLinear
t = Fit template for Linear. Learner: 'svm'
t
is a template object for a linear learner. All of the properties of t
are empty. When you pass t
to a training function, such as fitcecoc
for ECOC multiclass classification, the software sets the empty properties to their respective default values. For example, the software sets Type
to "classification"
. To modify the default values see the namevalue arguments for templateLinear
.
Train an ECOC model containing of multiple binary linear classification models that identify the software product given the frequency distribution of words on a documentation web page. For faster training time, transpose the predictor data, and specify that observations correspond to columns.
X = X'; rng(1); % For reproducibility Mdl = fitcecoc(X,Y,'Learners',t,'ObservationsIn','columns')
Mdl = CompactClassificationECOC ResponseName: 'Y' ClassNames: [comm dsp ecoder fixedpoint hdlcoder phased physmod simulink stats supportpkg symbolic vision xpc] ScoreTransform: 'none' BinaryLearners: {78x1 cell} CodingMatrix: [13x78 double]
Alternatively, you can train an ECOC model containing default linear classification models by specifying "Learners","Linear"
.
To conserve memory, fitcecoc
returns trained ECOC models containing linear classification learners in CompactClassificationECOC
model objects.
CrossValidate ECOC Classifier
Crossvalidate an ECOC classifier with SVM binary learners, and estimate the generalized classification error.
Load Fisher's iris data set. Specify the predictor data X
and the response data Y
.
load fisheriris X = meas; Y = species; rng(1); % For reproducibility
Create an SVM template, and standardize the predictors.
t = templateSVM('Standardize',true)
t = Fit template for SVM. Standardize: 1
t
is an SVM template. Most of the template object properties are empty. When training the ECOC classifier, the software sets the applicable properties to their default values.
Train the ECOC classifier, and specify the class order.
Mdl = fitcecoc(X,Y,'Learners',t,... 'ClassNames',{'setosa','versicolor','virginica'});
Mdl
is a ClassificationECOC
classifier. You can access its properties using dot notation.
Crossvalidate Mdl
using 10fold crossvalidation.
CVMdl = crossval(Mdl);
CVMdl
is a ClassificationPartitionedECOC
crossvalidated ECOC classifier.
Estimate the generalized classification error.
genError = kfoldLoss(CVMdl)
genError = 0.0400
The generalized classification error is 4%, which indicates that the ECOC classifier generalizes fairly well.
Estimate Posterior Probabilities Using ECOC Classifier
Train an ECOC classifier using SVM binary learners. First predict the trainingsample labels and class posterior probabilities. Then predict the maximum class posterior probability at each point in a grid. Visualize the results.
Load Fisher's iris data set. Specify the petal dimensions as the predictors and the species names as the response.
load fisheriris X = meas(:,3:4); Y = species; rng(1); % For reproducibility
Create an SVM template. Standardize the predictors, and specify the Gaussian kernel.
t = templateSVM('Standardize',true,'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'
namevalue pair argument. Specify the class order using the 'ClassNames'
namevalue pair argument. Display diagnostic messages during training by using the 'Verbose'
namevalue pair argument.
Mdl = fitcecoc(X,Y,'Learners',t,'FitPosterior',true,... '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 trainingsample labels and class posterior probabilities. Display diagnostic messages during the computation of labels and class posterior probabilities by using the 'Verbose'
namevalue pair argument.
[label,~,~,Posterior] = resubPredict(Mdl,'Verbose',1);
Predictions from all learners have been computed. Loss for all observations has been computed. Computing posterior probabilities...
Mdl.BinaryLoss
ans = 'quadratic'
The software assigns an observation to the class that yields the smallest average binary loss. Because 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
ans = 3x1 cell
{'setosa' }
{'versicolor'}
{'virginica' }
table(Y(idx),label(idx),Posterior(idx,:),... 'VariableNames',{'TrueLabel','PredLabel','Posterior'})
ans=10×3 table
TrueLabel PredLabel Posterior
______________ ______________ ______________________________________
{'virginica' } {'virginica' } 0.0039322 0.003987 0.99208
{'virginica' } {'virginica' } 0.017067 0.018263 0.96467
{'virginica' } {'virginica' } 0.014948 0.015856 0.9692
{'versicolor'} {'versicolor'} 2.2197e14 0.87318 0.12682
{'setosa' } {'setosa' } 0.999 0.00025092 0.00074638
{'versicolor'} {'virginica' } 2.2195e14 0.05943 0.94057
{'versicolor'} {'versicolor'} 2.2194e14 0.97001 0.029985
{'setosa' } {'setosa' } 0.999 0.00024991 0.0007474
{'versicolor'} {'versicolor'} 0.0085642 0.98259 0.0088487
{'setosa' } {'setosa' } 0.999 0.00025013 0.00074717
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.
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
Speed Up Training ECOC Classifiers Using Binning and Parallel Computing
Train a oneversusall ECOC classifier using a GentleBoost
ensemble of decision trees with surrogate splits. To speed up training, bin numeric predictors and use parallel computing. Binning is valid only when fitcecoc
uses a tree learner. After training, estimate the classification error using 10fold crossvalidation. Note that parallel computing requires Parallel Computing Toolbox™.
Load Sample Data
Load and inspect the arrhythmia
data set.
load arrhythmia
[n,p] = size(X)
n = 452
p = 279
isLabels = unique(Y); nLabels = numel(isLabels)
nLabels = 13
tabulate(categorical(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%
The data set contains 279
predictors, and the sample size of 452
is relatively small. Of the 16 distinct labels, only 13 are represented in the response (Y
). Each label describes various degrees of arrhythmia, and 54.20% of the observations are in class 1
.
Train OneVersusAll ECOC Classifier
Create an ensemble template. You must specify at least three arguments: a method, a number of learners, and the type of learner. For this example, specify 'GentleBoost'
for the method, 100
for the number of learners, and a decision tree template that uses surrogate splits because there are missing observations.
tTree = templateTree('surrogate','on'); tEnsemble = templateEnsemble('GentleBoost',100,tTree);
tEnsemble
is a template object. Most of its properties are empty, but the software fills them with their default values during training.
Train a oneversusall ECOC classifier using the ensembles of decision trees as binary learners. To speed up training, use binning and parallel computing.
Binning (
'NumBins',50
) — When you have a large training data set, you can speed up training (a potential decrease in accuracy) by using the'NumBins'
namevalue pair argument. This argument is valid only whenfitcecoc
uses a tree learner. If you specify the'NumBins'
value, then the software bins every numeric predictor into a specified number of equiprobable bins, and then grows trees on the bin indices instead of the original data. You can try'NumBins',50
first, and then change the'NumBins'
value depending on the accuracy and training speed.Parallel computing (
'Options',statset('UseParallel',true)
) — With a Parallel Computing Toolbox license, you can speed up the computation by using parallel computing, which sends each binary learner to a worker in the pool. The number of workers depends on your system configuration. When you use decision trees for binary learners,fitcecoc
parallelizes training using Intel® Threading Building Blocks (TBB) for dualcore systems and above. Therefore, specifying the'UseParallel'
option is not helpful on a single computer. Use this option on a cluster.
Additionally, specify that the prior probabilities are 1/K, where K = 13 is the number of distinct classes.
options = statset('UseParallel',true); Mdl = fitcecoc(X,Y,'Coding','onevsall','Learners',tEnsemble,... 'Prior','uniform','NumBins',50,'Options',options);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6).
Mdl
is a ClassificationECOC
model.
CrossValidation
Crossvalidate the ECOC classifier using 10fold crossvalidation.
CVMdl = crossval(Mdl,'Options',options);
Warning: One or more folds do not contain points from all the groups.
CVMdl
is a ClassificationPartitionedECOC
model. The warning indicates that some classes are not represented while the software trains at least one fold. Therefore, those folds cannot predict labels for the missing classes. You can inspect the results of a fold using cell indexing and dot notation. For example, access the results of the first fold by entering CVMdl.Trained{1}
.
Use the crossvalidated ECOC classifier to predict validationfold labels. You can compute the confusion matrix by using confusionchart
. Move and resize the chart by changing the inner position property to ensure that the percentages appear in the row summary.
oofLabel = kfoldPredict(CVMdl,'Options',options); ConfMat = confusionchart(Y,oofLabel,'RowSummary','totalnormalized'); ConfMat.InnerPosition = [0.10 0.12 0.85 0.85];
Reproduce Binned Data
Reproduce binned predictor data by using the BinEdges
property of the trained model and the discretize
function.
X = Mdl.X; % Predictor data Xbinned = zeros(size(X)); edges = Mdl.BinEdges; % Find indices of binned predictors. idxNumeric = find(~cellfun(@isempty,edges)); if iscolumn(idxNumeric) idxNumeric = idxNumeric'; end for j = idxNumeric x = X(:,j); % Convert x to array if x is a table. if istable(x) x = table2array(x); end % Group x into bins by using the discretize function. xbinned = discretize(x,[inf; edges{j}; inf]); Xbinned(:,j) = xbinned; end
Xbinned
contains the bin indices, ranging from 1 to the number of bins, for numeric predictors. Xbinned
values are 0
for categorical predictors. If X
contains NaN
s, then the corresponding Xbinned
values are NaN
s.
Optimize ECOC Classifier
Optimize hyperparameters automatically using fitcecoc
.
Load the fisheriris
data set.
load fisheriris
X = meas;
Y = species;
Find hyperparameters that minimize fivefold crossvalidation loss by using automatic hyperparameter optimization. For reproducibility, set the random seed and use the 'expectedimprovementplus'
acquisition function.
rng default Mdl = fitcecoc(X,Y,'OptimizeHyperparameters','auto',... 'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName',... 'expectedimprovementplus'))
===================================================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  Coding  BoxConstraint KernelScale  Standardize    result   runtime  (observed)  (estim.)      ===================================================================================================================================  1  Best  0.18667  15.793  0.18667  0.18667  onevsall  76.389  0.0012205  true   2  Best  0.10667  0.40033  0.10667  0.11235  onevsone  0.0013787  41.108  false   3  Best  0.04  1.0137  0.04  0.10177  onevsall  16.632  0.18987  false   4  Accept  0.046667  0.58649  0.04  0.091841  onevsone  0.04843  0.0042504  true   5  Accept  0.04  1.099  0.04  0.040003  onevsall  16.708  0.21334  false   6  Accept  0.33333  0.35362  0.04  0.040005  onevsall  0.0010041  21.936  false   7  Accept  0.47333  12.545  0.04  0.039969  onevsall  94.884  0.004214  false   8  Accept  0.04  0.40735  0.04  0.039876  onevsone  0.077785  0.010622  true   9  Accept  0.26  11.888  0.04  0.039858  onevsall  8.9153  0.0033389  false   10  Accept  0.046667  0.66439  0.04  0.039855  onevsall  4.9266  0.18135  false   11  Accept  0.04  0.39131  0.04  0.039845  onevsone  0.014352  0.024917  true   12  Accept  0.046667  0.40671  0.04  0.039728  onevsone  0.059581  0.15666  true   13  Accept  0.06  0.36833  0.04  0.039703  onevsone  0.004907  0.62229  true   14  Accept  0.046667  0.32772  0.04  0.039733  onevsone  0.0010462  0.018383  true   15  Accept  0.04  0.31935  0.04  0.039437  onevsone  0.0014013  0.0010097  true   16  Accept  0.04  0.44862  0.04  0.03971  onevsone  2.3093  0.038776  true   17  Accept  0.06  3.7593  0.04  0.038874  onevsone  4.1623  0.0016004  true   18  Accept  0.046667  1.7431  0.04  0.039388  onevsone  128.63  0.03404  true   19  Accept  0.04  0.30193  0.04  0.038396  onevsone  21.297  1.187  true   20  Accept  0.08  0.32875  0.04  0.038635  onevsall  33.105  8.1376  false  ===================================================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  Coding  BoxConstraint KernelScale  Standardize    result   runtime  (observed)  (estim.)      ===================================================================================================================================  21  Accept  0.04  0.40306  0.04  0.038644  onevsone  940.62  2.5021  true   22  Accept  0.08  0.39623  0.04  0.038577  onevsone  116.39  115.89  true   23  Accept  0.16667  0.48651  0.04  0.038565  onevsone  0.42894  42.359  true   24  Accept  0.04  0.32752  0.04  0.038555  onevsone  154.48  0.70993  true   25  Accept  0.08  3.4442  0.04  0.038539  onevsone  870.52  0.0010486  true   26  Accept  0.046667  0.40986  0.04  0.038542  onevsone  0.14081  0.17365  false   27  Accept  0.046667  0.29978  0.04  0.038539  onevsone  0.0040863  0.017832  false   28  Accept  0.046667  0.68917  0.04  0.038522  onevsone  0.14137  0.0017205  false   29  Accept  0.046667  0.48719  0.04  0.038529  onevsone  9.504  0.017258  false   30  Accept  0.046667  0.35353  0.04  0.038515  onevsone  18.974  2.1636  false  __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 77.204 seconds Total objective function evaluation time: 60.4428 Best observed feasible point: Coding BoxConstraint KernelScale Standardize ________ _____________ ___________ ___________ onevsall 16.632 0.18987 false Observed objective function value = 0.04 Estimated objective function value = 0.042035 Function evaluation time = 1.0137 Best estimated feasible point (according to models): Coding BoxConstraint KernelScale Standardize ________ _____________ ___________ ___________ onevsall 16.708 0.21334 false Estimated objective function value = 0.038515 Estimated function evaluation time = 0.94585
Mdl = ClassificationECOC ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' BinaryLearners: {3x1 cell} CodingName: 'onevsall' HyperparameterOptimizationResults: [1x1 BayesianOptimization]
Train Multiclass ECOC Model with SVMs and Tall Arrays
Create two multiclass ECOC models trained on tall data. Use linear binary learners for one of the models and kernel binary learners for the other. Compare the resubstitution classification error of the two models.
In general, you can perform multiclass classification of tall data by using fitcecoc
with linear or kernel binary learners. When you use fitcecoc
to train a model on tall arrays, you cannot use SVM binary learners directly. However, you can use either linear or kernel binary classification models that use SVMs.
When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. If you want to run the example using the local MATLAB session when you have Parallel Computing Toolbox, you can change the global execution environment by using the mapreducer
function.
Create a datastore that references the folder containing Fisher's iris data set. Specify 'NA'
values as missing data so that datastore
replaces them with NaN
values. Create tall versions of the predictor and response data.
ds = datastore('fisheriris.csv','TreatAsMissing','NA'); t = tall(ds);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6).
X = [t.SepalLength t.SepalWidth t.PetalLength t.PetalWidth]; Y = t.Species;
Standardize the predictor data.
Z = zscore(X);
Train a multiclass ECOC model that uses tall data and linear binary learners. By default, when you pass tall arrays to fitcecoc
, the software trains linear binary learners that use SVMs. Because the response data contains only three unique classes, change the coding scheme from oneversusall (which is the default when you use tall data) to oneversusone (which is the default when you use inmemory data).
For reproducibility, set the seeds of the random number generators using rng
and tallrng
. The results can vary depending on the number of workers and the execution environment for the tall arrays. For details, see Control Where Your Code Runs.
rng('default') tallrng('default') mdlLinear = fitcecoc(Z,Y,'Coding','onevsone')
Training binary learner 1 (Linear) out of 3. Training binary learner 2 (Linear) out of 3. Training binary learner 3 (Linear) out of 3.
mdlLinear = CompactClassificationECOC ResponseName: 'Y' ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' BinaryLearners: {3×1 cell} CodingMatrix: [3×3 double] Properties, Methods
mdlLinear
is a CompactClassificationECOC
model composed of three binary learners.
Train a multiclass ECOC model that uses tall data and kernel binary learners. First, create a templateKernel
object to specify the properties of the kernel binary learners; in particular, increase the number of expansion dimensions to $${2}^{16}$$.
tKernel = templateKernel('NumExpansionDimensions',2^16)
tKernel = Fit template for classification Kernel. BetaTolerance: [] BlockSize: [] BoxConstraint: [] Epsilon: [] NumExpansionDimensions: 65536 GradientTolerance: [] HessianHistorySize: [] IterationLimit: [] KernelScale: [] Lambda: [] Learner: 'svm' LossFunction: [] Stream: [] VerbosityLevel: [] Version: 1 Method: 'Kernel' Type: 'classification'
By default, the kernel binary learners use SVMs.
Pass the templateKernel
object to fitcecoc
and change the coding scheme to oneversusone.
mdlKernel = fitcecoc(Z,Y,'Learners',tKernel,'Coding','onevsone')
Training binary learner 1 (Kernel) out of 3. Training binary learner 2 (Kernel) out of 3. Training binary learner 3 (Kernel) out of 3.
mdlKernel = CompactClassificationECOC ResponseName: 'Y' ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' BinaryLearners: {3×1 cell} CodingMatrix: [3×3 double] Properties, Methods
mdlKernel
is also a CompactClassificationECOC
model composed of three binary learners.
Compare the resubstitution classification error of the two models.
errorLinear = gather(loss(mdlLinear,Z,Y))
Evaluating tall expression using the Parallel Pool 'local':  Pass 1 of 1: Completed in 1.4 sec Evaluation completed in 1.6 sec
errorLinear = 0.0333
errorKernel = gather(loss(mdlKernel,Z,Y))
Evaluating tall expression using the Parallel Pool 'local':  Pass 1 of 1: Completed in 15 sec Evaluation completed in 16 sec
errorKernel = 0.0067
mdlKernel
misclassifies a smaller percentage of the training data than mdlLinear
.
Input Arguments
Tbl
— Sample data
table
Sample data, specified as a table. Each row of Tbl
corresponds
to one observation, and each column corresponds to one predictor.
Optionally, Tbl
can contain one additional column
for the response variable. Multicolumn variables and cell arrays other
than cell arrays of character vectors are not accepted.
If Tbl
contains the response variable, and
you want to use all remaining variables in Tbl
as
predictors, then specify the response variable using ResponseVarName
.
If Tbl
contains the response variable, and
you want to use only a subset of the remaining variables in Tbl
as
predictors, specify a formula using formula
.
If Tbl
does not contain the response variable,
specify a response variable using Y
. The length
of response variable and the number of Tbl
rows
must be equal.
Data Types: table
ResponseVarName
— Response variable name
name of variable in Tbl
Response variable name, specified as the name of a variable in
Tbl
.
You must specify ResponseVarName
as a character vector or string scalar.
For example, if the response variable Y
is
stored as Tbl.Y
, then specify it as
"Y"
. Otherwise, the software
treats all columns of Tbl
, including
Y
, as predictors when training
the model.
The response variable must be a categorical, character, or string array; a logical or numeric
vector; or a cell array of character vectors. If
Y
is a character array, then each
element of the response variable must correspond to one row of
the array.
A good practice is to specify the order of the classes by using the
ClassNames
namevalue
argument.
Data Types: char
 string
formula
— Explanatory model of response variable and subset of predictor variables
character vector  string scalar
Explanatory model of the response variable and a subset of the predictor variables,
specified as a character vector or string scalar in the form
"Y~x1+x2+x3"
. In this form, Y
represents the
response variable, and x1
, x2
, and
x3
represent the predictor variables.
To specify a subset of variables in Tbl
as predictors for
training the model, use a formula. If you specify a formula, then the software does not
use any variables in Tbl
that do not appear in
formula
.
The variable names in the formula must be both variable names in Tbl
(Tbl.Properties.VariableNames
) and valid MATLAB^{®} identifiers. You can verify the variable names in Tbl
by
using the isvarname
function. If the variable names
are not valid, then you can convert them by using the matlab.lang.makeValidName
function.
Data Types: char
 string
Y
— Class labels
categorical array  character array  string array  logical vector  numeric vector  cell array of character vectors
Class labels to which the ECOC model is trained, specified as a categorical, character, or string array, logical or numeric vector, or cell array of character vectors.
If Y
is a character array, then each element
must correspond to one row of the array.
The length of Y
and the number of rows of Tbl
or X
must
be equal.
It is good practice to specify the class order using the ClassNames
namevalue
pair argument.
Data Types: categorical
 char
 string
 logical
 single
 double
 cell
X
— Predictor data
full matrix  sparse matrix
Predictor data, specified as a full or sparse matrix.
The length of Y
and the number of observations
in X
must be equal.
To specify the names of the predictors in the order of their
appearance in X
, use the PredictorNames
namevalue
pair argument.
Note
For linear classification learners, if you orient
X
so that observations correspond to columns and specify'ObservationsIn','columns'
, then you can experience a significant reduction in optimizationexecution time.For all other learners, orient
X
so that observations correspond to rows.fitcecoc
supports sparse matrices for training linear classification models only.
Data Types: double
 single
Note
The software treats NaN
, empty character vector
(''
), empty string (""
),
<missing>
, and <undefined>
elements as missing data. The software removes rows of X
corresponding to missing values in Y
. However, the treatment of
missing values in X
varies among binary learners. For details,
see the training functions for your binary learners: fitcdiscr
, fitckernel
, fitcknn
, fitclinear
, fitcnb
, fitcsvm
, fitctree
, or fitcensemble
. Removing observations decreases the effective training
or crossvalidation sample size.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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: 'Learners','tree','Coding','onevsone','CrossVal','on'
specifies to use decision trees for all binary learners, a oneversusone coding
design, and to implement 10fold crossvalidation.
Note
You cannot use any crossvalidation namevalue argument together with the
'OptimizeHyperparameters'
namevalue argument. You can modify the
crossvalidation for 'OptimizeHyperparameters'
only by using the
'HyperparameterOptimizationOptions'
namevalue argument.
Coding
— Coding design
'onevsone'
(default)  'allpairs'
 'binarycomplete'
 'denserandom'
 'onevsall'
 'ordinal'
 'sparserandom'
 'ternarycomplete'
 numeric matrix
Coding design name, specified as the commaseparated pair consisting
of 'Coding'
and a numeric matrix or a value in
this table.
Value  Number of Binary Learners  Description 

'allpairs' and 'onevsone'  K(K – 1)/2  For each binary learner, one class is positive, another is negative, and the software ignores the rest. This design exhausts all combinations of class pair assignments. 
'binarycomplete'  $${2}^{(K1)}1$$  This design partitions the classes into all binary combinations, and does not ignore any
classes. For each binary learner, all class assignments are
–1 and 1 with at least one positive
class and one negative class in the assignment. 
'denserandom'  Random, but approximately 10 log_{2}K  For each binary learner, the software randomly assigns classes into positive or negative classes, with at least one of each type. For more details, see Random Coding Design Matrices. 
'onevsall'  K  For each binary learner, one class is positive and the rest are negative. This design exhausts all combinations of positive class assignments. 
'ordinal'  K – 1  For the first binary learner, the first class is negative and the rest are positive. For the second binary learner, the first two classes are negative and the rest are positive, and so on. 
'sparserandom'  Random, but approximately 15 log_{2}K  For each binary learner, the software randomly assigns classes as positive or negative with probability 0.25 for each, and ignores classes with probability 0.5. For more details, see Random Coding Design Matrices. 
'ternarycomplete'  $$\left({3}^{K}{2}^{(K+1)}+1\right)/2$$  This design partitions the classes into all ternary combinations. All class assignments are
0 , –1 , and 1 with
at least one positive class and one negative class in each assignment. 
You can also specify a coding design using a custom coding matrix, which is a
KbyL matrix. Each row corresponds to a class
and each column corresponds to a binary learner. The class order (rows) corresponds to
the order in ClassNames
. Create the
matrix by following these guidelines:
Every element of the custom coding matrix must be
–1
,0
, or1
, and the value must correspond to a dichotomous class assignment. ConsiderCoding(i,j)
, the class that learnerj
assigns to observations in classi
.Value Dichotomous Class Assignment –1
Learner j
assigns observations in classi
to a negative class.0
Before training, learner j
removes observations in classi
from the data set.1
Learner j
assigns observations in classi
to a positive class.Every column must contain at least one
–1
and one1
.For all column indices
i
,j
wherei
≠j
,Coding(:,i)
cannot equalCoding(:,j)
, andCoding(:,i)
cannot equal–Coding(:,j)
.All rows of the custom coding matrix must be different.
For more details on the form of custom coding design matrices, see Custom Coding Design Matrices.
Example: 'Coding','ternarycomplete'
Data Types: char
 string
 double
 single
 int16
 int32
 int64
 int8
FitPosterior
— Flag indicating whether to transform scores to posterior probabilities
false
or 0
(default)  true
or 1
Flag indicating whether to transform scores to posterior probabilities,
specified as the commaseparated pair consisting of 'FitPosterior'
and
a true
(1
) or false
(0
).
If FitPosterior
is true
,
then the software transforms binarylearner classification scores
to posterior probabilities. You can obtain posterior probabilities
by using kfoldPredict
, predict
,
or resubPredict
.
fitcecoc
does not support fitting posterior probabilities if:
The ensemble method is
AdaBoostM2
,LPBoost
,RUSBoost
,RobustBoost
, orTotalBoost
.The binary learners (
Learners
) are linear or kernel classification models that implement SVM. To obtain posterior probabilities for linear or kernel classification models, implement logistic regression instead.
Example: 'FitPosterior',true
Data Types: logical
Learners
— Binary learner templates
'svm'
(default)  'discriminant'
 'kernel'
 'knn'
 'linear'
 'naivebayes'
 'tree'
 template object  cell vector of template objects
Binary learner templates, specified as the commaseparated pair consisting of
'Learners'
and a character vector, string scalar, template
object, or cell vector of template objects. Specifically, you can specify binary
classifiers such as SVM, and the ensembles that use GentleBoost
,
LogitBoost
, and RobustBoost
, to solve
multiclass problems. However, fitcecoc
also supports multiclass
models as binary classifiers.
If
Learners
is a character vector or string scalar, then the software trains each binary learner using the default values of the specified algorithm. This table summarizes the available algorithms.Value Description 'discriminant'
Discriminant analysis. For default options, see templateDiscriminant
.'kernel'
Kernel classification model. For default options, see templateKernel
.'knn'
knearest neighbors. For default options, see templateKNN
.'linear'
Linear classification model. For default options, see templateLinear
.'naivebayes'
Naive Bayes. For default options, see templateNaiveBayes
.'svm'
SVM. For default options, see templateSVM
.'tree'
Classification trees. For default options, see templateTree
.If
Learners
is a template object, then each binary learner trains according to the stored options. You can create a template object using:templateDiscriminant
, for discriminant analysis.templateEnsemble
, for ensemble learning. You must at least specify the learning method (Method
), the number of learners (NLearn
), and the type of learner (Learners
). You cannot use theAdaBoostM2
ensemble method for binary learning.templateKernel
, for kernel classification.templateKNN
, for knearest neighbors.templateLinear
, for linear classification.templateNaiveBayes
, for naive Bayes.templateSVM
, for SVM.templateTree
, for classification trees.
If
Learners
is a cell vector of template objects, then:Cell j corresponds to binary learner j (in other words, column j of the coding design matrix), and the cell vector must have length L. L is the number of columns in the coding design matrix. For details, see
Coding
.To use one of the builtin loss functions for prediction, then all binary learners must return a score in the same range. For example, you cannot include default SVM binary learners with default naive Bayes binary learners. The former returns a score in the range (∞,∞), and the latter returns a posterior probability as a score. Otherwise, you must provide a custom loss as a function handle to functions such as
predict
andloss
.You cannot specify linear classification model learner templates with any other template.
Similarly, you cannot specify kernel classification model learner templates with any other template.
By default, the software trains learners using default SVM templates.
Example: 'Learners','tree'
NumBins
— Number of bins for numeric predictors
[]
(empty) (default)  positive integer scalar
Number of bins for numeric predictors, specified as the
commaseparated pair consisting of 'NumBins'
and a
positive integer scalar. This argument is valid only when
fitcecoc
uses a tree learner, that is,
'Learners'
is either 'tree'
or a template object created by using templateTree
, or a template
object created by using templateEnsemble
with tree
weak learners.
If the
'NumBins'
value is empty (default), thenfitcecoc
does not bin any predictors.If you specify the
'NumBins'
value as a positive integer scalar (numBins
), thenfitcecoc
bins every numeric predictor into at mostnumBins
equiprobable bins, and then grows trees on the bin indices instead of the original data.The number of bins can be less than
numBins
if a predictor has fewer thannumBins
unique values.fitcecoc
does not bin categorical predictors.
When you use a large training data set, this binning option speeds up training but might cause
a potential decrease in accuracy. You can try 'NumBins',50
first, and
then change the value depending on the accuracy and training speed.
A trained model stores the bin edges in the BinEdges
property.
Example: 'NumBins',50
Data Types: single
 double
NumConcurrent
— Number of binary learners concurrently trained
1
(default)  positive integer scalar
Number of binary learners concurrently trained, specified as the
commaseparated pair consisting of 'NumConcurrent'
and a positive integer scalar. The default value is
1
, which means fitcecoc
trains
the binary learners sequentially.
Note
This option applies only when you use
fitcecoc
on tall arrays. See Tall Arrays
for more information.
Data Types: single
 double
ObservationsIn
— Predictor data observation dimension
'rows'
(default)  'columns'
Predictor data observation dimension, specified as the commaseparated
pair consisting of 'ObservationsIn'
and
'columns'
or 'rows'
.
Note
For linear classification learners, if you orient
X
so that observations correspond to columns and specify'ObservationsIn','columns'
, then you can experience a significant reduction in optimizationexecution time.For all other learners, orient
X
so that observations correspond to rows.
Example: 'ObservationsIn','columns'
Verbose
— Verbosity level
0
(default)  1
 2
Verbosity level, specified as the commaseparated pair consisting of
'Verbose'
and 0
,
1
, or 2
.
Verbose
controls the amount of diagnostic
information per binary learner that the software displays in the Command
Window.
This table summarizes the available verbosity level options.
Value  Description 

0  The software does not display diagnostic information. 
1  The software displays diagnostic messages every time it trains a new binary learner. 
2  The software displays extra diagnostic messages every time it trains a new binary learner. 
Each binary learner has its own verbosity level that is independent of
this namevalue pair argument. To change the verbosity level of a binary
learner, create a template object and specify the
'Verbose'
namevalue pair argument. Then, pass
the template object to fitcecoc
by using the
'Learners'
namevalue pair argument.
Example: 'Verbose',1
Data Types: double
 single
CrossVal
— Flag to train crossvalidated classifier
'off'
(default)  'on'
Flag to train a crossvalidated classifier, specified as the
commaseparated pair consisting of 'Crossval'
and
'on'
or 'off'
.
If you specify 'on'
, then the software trains a
crossvalidated classifier with 10 folds.
You can override this crossvalidation setting using one of the
CVPartition
, Holdout
,
KFold
, or Leaveout
namevalue pair arguments. You can only use one crossvalidation
namevalue pair argument at a time to create a crossvalidated
model.
Alternatively, crossvalidate later by passing
Mdl
to crossval
.
Example: 'Crossval','on'
CVPartition
— Crossvalidation partition
[]
(default)  cvpartition
object
Crossvalidation partition, specified as a cvpartition
object that specifies the type of crossvalidation and the
indexing for the training and validation sets.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Suppose you create a random partition for 5fold crossvalidation on 500
observations by using cvp = cvpartition(500,KFold=5)
. Then, you can
specify the crossvalidation partition by setting
CVPartition=cvp
.
Holdout
— Fraction of data for holdout validation
scalar value in the range (0,1)
Fraction of the data used for holdout validation, specified as a scalar value in the range
[0,1]. If you specify Holdout=p
, then the software completes these
steps:
Randomly select and reserve
p*100
% of the data as validation data, and train the model using the rest of the data.Store the compact trained model in the
Trained
property of the crossvalidated model.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Holdout=0.1
Data Types: double
 single
KFold
— Number of folds
10
(default)  positive integer value greater than 1
Number of folds to use in the crossvalidated model, specified as a positive integer value
greater than 1. If you specify KFold=k
, then the software completes
these steps:
Randomly partition the data into
k
sets.For each set, reserve the set as validation data, and train the model using the other
k
– 1 sets.Store the
k
compact trained models in ak
by1 cell vector in theTrained
property of the crossvalidated model.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: KFold=5
Data Types: single
 double
Leaveout
— Leaveoneout crossvalidation flag
'off'
(default)  'on'
Leaveoneout crossvalidation flag, specified as the commaseparated
pair consisting of 'Leaveout'
and
'on'
or 'off'
. If you specify
'Leaveout','on'
, then, for each of the
n observations, where n is
size(Mdl.X,1)
, the software:
Reserves the observation as validation data, and trains the model using the other n – 1 observations
Stores the n compact, trained models in the cells of a nby1 cell vector in the
Trained
property of the crossvalidated model.
To create a crossvalidated model, you can use one of these four
options only: CVPartition
,
Holdout
, KFold
, or
Leaveout
.
Note
Leaveoneout is not recommended for crossvalidating ECOC models composed of linear or kernel classification model learners.
Example: 'Leaveout','on'
CategoricalPredictors
— Categorical predictors list
vector of positive integers  logical vector  character matrix  string array  cell array of character vectors  'all'
Categorical predictors list, specified as one of the values in this table.
Value  Description 

Vector of positive integers 
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If 
Logical vector 
A 
Character matrix  Each row of the matrix is the name of a predictor variable. The names must match the entries in PredictorNames . Pad the names with extra blanks so each row of the character matrix has the same length. 
String array or cell array of character vectors  Each element in the array is the name of a predictor variable. The names must match the entries in PredictorNames . 
"all"  All predictors are categorical. 
Specification of 'CategoricalPredictors'
is
appropriate if:
At least one predictor is categorical and all binary learners are classification trees, naive Bayes learners, SVMs, linear learners, kernel learners, or ensembles of classification trees.
All predictors are categorical and at least one binary learner is kNN.
If you specify 'CategoricalPredictors'
for any other learner, then the software warns that it cannot train that
binary learner. For example, the software cannot train discriminant
analysis classifiers using categorical predictors.
Each learner identifies and treats categorical predictors in the same
way as the fitting function corresponding to the learner. See 'CategoricalPredictors'
of
fitckernel
for kernel learners, 'CategoricalPredictors'
of fitcknn
for knearest learners, 'CategoricalPredictors'
of
fitclinear
for linear learners, 'CategoricalPredictors'
of fitcnb
for naive Bayes learners, 'CategoricalPredictors'
of fitcsvm
for SVM learners, and 'CategoricalPredictors'
of fitctree
for tree learners.
Example: 'CategoricalPredictors','all'
Data Types: single
 double
 logical
 char
 string
 cell
ClassNames
— Names of classes to use for training
categorical array  character array  string array  logical vector  numeric vector  cell array of character vectors
Names of classes to use for training, specified as a categorical, character, or string
array; a logical or numeric vector; or a cell array of character vectors.
ClassNames
must have the same data type as the response variable
in Tbl
or Y
.
If ClassNames
is a character array, then each element must correspond to one row of the array.
Use ClassNames
to:
Specify the order of the classes during training.
Specify the order of any input or output argument dimension that corresponds to the class order. For example, use
ClassNames
to specify the order of the dimensions ofCost
or the column order of classification scores returned bypredict
.Select a subset of classes for training. For example, suppose that the set of all distinct class names in
Y
is["a","b","c"]
. To train the model using observations from classes"a"
and"c"
only, specify"ClassNames",["a","c"]
.
The default value for ClassNames
is the set of all distinct class names in the response variable in Tbl
or Y
.
Example: "ClassNames",["b","g"]
Data Types: categorical
 char
 string
 logical
 single
 double
 cell
Cost
— Misclassification cost
square matrix  structure array
Misclassification cost, specified as the commaseparated pair
consisting of 'Cost'
and a square matrix or
structure. If you specify:
The square matrix
Cost
, thenCost(i,j)
is the cost of classifying a point into classj
if its true class isi
. That is, the rows correspond to the true class and the columns correspond to the predicted class. To specify the class order for the corresponding rows and columns ofCost
, additionally specify theClassNames
namevalue pair argument.The structure
S
, then it must have two fields:S.ClassNames
, which contains the class names as a variable of the same data type asY
S.ClassificationCosts
, which contains the cost matrix with rows and columns ordered as inS.ClassNames
The default is ones(
, where
K
) 
eye(K
)K
is the number of distinct
classes.
Example: 'Cost',[0 1 2 ; 1 0 2; 2 2
0]
Data Types: double
 single
 struct
Options
— Parallel computing options
[]
(default)  structure array returned by statset
Parallel computing options, specified as the commaseparated pair consisting of
'Options'
and a structure array returned by statset
. Parallel computation requires Parallel Computing
Toolbox™. fitcecoc
uses
'Streams'
, 'UseParallel'
, and
'UseSubtreams'
fields.
This table summarizes the available options.
Option  Description 

'Streams' 
A
In that case, use a cell array of the same size as the
parallel pool. If a parallel pool is not open, then the software
tries to open one (depending on your preferences), and

'UseParallel'  If you have Parallel Computing Toolbox, then you can invoke a
pool of workers by setting
When you use
decision trees for binary learners,

'UseSubstreams'  Set to true to compute in parallel using
the stream specified by 'Streams' . Default is false .
For example, set Streams to a type allowing substreams,
such as'mlfg6331_64' or 'mrg32k3a' . 
A best practice to ensure more
predictable results is to use parpool
(Parallel Computing Toolbox) and
explicitly create a parallel pool before you invoke parallel computing
using fitcecoc
.
Example: 'Options',statset('UseParallel',true)
Data Types: struct
PredictorNames
— Predictor variable names
string array of unique names  cell array of unique character vectors
Predictor variable names, specified as a string array of unique names or cell array of unique
character vectors. The functionality of PredictorNames
depends on the
way you supply the training data.
If you supply
X
andY
, then you can usePredictorNames
to assign names to the predictor variables inX
.The order of the names in
PredictorNames
must correspond to the column order ofX
. That is,PredictorNames{1}
is the name ofX(:,1)
,PredictorNames{2}
is the name ofX(:,2)
, and so on. Also,size(X,2)
andnumel(PredictorNames)
must be equal.By default,
PredictorNames
is{'x1','x2',...}
.
If you supply
Tbl
, then you can usePredictorNames
to choose which predictor variables to use in training. That is,fitcecoc
uses only the predictor variables inPredictorNames
and the response variable during training.PredictorNames
must be a subset ofTbl.Properties.VariableNames
and cannot include the name of the response variable.By default,
PredictorNames
contains the names of all predictor variables.A good practice is to specify the predictors for training using either
PredictorNames
orformula
, but not both.
Example: "PredictorNames",["SepalLength","SepalWidth","PetalLength","PetalWidth"]
Data Types: string
 cell
Prior
— Prior probabilities
'empirical'
(default)  'uniform'
 numeric vector  structure array
Prior probabilities for each class, specified as the commaseparated
pair consisting of 'Prior'
and a value in this
table.
Value  Description 

'empirical'  The class prior probabilities are the class
relative frequencies in
Y . 
'uniform'  All class prior probabilities are equal to 1/K, where K is the number of classes. 
numeric vector  Each element is a class prior probability. Order
the elements according to
Mdl .ClassNames
or specify the order using the
ClassNames namevalue pair
argument. The software normalizes the elements such
that they sum to 1 . 
structure 
A structure

For more details on how the software incorporates class prior probabilities, see Prior Probabilities and Misclassification Cost.
Example: struct('ClassNames',{{'setosa','versicolor','virginica'}},'ClassProbs',1:3)
Data Types: single
 double
 char
 string
 struct
ResponseName
— Response variable name
"Y"
(default)  character vector  string scalar
Response variable name, specified as a character vector or string scalar.
If you supply
Y
, then you can useResponseName
to specify a name for the response variable.If you supply
ResponseVarName
orformula
, then you cannot useResponseName
.
Example: "ResponseName","response"
Data Types: char
 string
Weights
— Observation weights
numeric vector of positive values  name of variable in Tbl
Observation weights, specified as the commaseparated pair consisting
of 'Weights'
and a numeric vector of positive values
or name of a variable in Tbl
. The software weighs
the observations in each row of X
or Tbl
with
the corresponding value in Weights
. The size of Weights
must
equal the number of rows of X
or Tbl
.
If you specify the input data as a table Tbl
, then
Weights
can be the name of a variable in Tbl
that contains a numeric vector. In this case, you must specify
Weights
as a character vector or string scalar. For example, if
the weights vector W
is stored as Tbl.W
, then
specify it as 'W'
. Otherwise, the software treats all columns of
Tbl
, including W
, as predictors or the
response when training the model.
The software normalizes Weights
to sum up
to the value of the prior probability in the respective class.
By default, Weights
is ones(
,
where n
,1)n
is the number of observations in X
or Tbl
.
Data Types: double
 single
 char
 string
OptimizeHyperparameters
— Parameters to optimize
'none'
(default)  'auto'
 'all'
 string array or cell array of eligible parameter names  vector of optimizableVariable
objects
Parameters to optimize, specified as the commaseparated pair
consisting of 'OptimizeHyperparameters'
and one of
the following:
'none'
— Do not optimize.'auto'
— Use{'Coding'}
along with the default parameters for the specifiedLearners
:Learners
='svm'
(default) —{'BoxConstraint','KernelScale','Standardize'}
Learners
='discriminant'
—{'Delta','Gamma'}
Learners
='kernel'
—{'KernelScale','Lambda','Standardize'}
Learners
='knn'
—{'Distance','NumNeighbors','Standardize'}
Learners
='linear'
—{'Lambda','Learner'}
Learners
='tree'
—{'MinLeafSize'}
'all'
— Optimize all eligible parameters.String array or cell array of eligible parameter names
Vector of
optimizableVariable
objects, typically the output ofhyperparameters
The optimization attempts to minimize the crossvalidation loss
(error) for fitcecoc
by varying the parameters. For
information about crossvalidation loss in a different context, see
Classification Loss. To control the
crossvalidation type and other aspects of the optimization, use the
HyperparameterOptimizationOptions
namevalue
pair.
Note
The values of 'OptimizeHyperparameters'
override any values you specify
using other namevalue arguments. For example, setting
'OptimizeHyperparameters'
to 'auto'
causes
fitcecoc
to optimize hyperparameters corresponding to the
'auto'
option and to ignore any specified values for the
hyperparameters.
The eligible parameters for fitcecoc
are:
Coding
—fitcecoc
searches among'onevsall'
and'onevsone'
.The eligible hyperparameters for the chosen
Learners
, as specified in this table.Learners Eligible Hyperparameters
(Bold = Default)Default Range 'discriminant'
Delta
Logscaled in the range [1e6,1e3]
DiscrimType
'linear'
,'quadratic'
,'diagLinear'
,'diagQuadratic'
,'pseudoLinear'
, and'pseudoQuadratic'
Gamma
Real values in [0,1]
'kernel'
Lambda
Positive values logscaled in the range [1e3/NumObservations,1e3/NumObservations]
KernelScale
Positive values logscaled in the range [1e3,1e3]
Learner
'svm'
and'logistic'
NumExpansionDimensions
Integers logscaled in the range [100,10000]
Standardize
'true'
and'false'
'knn'
Distance
'cityblock'
,'chebychev'
,'correlation'
,'cosine'
,'euclidean'
,'hamming'
,'jaccard'
,'mahalanobis'
,'minkowski'
,'seuclidean'
, and'spearman'
DistanceWeight
'equal'
,'inverse'
, and'squaredinverse'
Exponent
Positive values in [0.5,3]
NumNeighbors
Positive integer values logscaled in the range [1, max(2,round(NumObservations/2))]
Standardize
'true'
and'false'
'linear'
Lambda
Positive values logscaled in the range [1e5/NumObservations,1e5/NumObservations]
Learner
'svm'
and'logistic'
Regularization
'ridge'
and'lasso'
When
Regularization
is'ridge'
, the function uses a Limitedmemory BFGS (LBFGS) solver by default.When
Regularization
is'lasso'
, the function uses a Sparse Reconstruction by Separable Approximation (SpaRSA) solver by default.
'svm'
BoxConstraint
Positive values logscaled in the range [1e3,1e3]
KernelScale
Positive values logscaled in the range [1e3,1e3]
KernelFunction
'gaussian'
,'linear'
, and'polynomial'
PolynomialOrder
Integers in the range [2,4]
Standardize
'true'
and'false'
'tree'
MaxNumSplits
Integers logscaled in the range [1,max(2,NumObservations1)]
MinLeafSize
Integers logscaled in the range [1,max(2,floor(NumObservations/2))]
NumVariablesToSample
Integers in the range [1,max(2,NumPredictors)]
SplitCriterion
'gdi'
,'deviance'
, and'twoing'
Alternatively, use
hyperparameters
with your chosenLearners
, such asload fisheriris % hyperparameters requires data and learner params = hyperparameters('fitcecoc',meas,species,'svm');
To see the eligible and default hyperparameters, examine
params
.
Set nondefault parameters by passing a vector of
optimizableVariable
objects that have nondefault
values. For example,
load fisheriris params = hyperparameters('fitcecoc',meas,species,'svm'); params(2).Range = [1e4,1e6];
Pass params
as the value of
OptimizeHyperparameters
.
By default, the iterative display appears at the command line,
and plots appear according to the number of hyperparameters in the optimization. For the
optimization and plots, the objective function is the misclassification rate. To control the
iterative display, set the Verbose
field of the
'HyperparameterOptimizationOptions'
namevalue argument. To control the
plots, set the ShowPlots
field of the
'HyperparameterOptimizationOptions'
namevalue argument.
For an example, see Optimize ECOC Classifier.
Example: 'auto'
HyperparameterOptimizationOptions
— Options for optimization
structure
Options for optimization, specified as a structure. This argument modifies the effect of the
OptimizeHyperparameters
namevalue argument. All fields in the
structure are optional.
Field Name  Values  Default 

Optimizer 
 'bayesopt' 
AcquisitionFunctionName 
Acquisition functions whose names include
 'expectedimprovementpersecondplus' 
MaxObjectiveEvaluations  Maximum number of objective function evaluations.  30 for 'bayesopt' and
'randomsearch' , and the entire grid for
'gridsearch' 
MaxTime  Time limit, specified as a positive real scalar. The time limit is in seconds, as
measured by  Inf 
NumGridDivisions  For 'gridsearch' , the number of values in each dimension. The value can be
a vector of positive integers giving the number of
values for each dimension, or a scalar that
applies to all dimensions. This field is ignored
for categorical variables.  10 
ShowPlots  Logical value indicating whether to show plots. If true , this field plots
the best observed objective function value against the iteration number. If you
use Bayesian optimization (Optimizer is
'bayesopt' ), then this field also plots the best
estimated objective function value. The best observed objective function values
and best estimated objective function values correspond to the values in the
BestSoFar (observed) and BestSoFar
(estim.) columns of the iterative display, respectively. You can
find these values in the properties ObjectiveMinimumTrace and EstimatedObjectiveMinimumTrace of
Mdl.HyperparameterOptimizationResults . If the problem
includes one or two optimization parameters for Bayesian optimization, then
ShowPlots also plots a model of the objective function
against the parameters.  true 
SaveIntermediateResults  Logical value indicating whether to save results when Optimizer is
'bayesopt' . If
true , this field overwrites a
workspace variable named
'BayesoptResults' at each
iteration. The variable is a BayesianOptimization object.  false 
Verbose  Display at the command line:
For details, see the  1 
UseParallel  Logical value indicating whether to run Bayesian optimization in parallel, which requires Parallel Computing Toolbox. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization.  false 
Repartition  Logical value indicating whether to repartition the crossvalidation at every
iteration. If this field is The setting
 false 
Use no more than one of the following three options.  
CVPartition  A cvpartition object, as created by cvpartition  'Kfold',5 if you do not specify a crossvalidation
field 
Holdout  A scalar in the range (0,1) representing the holdout fraction  
Kfold  An integer greater than 1 
Example: 'HyperparameterOptimizationOptions',struct('MaxObjectiveEvaluations',60)
Data Types: struct
Output Arguments
Mdl
— Trained ECOC model
ClassificationECOC
model object  CompactClassificationECOC
model object  ClassificationPartitionedECOC
crossvalidated model
object  ClassificationPartitionedLinearECOC
crossvalidated
model object  ClassificationPartitionedKernelECOC
crossvalidated
model object
Trained ECOC classifier, returned as a ClassificationECOC
or
CompactClassificationECOC
model
object, or a ClassificationPartitionedECOC
, ClassificationPartitionedLinearECOC
, or
ClassificationPartitionedKernelECOC
crossvalidated
model object.
This table shows how the types of model objects returned by fitcecoc
depend on the type of binary learners you specify and whether you perform
crossvalidation.
Linear Classification Model Learners  Kernel Classification Model Learners  CrossValidation  Returned Model Object 

No  No  No  ClassificationECOC 
No  No  Yes  ClassificationPartitionedECOC 
Yes  No  No  CompactClassificationECOC 
Yes  No  Yes  ClassificationPartitionedLinearECOC 
No  Yes  No  CompactClassificationECOC 
No  Yes  Yes  ClassificationPartitionedKernelECOC 
HyperparameterOptimizationResults
— Description of crossvalidation optimization of hyperparameters
BayesianOptimization
object  table of hyperparameters and associated values
Description of the crossvalidation optimization of hyperparameters,
returned as a BayesianOptimization
object or a
table of hyperparameters and associated values.
HyperparameterOptimizationResults
is nonempty when
the OptimizeHyperparameters
namevalue pair argument is
nonempty and the Learners
namevalue pair argument
designates linear or kernel binary learners. The value depends on the
setting of the HyperparameterOptimizationOptions
namevalue pair argument:
'bayesopt'
(default) — Object of classBayesianOptimization
'gridsearch'
or'randomsearch'
— Table of hyperparameters used, observed objective function values (crossvalidation loss), and rank of observation from smallest (best) to highest (worst)
Data Types: table
Limitations
fitcecoc
supports sparse matrices for training linear classification models only. For all other models, supply a full matrix of predictor data instead.
More About
ErrorCorrecting Output Codes Model
An errorcorrecting output codes (ECOC) model reduces the problem of classification with three or more classes to a set of binary classification problems.
ECOC classification requires a coding design, which determines the classes that the binary learners train on, and a decoding scheme, which determines how the results (predictions) of the binary classifiers are aggregated.
Assume the following:
The classification problem has three classes.
The coding design is oneversusone. For three classes, this coding design is
$$\begin{array}{cccc}& \text{Learner1}& \text{Learner2}& \text{Learner3}\\ \text{Class1}& 1& 1& 0\\ \text{Class2}& 1& 0& 1\\ \text{Class3}& 0& 1& 1\end{array}$$
You can specify a different coding design by using the
Coding
namevalue argument when you create a classification model.The model determines the predicted class by using the lossweighted decoding scheme with the binary loss function g. The software also supports the lossbased decoding scheme. You can specify the decoding scheme and binary loss function by using the
Decoding
andBinaryLoss
namevalue arguments, respectively, when you call object functions, such aspredict
,loss
,margin
,edge
, and so on.
The ECOC algorithm follows these steps.
Learner 1 trains on observations in Class 1 or Class 2, and treats Class 1 as the positive class and Class 2 as the negative class. The other learners are trained similarly.
Let M be the coding design matrix with elements m_{kl}, and s_{l} be the predicted classification score for the positive class of learner l. The algorithm assigns a new observation to the class ($$\widehat{k}$$) that minimizes the aggregation of the losses for the B binary learners.
$$\widehat{k}=\underset{k}{\text{argmin}}\frac{{\displaystyle \sum}_{l=1}^{B}\left{m}_{kl}\rightg\left({m}_{kl},{s}_{l}\right)}{{\displaystyle \sum}_{l=1}^{B}\left{m}_{kl}\right}.$$
ECOC models can improve classification accuracy, compared to other multiclass models [2].
Coding Design
The coding design is a matrix whose elements direct which classes are trained by each binary learner, that is, how the multiclass problem is reduced to a series of binary problems.
Each row of the coding design corresponds to a distinct class, and each column corresponds to a binary learner. In a ternary coding design, for a particular column (or binary learner):
A row containing 1 directs the binary learner to group all observations in the corresponding class into a positive class.
A row containing –1 directs the binary learner to group all observations in the corresponding class into a negative class.
A row containing 0 directs the binary learner to ignore all observations in the corresponding class.
Coding design matrices with large, minimal, pairwise row distances based on the Hamming measure are optimal. For details on the pairwise row distance, see Random Coding Design Matrices and [3].
This table describes popular coding designs.
Coding Design  Description  Number of Learners  Minimal Pairwise Row Distance 

oneversusall (OVA)  For each binary learner, one class is positive and the rest are negative. This design exhausts all combinations of positive class assignments.  K  2 
oneversusone (OVO)  For each binary learner, one class is positive, one class is negative, and the rest are ignored. This design exhausts all combinations of class pair assignments.  K(K – 1)/2  1 
binary complete  This design partitions the classes into all binary
combinations, and does not ignore any classes. That is, all class
assignments are  2^{K – 1} – 1  2^{K – 2} 
ternary complete  This design partitions the classes into all ternary
combinations. That is, all class assignments are
 (3^{K} – 2^{K + 1} + 1)/2  3^{K – 2} 
ordinal  For the first binary learner, the first class is negative and the rest are positive. For the second binary learner, the first two classes are negative and the rest are positive, and so on.  K – 1  1 
dense random  For each binary learner, the software randomly assigns classes into positive or negative classes, with at least one of each type. For more details, see Random Coding Design Matrices.  Random, but approximately 10 log_{2}K  Variable 
sparse random  For each binary learner, the software randomly assigns classes as positive or negative with probability 0.25 for each, and ignores classes with probability 0.5. For more details, see Random Coding Design Matrices.  Random, but approximately 15 log_{2}K  Variable 
This plot compares the number of binary learners for the coding designs with an increasing number of classes (K).
Tips
The number of binary learners grows with the number of classes. For a problem with many classes, the
binarycomplete
andternarycomplete
coding designs are not efficient. However:If K ≤ 4, then use
ternarycomplete
coding design rather thansparserandom
.If K ≤ 5, then use
binarycomplete
coding design rather thandenserandom
.
You can display the coding design matrix of a trained ECOC classifier by entering
Mdl.CodingMatrix
into the Command Window.You should form a coding matrix using intimate knowledge of the application, and taking into account computational constraints. If you have sufficient computational power and time, then try several coding matrices and choose the one with the best performance (e.g., check the confusion matrices for each model using
confusionchart
).Leaveoneout crossvalidation (
Leaveout
) is inefficient for data sets with many observations. Instead, use kfold crossvalidation (KFold
).
After training a model, you can generate C/C++ code that predicts labels for new data. Generating C/C++ code requires MATLAB Coder™. For details, see Introduction to Code Generation.
Algorithms
Custom Coding Design Matrices
Custom coding matrices must have a certain form. The software validates a custom coding matrix by ensuring:
Every element is –1, 0, or 1.
Every column contains as least one –1 and one 1.
For all distinct column vectors u and v, u ≠ v and u ≠ –v.
All row vectors are unique.
The matrix can separate any two classes. That is, you can move from any row to any other row following these rules:
Move vertically from 1 to –1 or –1 to 1.
Move horizontally from a nonzero element to another nonzero element.
Use a column of the matrix for a vertical move only once.
If it is not possible to move from row i to row j using these rules, then classes i and j cannot be separated by the design. For example, in the coding design
$$\left[\begin{array}{cc}1& 0\\ 1& 0\\ 0& 1\\ 0& 1\end{array}\right]$$
classes 1 and 2 cannot be separated from classes 3 and 4 (that is, you cannot move horizontally from –1 in row 2 to column 2 because that position contains a 0). Therefore, the software rejects this coding design.
Parallel Computing
If you use parallel computing (see Options
),
then fitcecoc
trains binary learners in parallel.
Prior Probabilities and Misclassification Cost
If you specify the Cost
,
Prior
, and Weights
namevalue arguments, the
output model object stores the specified values in the Cost
,
Prior
, and W
properties, respectively. The
Cost
property stores the userspecified cost matrix as is. The
Prior
and W
properties store the prior probabilities
and observation weights, respectively, after normalization. For details, see Misclassification Cost Matrix, Prior Probabilities, and Observation Weights.
For each binary learner, the software normalizes the prior probabilities into a
vector of two elements, and normalizes the cost matrix into a 2by2 matrix. Then,
the software adjusts the prior probability vector by incorporating the penalties
described in the 2by2 cost matrix, and sets the cost matrix to the default cost
matrix. The Cost
and Prior
properties of the
binary learners in Mdl
(Mdl.BinaryLearners
)
store the adjusted values. Specifically, the software completes these steps:
The software normalizes the specified class prior probabilities (
Prior
) for each binary learner. Let M be the coding design matrix and I(A,c) be an indicator matrix. The indicator matrix has the same dimensions as A. If the corresponding element of A is c, then the indicator matrix has elements equaling one, and zero otherwise. Let M_{+1} and M_{1} be KbyL matrices such that:M_{+1} = M○I(M,1), where ○ is elementwise multiplication (that is,
Mplus = M.*(M == 1)
). Also, let $${m}_{l}^{(+1)}$$ be column vector l of M_{+1}.M_{1} = M○I(M,1) (that is,
Mminus = M.*(M == 1)
). Also, let $${m}_{l}^{(1)}$$ be column vector l of M_{1}.
Let $${\pi}_{l}^{+1}={m}_{l}^{(+1)}\xb0\pi $$ and $${\pi}_{l}^{1}={m}_{l}^{(1)}\xb0\pi $$, where π is the vector of specified, class prior probabilities (
Prior
).Then, the positive and negative, scalar class prior probabilities for binary learner l are
$${\widehat{\pi}}_{l}^{(j)}=\frac{{\Vert {\pi}_{l}^{(j)}\Vert}_{1}}{{\Vert {\pi}_{l}^{(+1)}\Vert}_{1}+{\Vert {\pi}_{l}^{(1)}\Vert}_{1}},$$
where j = {1,1} and $${\Vert a\Vert}_{1}$$ is the onenorm of a.
The software normalizes the KbyK cost matrix C (
Cost
) for each binary learner. For binary learner l, the cost of classifying a negativeclass observation into the positive class is$${c}_{l}^{+}={\left({\pi}_{l}^{(1)}\right)}^{\top}C{\pi}_{l}^{(+1)}.$$
Similarly, the cost of classifying a positiveclass observation into the negative class is
$${c}_{l}^{+}={\left({\pi}_{l}^{(+1)}\right)}^{\top}C{\pi}_{l}^{(1)}.$$
The cost matrix for binary learner l is
$${C}_{l}=\left[\begin{array}{cc}0& {c}_{l}^{+}\\ {c}_{l}^{+}& 0\end{array}\right].$$
ECOC models accommodate misclassification costs by incorporating them with class prior probabilities. The software adjusts the class prior probabilities and sets the cost matrix to the default cost matrix for binary learners as follows:
$$\begin{array}{c}{\overline{\pi}}_{l}^{1}=\frac{{c}_{l}^{+}{\widehat{\pi}}_{l}^{1}}{{c}_{l}^{+}{\widehat{\pi}}_{l}^{1}+{c}^{+}{\widehat{\pi}}_{l}^{+1}},\\ {\overline{\pi}}_{l}^{+1}=\frac{{c}_{l}^{+}{\widehat{\pi}}_{l}^{+1}}{{c}_{l}^{+}{\widehat{\pi}}_{l}^{1}+{c}^{+}{\widehat{\pi}}_{l}^{+1}},\\ {\overline{C}}_{l}=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right].\end{array}$$
Random Coding Design Matrices
For a given number of classes K, the software generates random coding design matrices as follows.
The software generates one of these matrices:
Dense random — The software assigns 1 or –1 with equal probability to each element of the KbyL_{d} coding design matrix, where $${L}_{d}\approx \lceil 10{\mathrm{log}}_{2}K\rceil $$.
Sparse random — The software assigns 1 to each element of the KbyL_{s} coding design matrix with probability 0.25, –1 with probability 0.25, and 0 with probability 0.5, where $${L}_{s}\approx \lceil 15{\mathrm{log}}_{2}K\rceil $$.
If a column does not contain at least one 1 and one –1, then the software removes that column.
For distinct columns u and v, if u = v or u = –v, then the software removes v from the coding design matrix.
The software randomly generates 10,000 matrices by default, and retains the matrix with the largest, minimal, pairwise row distance based on the Hamming measure ([3]) given by
$$\Delta ({k}_{1},{k}_{2})=0.5{\displaystyle \sum}_{l=1}^{L}\left{m}_{{k}_{1}l}\right\left{m}_{{k}_{2}l}\right\left{m}_{{k}_{1}l}{m}_{{k}_{2}l}\right,$$
where m_{kjl} is an element of coding design matrix j.
Support Vector Storage
By default and for efficiency, fitcecoc
empties the Alpha
, SupportVectorLabels
,
and SupportVectors
properties
for all linear SVM binary learners. fitcecoc
lists Beta
, rather than
Alpha
, in the model display.
To store Alpha
, SupportVectorLabels
, and
SupportVectors
, pass a linear SVM template that specifies storing
support vectors to fitcecoc
. For example,
enter:
t = templateSVM('SaveSupportVectors',true) Mdl = fitcecoc(X,Y,'Learners',t);
You can remove the support vectors and related values by passing the resulting
ClassificationECOC
model to
discardSupportVectors
.
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] Fürnkranz, Johannes. “Round Robin Classification.” J. Mach. Learn. Res., Vol. 2, 2002, pp. 721–747.
[3] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of errorcorrecting output codes.” Pattern Recog. Lett., Vol. 30, Issue 3, 2009, pp. 285–297.
[4] Escalera, S., O. Pujol, and P. Radeva. “On the decoding process in ternary errorcorrecting output codes.” IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 32, Issue 7, 2010, pp. 120–134.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Usage notes and limitations:
Supported syntaxes are:
Mdl = fitcecoc(X,Y)
Mdl = fitcecoc(X,Y,Name,Value)
[Mdl,FitInfo,HyperparameterOptimizationResults] = fitcecoc(X,Y,Name,Value)
—fitcecoc
returns the additional output argumentsFitInfo
andHyperparameterOptimizationResults
when you specify the'OptimizeHyperparameters'
namevalue pair argument.
The
FitInfo
output argument is an empty structure array currently reserved for possible future use.Options related to crossvalidation are not supported. The supported namevalue pair arguments are:
'ClassNames'
'Cost'
'Coding'
— Default value is'onevsall'
.'HyperparameterOptimizationOptions'
— For crossvalidation, tall optimization supports only'Holdout'
validation. By default, the software selects and reserves 20% of the data as holdout validation data, and trains the model using the rest of the data. You can specify a different value for the holdout fraction by using this argument. For example, specify'HyperparameterOptimizationOptions',struct('Holdout',0.3)
to reserve 30% of the data as validation data.'Learners'
— Default value is'linear'
. You can specify'linear'
,'kernel'
, atemplateLinear
ortemplateKernel
object, or a cell array of such objects.'OptimizeHyperparameters'
— When you use linear binary learners, the value of the'Regularization'
hyperparameter must be'ridge'
.'Prior'
'Verbose'
— Default value is1
.'Weights'
This additional namevalue pair argument is specific to tall arrays:
'NumConcurrent'
— A positive integer scalar specifying the number of binary learners that are trained concurrently by combining file I/O operations. The default value for'NumConcurrent'
is1
, which meansfitcecoc
trains the binary learners sequentially.'NumConcurrent'
is most beneficial when the input arrays cannot fit into the distributed cluster memory. Otherwise, the input arrays can be cached and speedup is negligible.If you run your code on Apache^{®} Spark™,
NumConcurrent
is upper bounded by the memory available for communications. Check the'spark.executor.memory'
and'spark.driver.memory'
properties in your Apache Spark configuration. Seeparallel.cluster.Hadoop
(Parallel Computing Toolbox) for more details. For more information on Apache Spark and other execution environments that control where your code runs, see Extend Tall Arrays with Other Products.
For more information, see Tall Arrays.
Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.
To run in parallel, set the 'UseParallel'
option to
true
in one of these ways:
Set the
'UseParallel'
field of the options structure totrue
usingstatset
and specify the'Options'
namevalue pair argument in the call tofitceoc
.For example:
'Options',statset('UseParallel',true)
For more information, see the
'Options'
namevalue pair argument.Perform parallel hyperparameter optimization by using the
'HyperparameterOptions',struct('UseParallel',true)
namevalue pair argument in the call tofitceoc
.For more information on parallel hyperparameter optimization, see Parallel Bayesian Optimization.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
You can specify the namevalue argument
'Learners'
only as one of the learners specified in this table.Learner Learner Name Template Object Creation Function Information About gpuArray
Supportsupport vector machine 'svm'
templateSVM
GPU Arrays for fitcsvm
knearest neighbors 'knn'
templateKNN
GPU Arrays for fitcknn
classification tree 'tree'
templateTree
GPU Arrays for fitctree
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2014bR2023b: "auto"
option of OptimizeHyperparameters
includes Standardize
when the binary learners are kernel,
knearest neighbor (KNN), or support vector machine (SVM)
classifiers
Starting in R2023b, when you specify "kernel"
,
"knn"
, or "svm"
as the
Learners
value and "auto"
as the
OptimizeHyperparameters
value,
fitcecoc
includes Standardize
as an
optimizable hyperparameter.
R2022a: Regularization method determines the linear learner solver used during hyperparameter optimization
Starting in R2022a, when you specify to optimize hyperparameters for an ECOC model
with linear binary learners ('linear'
or templateLinear
) and do not specify to use a particular solver,
fitcecoc
uses either a Limitedmemory BFGS (LBFGS)
solver or a Sparse Reconstruction by Separable Approximation (SpaRSA) solver,
depending on the regularization type selected during each iteration of the
hyperparameter optimization.
When
Regularization
is'ridge'
, the function sets theSolver
value to'lbfgs'
by default.When
Regularization
is'lasso'
, the function sets theSolver
value to'sparsa'
by default.
In previous releases, the default solver selection during hyperparameter
optimization depended on various factors, including the regularization type, learner
type, and number of predictors. For more information, see Solver
.
MATLAB 命令
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