CompactClassificationECOC

Compact multiclass model for support vector machines (SVMs) and other classifiers

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Description

CompactClassificationECOCis a compact version of the multiclass error-correcting output codes (ECOC) model. The compact classifier does not include the data used for training the multiclass ECOC model. Therefore, you cannot perform certain tasks, such as cross-validation, using the compact classifier. Use a compact multiclass ECOC model for tasks such as classifying new data (predict).

Creation

You can create aCompactClassificationECOCmodel in two ways:

Create a compact ECOC model from a trainedClassificationECOCmodel by using thecompactobject function.
Create a compact ECOC model by using thefitcecocfunction and specifying the“学习者”name-value pair argument as'linear','kernel', atemplateLinearortemplateKernelobject, or a cell array of such objects.

Properties

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After you create aCompactClassificationECOCmodel object, you can use dot notation to access its properties. For an example, seeTrain and Cross-Validate ECOC Classifier.

ECOC Properties

`BinaryLearners`—Trained binary learners
cell vector of model objects

Trained binary learners, specified as a cell vector of model objects. The number of binary learners depends on the number of classes inYand the coding design.

The software trainsBinaryLearner{j}according to the binary problem specified byCodingMatrix(:,j). For example, for multiclass learning using SVM learners, each element ofBinaryLearnersis aCompactClassificationSVMclassifier.

Data Types:cell

`BinaryLoss`—Binary learner loss function
`'binodeviance'`|`'exponential'`|`“汉明”`|`'hinge'`|`'linear'`|`'logit'`|`'quadratic'`

Binary learner loss function, specified as a character vector representing the loss function name.

This table identifies the defaultBinaryLossvalue, which depends on the score ranges returned by the binary learners.

Assumption	Default Value
All binary learners are any of the following: Classification decision trees Discriminant analysis models k-nearest neighbor models Linear or kernel classification models of logistic regression learners Naive Bayes models	`'quadratic'`
All binary learners are SVMs or linear or kernel classification models of SVM learners.	`'hinge'`
All binary learners are ensembles trained by`AdaboostM1`or`GentleBoost`.	`'exponential'`
All binary learners are ensembles trained by`LogitBoost`.	`'binodeviance'`
You specify to predict class posterior probabilities by setting`'FitPosterior',true`in`fitcecoc`.	`'quadratic'`
Binary learners are heterogeneous and use different loss functions.	`“汉明”`

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

To potentially increase accuracy, specify a binary loss function other than the default during a prediction or loss computation by using theBinaryLossname-value argument ofpredictorloss. For more information, seeBinary Loss.

Data Types:char

`CodingMatrix`—Class assignment codes
numeric matrix

Class assignment codes for the binary learners, specified as a numeric matrix.CodingMatrixis aK-by-Lmatrix, whereKis the number of classes andLis the number of binary learners.

The elements ofCodingMatrixare–1,0, and1, and the values correspond to dichotomous class assignments. This table describes how learnerjassigns observations in classito a dichotomous class corresponding to the value ofCodingMatrix(i,j).

Value	Dichotomous Class Assignment
`–1`	Learner`j`assigns observations in class`i`to a negative class.
`0`	Before training, learner`j`removes observations in class`i`from the data set.
`1`	Learner`j`assigns observations in class`i`to a positive class.

Data Types:double|single|int8|int16|int32|int64

`LearnerWeights`—Binary learner weights
numeric row vector

Binary learner weights, specified as a numeric row vector. The length ofLearnerWeightsis equal to the number of binary learners (length(Mdl.BinaryLearners)).

LearnerWeights(j)is the sum of the observation weights that binary learnerjuses to train its classifier.

The software usesLearnerWeightsto fit posterior probabilities by minimizing the Kullback-Leibler divergence. The software ignoresLearnerWeightswhen it uses the quadratic programming method of estimating posterior probabilities.

Data Types:double|single

Other Classification Properties

`CategoricalPredictors`—Categorical predictor indices
vector of positive integers|`[]`

Categorical predictor indices, specified as a vector of positive integers.CategoricalPredictorscontains index values indicating that the corresponding predictors are categorical. The index values are between 1 andp, wherep预测的数量被用来训练模式l. If none of the predictors are categorical, then this property is empty ([]).

Data Types:single|double

`ClassNames`—Unique class labels
categorical array|character array|logical vector|numeric vector|cell array of character vectors

Unique class labels used in training, specified as a categorical or character array, logical or numeric vector, or cell array of character vectors.ClassNames有the same data type as the class labelsY.(The software treats string arrays as cell arrays of character vectors.)ClassNamesalso determines the class order.

`Cost`—Misclassification costs
square numeric matrix

This property is read-only.

Misclassification costs, specified as a square numeric matrix.Cost有Krows and columns, whereKis the number of classes.

Cost(i,j)is the cost of classifying a point into classjif its true class isi. The order of the rows and columns ofCostcorresponds to the order of the classes inClassNames.

Data Types:double

`PredictorNames`—Predictor names
cell array of character vectors

Predictor names in order of their appearance in the predictor data, specified as a cell array of character vectors. The length ofPredictorNamesis equal to the number of variables in the training dataXorTblused as predictor variables.

Data Types:cell

`ExpandedPredictorNames`—Expanded predictor names
cell array of character vectors

Expanded predictor names, specified as a cell array of character vectors.

If the model uses encoding for categorical variables, thenExpandedPredictorNamesincludes the names that describe the expanded variables. Otherwise,ExpandedPredictorNamesis the same asPredictorNames.

Data Types:cell

`Prior`—Prior class probabilities
numeric vector

This property is read-only.

Prior class probabilities, specified as a numeric vector.Prior有as many elements as the number of classes inClassNames, and the order of the elements corresponds to the order of the classes inClassNames.

fitcecocincorporates misclassification costs differently among different types of binary learners.

Data Types:double

`ResponseName`—Response variable name
character vector

Response variable name, specified as a character vector.

Data Types:char

`ScoreTransform`—Score transformation function to apply to predicted scores
`'none'`

This property is read-only.

Score transformation function to apply to the predicted scores, specified as'none'. An ECOC model does not support score transformation.

Object Functions

`compareHoldout`	Compare accuracies of two classification models using new data
`discardSupportVectors`	Discard support vectors of linear SVM binary learners in ECOC model
`edge`	Classification edge for multiclass error-correcting output codes (ECOC) model
`gather`	Gather properties ofStatistics and Machine Learning Toolboxobject from GPU
`incrementalLearner`	Convert multiclass error-correcting output codes (ECOC) model to incremental learner
`lime`	Local interpretable model-agnostic explanations (LIME)
`loss`	Classification loss for multiclass error-correcting output codes (ECOC) model
`margin`	Classification margins for multiclass error-correcting output codes (ECOC) model
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predict`	Classify observations using multiclass error-correcting output codes (ECOC) model
`shapley`	Shapley values
`selectModels`	Choose subset of multiclass ECOC models composed of binary`ClassificationLinear`learners
`update`	Update model parameters for code generation

Examples

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Reduce Size of Full ECOC Model

Open Live Script

Reduce the size of a full ECOC model by removing the training data. Full ECOC models (ClassificationECOCmodels) hold the training data. To improve efficiency, use a smaller classifier.

Load Fisher's iris data set. Specify the predictor dataX, the response dataY和类的顺序Y.

loadfisheririsX = meas; Y = categorical(species); classOrder = unique(Y);

Train an ECOC model using SVM binary classifiers. Standardize the predictor data using an SVM templatet, and specify the order of the classes. During training, the software uses default values for empty options int.

t = templateSVM('Standardize',true); Mdl = fitcecoc(X,Y,“学习者”,t,'ClassNames',classOrder);

Mdlis aClassificationECOCmodel.

Reduce the size of the ECOC model.

CompactMdl = compact(Mdl)

CompactMdl = CompactClassificationECOC ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [setosa versicolor virginica] ScoreTransform: 'none' BinaryLearners: {3x1 cell} CodingMatrix: [3x3 double] Properties, Methods

CompactMdlis aCompactClassificationECOCmodel.CompactMdldoes not store all of the properties thatMdlstores. In particular, it does not store the training data.

Display the amount of memory each classifier uses.

whos('CompactMdl','Mdl')

Name Size Bytes Class Attributes CompactMdl 1x1 15116 classreg.learning.classif.CompactClassificationECOC Mdl 1x1 28357 ClassificationECOC

The full ECOC model (Mdl) is approximately double the size of the compact ECOC model (CompactMdl).

To label new observations efficiently, you can removeMdlfrom the MATLAB® Workspace, and then passCompactMdland new predictor values topredict.

Train and Cross-Validate ECOC Classifier

Open Live Script

火车和旨在ECOC分类器使用different binary learners and the one-versus-all coding design.

Load Fisher's iris data set. Specify the predictor dataXand the response dataY. Determine the class names and the number of classes.

loadfisheririsX = meas; Y = species; classNames = unique(species(~strcmp(species,'')))% Remove empty classes

classNames =3x1 cell{'setosa' } {'versicolor'} {'virginica' }

K = numel(classNames)%的数量classes

K = 3

You can useclassNamesto specify the order of the classes during training.

For a one-versus-all coding design, this example hasK= 3 binary learners. Specify templates for the binary learners such that:

Binary learner 1 and 2 are naive Bayes classifiers. By default, each predictor is conditionally, normally distributed given its label.
Binary learner 3 is an SVM classifier. Specify to use the Gaussian kernel.

rng(1);% For reproducibilitytNB = templateNaiveBayes(); tSVM = templateSVM('KernelFunction','gaussian'); tLearners = {tNB tNB tSVM};

tNBandtSVMare template objects for naive Bayes and SVM learning, respectively. The objects indicate which options to use during training. Most of their properties are empty, except those specified by name-value pair arguments. During training, the software fills in the empty properties with their default values.

火车和旨在ECOC分类器使用the binary learner templates and the one-versus-all coding design. Specify the order of the classes. By default, naive Bayes classifiers use posterior probabilities as scores, whereas SVM classifiers use distances from the decision boundary. Therefore, to aggregate the binary learners, you must specify to fit posterior probabilities.

CVMdl = fitcecoc(X,Y,'ClassNames',classNames,'CrossVal','on',...“学习者”,tLearners,'FitPosterior',true);

CVMdlis aClassificationPartitionedECOCcross-validated model. By default, the software implements 10-fold cross-validation. The scores across the binary learners have the same form (that is, they are posterior probabilities), so the software can aggregate the results of the binary classifications properly.

Inspect one of the trained folds using dot notation.

CVMdl.Trained{1}

ans = CompactClassificationECOC ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' BinaryLearners: {3x1 cell} CodingMatrix: [3x3 double] Properties, Methods

Each fold is aCompactClassificationECOCmodel trained on 90% of the data.

You can access the results of the binary learners using dot notation and cell indexing. Display the trained SVM classifier (the third binary learner) in the first fold.

CVMdl.Trained{1}.BinaryLearners{3}

ans = CompactClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [-1 1] ScoreTransform: '@(S)sigmoid(S,-4.016619e+00,-3.243499e-01)' Alpha: [33x1 double] Bias: -0.1345 KernelParameters: [1x1 struct] SupportVectors: [33x4 double] SupportVectorLabels: [33x1 double] Properties, Methods

Estimate the generalization error.

genError = kfoldLoss(CVMdl)

genError = 0.0333

On average, the generalization error is approximately 3%.

More About

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Error-Correcting Output Codes Model

Anerror-correcting output codes (ECOC) modelreduces 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 one-versus-one. For three classes, this coding design is

$\begin{matrix} Learner 1 & Learner 2 & Learner 3 \\ Class 1 & 1 & 1 & 0 \\ Class 2 & - 1 & 0 & 1 \\ Class 3 & 0 & - 1 & - 1 \end{matrix}$

You can specify a different coding design by using theCodingname-value argument when you create a classification model.
The model determines the predicted class by using the loss-weighted decoding scheme with the binary loss functiong. The software also supports the loss-based decoding scheme. You can specify the decoding scheme and binary loss function by using theDecodingandBinaryLossname-value 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.
LetMbe the coding design matrix with elementsm_kl, ands_lbe the predicted classification score for the positive class of learnerl. The algorithm assigns a new observation to the class ( $\hat{k}$ ) that minimizes the aggregation of the losses for theBbinary learners.

$\hat{k} = \underset{k}{argmin} \frac{\sum_{l = 1}^{B} | m_{k l} | g (m_{k l}, s_{l})}{\sum_{l = 1}^{B} | m_{k l} |} .$

ECOC models can improve classification accuracy, compared to other multiclass models[1].

Coding Design

Thecoding designis 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, seeRandom Coding Design Matricesand［2］.

This table describes popular coding designs.

Coding Design	Description	Number of Learners	Minimal Pairwise Row Distance
one-versus-all (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
one-versus-one (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`–1`and`1`with at least one positive class and one negative class in the assignment for each binary learner.	2^{K– 1}– 1	2^{K– 2}
ternary complete	This design partitions the classes into all ternary combinations. That is, all class assignments are`0`,`–1`, and`1`with at least one positive class and one negative class in the assignment for each binary learner.	(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, seeRandom Coding Design Matrices.	Random, but approximately 10 log₂K	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, seeRandom Coding Design Matrices.	Random, but approximately 15 log₂K	Variable

This plot compares the number of binary learners for the coding designs with an increasing number of classes (K).

Algorithms

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Random Coding Design Matrices

For a given number of classesK, the software generates random coding design matrices as follows.

The software generates one of these matrices:
1. Dense random — The software assigns 1 or –1 with equal probability to each element of theK-by-L_dcoding design matrix, where $L_{d} \approx ⌈ 10 \log_{2} K ⌉$ .
2. Sparse random — The software assigns 1 to each element of theK-by-L_scoding design matrix with probability 0.25, –1 with probability 0.25, and 0 with probability 0.5, where $L_{s} \approx ⌈ 15 \log_{2} K ⌉$ .
If a column does not contain at least one 1 and one –1, then the software removes that column.
对于不同的列uandv, ifu=voru= –v, then the software removesvfrom 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 (［2］) given by

$Δ (k_{1}, k_{2}) = 0.5 \sum_{l = 1}^{L} | m_{k_{1} l} | | m_{k_{2} l} | | m_{k_{1} l} - m_{k_{2} l} |,$

wherem_{k_jl}is an element of coding design matrixj.

Support Vector Storage

By default and for efficiency,fitcecocempties theAlpha,SupportVectorLabels, andSupportVectorsproperties for all linear SVM binary learners.fitcecoclistsBeta, rather thanAlpha, in the model display.

To storeAlpha,SupportVectorLabels, andSupportVectors, pass a linear SVM template that specifies storing support vectors tofitcecoc. For example, enter:

t = templateSVM('SaveSupportVectors',true) Mdl = fitcecoc(X,Y,“学习者”,t);

You can remove the support vectors and related values by passing the resultingClassificationECOCmodel todiscardSupportVectors.

References

[1] Fürnkranz, Johannes. “Round Robin Classification.”J. Mach. Learn. Res., Vol. 2, 2002, pp. 721–747.

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Thepredictandupdatefunctions support code generation.
When you train an ECOC model by usingfitcecoc, the following restrictions apply.
- All binary learners must be SVM classifiers or linear classification models. For theLearnersname-value argument, you can specify:
  - 'svm'or'linear'
  - An SVM template object or a cell array of such objects (seetemplateSVM)
  - A linear classification model template object or a cell array of such objects (seetemplateLinear)
- Code generation limitations for the binary learners used in the ECOC classifier also apply to the ECOC classifier. For linear classification models, you can specify only one regularization strength—'auto'or a nonnegative scalar for theLambdaname-value argument.
- For code generation with a coder configurer, the following additional restrictions apply.
  - If you use a cell array of SVM template objects, the value ofStandardizefor SVM learners must be consistent. For example, if you specify'Standardize',truefor one SVM learner, you must specify the same value for all SVM learners.
  - If you use a cell array of SVM template objects, and you use one SVM learner with a linear kernel ('KernelFunction','linear') and another with a different type of kernel function, then you must specify'SaveSupportVectors',truefor the learner with a linear kernel.
  - Categorical predictors (logical,categorical,char,string, orcell) are not supported. You cannot use theCategoricalPredictorsname-value argument.To include categorical predictors in a model, preprocess them by usingdummyvarbefore fitting the model.
  - Class labels with thecategoricaldata type are not supported. Both the class label value in the training data (TblorY) and the value of theClassNamesname-value argument cannot be an array with thecategoricaldata type.
  - For more details, seeClassificationECOCCoderConfigurer. For information on name-value arguments that you cannot modify when you retrain a model, seeTips.

For more information, seeIntroduction to Code Generation.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The following object functions fully support GPU arrays:
- discardSupportVectors
- gather
The following object functions offer limited support for GPU arrays:
The object functions execute on a GPU if either of the following apply:
- The model was fitted with GPU arrays.
- The predictor data that you pass to the object function is a GPU array.

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

他的版本tory

Introduced in R2014b

CompactClassificationECOC

Description

Creation

Properties

ECOC Properties

BinaryLearners—Trained binary learnerscell vector of model objects

BinaryLoss—Binary learner loss function'binodeviance'|'exponential'|“汉明”|'hinge'|'linear'|'logit'|'quadratic'

CodingMatrix—Class assignment codesnumeric matrix

LearnerWeights—Binary learner weightsnumeric row vector

Other Classification Properties

CategoricalPredictors—Categorical predictor indicesvector of positive integers|[]

ClassNames—Unique class labelscategorical array|character array|logical vector|numeric vector|cell array of character vectors

Cost—Misclassification costssquare numeric matrix

PredictorNames—Predictor namescell array of character vectors

ExpandedPredictorNames—Expanded predictor namescell array of character vectors

Prior—Prior class probabilitiesnumeric vector

ResponseName—Response variable namecharacter vector

ScoreTransform—Score transformation function to apply to predicted scores'none'

Object Functions

Examples

Reduce Size of Full ECOC Model

Train and Cross-Validate ECOC Classifier

More About

Error-Correcting Output Codes Model

Coding Design

Algorithms

Random Coding Design Matrices

Support Vector Storage

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

他的版本tory

See Also

`BinaryLearners`—Trained binary learners
cell vector of model objects

`BinaryLoss`—Binary learner loss function
`'binodeviance'`|`'exponential'`|`“汉明”`|`'hinge'`|`'linear'`|`'logit'`|`'quadratic'`

`CodingMatrix`—Class assignment codes
numeric matrix

`LearnerWeights`—Binary learner weights
numeric row vector

`CategoricalPredictors`—Categorical predictor indices
vector of positive integers|`[]`

`ClassNames`—Unique class labels
categorical array|character array|logical vector|numeric vector|cell array of character vectors

`Cost`—Misclassification costs
square numeric matrix

`PredictorNames`—Predictor names
cell array of character vectors

`ExpandedPredictorNames`—Expanded predictor names
cell array of character vectors

`Prior`—Prior class probabilities
numeric vector

`ResponseName`—Response variable name
character vector

`ScoreTransform`—Score transformation function to apply to predicted scores
`'none'`

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.