CompactClassificationECOC

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

Description

CompactClassificationECOC is 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 a CompactClassificationECOC model in two ways:

• Create a compact ECOC model from a trained ClassificationECOC model by using the compact object function.

• Create a compact ECOC model by using the fitcecoc function and specifying the 'Learners' name-value pair argument as 'linear', 'kernel', a templateLinear or templateKernel object, or a cell array of such objects.

Properties

After you create a CompactClassificationECOC model object, you can use dot notation to access its properties. For an example, see Train 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 in Y and the coding design.

The software trains BinaryLearner{j} according to the binary problem specified by CodingMatrix(:,j). For example, for multiclass learning using SVM learners, each element of BinaryLearners is a CompactClassificationSVM classifier.

Data Types: cell

BinaryLoss — Binary learner loss function

'binodeviance' | 'exponential' | 'hamming' | 'hinge' | 'linear' | 'logit' | 'quadratic'

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

If you train using binary learners that use different loss functions, then the software sets BinaryLoss to 'hamming'. To potentially increase accuracy, specify a binary loss function other than the default during a prediction or loss computation by using the 'BinaryLoss' name-value pair argument of predict or loss.

Data Types: char

CodingMatrix — Class assignment codes

numeric matrix

Class assignment codes for the binary learners, specified as a numeric matrix. CodingMatrix is a K-by-L matrix, where K is the number of classes and L is the number of binary learners.

The elements of CodingMatrix are –1, 0, or 1, and the values correspond to dichotomous class assignments. This table describes how learner j assigns observations in class i to a dichotomous class corresponding to the value of CodingMatrix(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 of LeanerWeights is equal to the number of binary learners (length(Mdl.BinaryLearners)).

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

The software uses LearnerWeights to fit posterior probabilities by minimizing the Kullback-Leibler divergence. The software ignores LearnerWeights when 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. CategoricalPredictors contains index values corresponding to the columns of the predictor data that contain categorical predictors. 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 has the same data type as the class labels Y. (The software treats string arrays as cell arrays of character vectors.) ClassNames also determines the class order.

Data Types: categorical | char | logical | single | double | cell

Cost — Misclassification costs

square numeric matrix

This property is read-only.

Misclassification costs, specified as a square numeric matrix. Cost has K rows and columns, where K is the number of classes.

Cost(i,j) is the cost of classifying a point into class j if its true class is i. The order of the rows and columns of Cost corresponds to the order of the classes in ClassNames.

fitcecoc incorporates misclassification costs differently among different types of binary learners.

Data Types: double

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, then ExpandedPredictorNames includes the names that describe the expanded variables. Otherwise, ExpandedPredictorNames is the same as PredictorNames.

PredictorNames — Predictor names

cell array of character vectors

Predictor names in order of their appearance in the predictor data X, specified as a cell array of character vectors. The length of PredictorNames is equal to the number of columns in X.

Data Types: cell

Prior — Prior class probabilities

numeric vector

This property is read-only.

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

fitcecoc incorporates 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

'doublelogit' | 'invlogit' | 'ismax' | 'logit' | 'none' | function handle | ...

Score transformation function to apply to predicted scores, specified as a function name or function handle.

To change the score transformation function to function, for example, use dot notation.

• For a built-in function, enter this code and replace function with a value in the table.

  Mdl.ScoreTransform = 'function';

  Value	Description
  'doublelogit'	1/(1 + e–2x)
  'invlogit'	log(x / (1 – x))
  'ismax'	Sets the score for the class with the largest score to 1, and sets the scores for all other classes to 0
  'logit'	1/(1 + e–x)
  'none' or 'identity'	x (no transformation)
  'sign'	–1 for x < 0 0 for x = 0 1 for x > 0
  'symmetric'	2x – 1
  'symmetricismax'	Sets the score for the class with the largest score to 1, and sets the scores for all other classes to –1
  'symmetriclogit'	2/(1 + e–x) – 1

• For a MATLAB^® function or a function that you define, enter its function handle.

  Mdl.ScoreTransform = @function;

  function must accept a matrix (the original scores) and return a matrix of the same size (the transformed scores).

Data Types: char | function_handle

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
loss	Classification loss for multiclass error-correcting output codes (ECOC) model
margin	Classification margins for multiclass error-correcting output codes (ECOC) model
predict	Classify observations using multiclass error-correcting output codes (ECOC) model
selectModels	Choose subset of multiclass ECOC models composed of binary ClassificationLinear learners
update	Update model parameters for code generation

Examples

Reduce Size of Full ECOC Model

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

Load Fisher's iris data set. Specify the predictor data X, the response data Y, and the order of the classes in Y.

load fisheriris
X = meas;
Y = categorical(species);
classOrder = unique(Y);

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

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

Mdl is a ClassificationECOC model.

Reduce the size of the ECOC model.

CompactMdl = compact(Mdl)

CompactMdl = 
  classreg.learning.classif.CompactClassificationECOC
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: [setosa    versicolor    virginica]
           ScoreTransform: 'none'
           BinaryLearners: {3x1 cell}
             CodingMatrix: [3x3 double]


  Properties, Methods

CompactMdl is a CompactClassificationECOC model. CompactMdl does not store all of the properties that Mdl stores. 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             14444  classreg.learning.classif.CompactClassificationECOC              
  Mdl             1x1             27551  ClassificationECOC                                               

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

To label new observations efficiently, you can remove Mdl from the MATLAB® Workspace, and then pass CompactMdl and new predictor values to predict.

Train and Cross-Validate ECOC Classifier

Train and cross-validate an ECOC classifier using different binary learners and the one-versus-all coding design.

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

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

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

K = numel(classNames) % Number of classes

K = 3

You can use classNames to specify the order of the classes during training.

For a one-versus-all coding design, this example has K = 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 reproducibility
tNB = templateNaiveBayes();
tSVM = templateSVM('KernelFunction','gaussian');
tLearners = {tNB tNB tSVM};

tNB and tSVM are 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.

Train and cross-validate an ECOC classifier using 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',...
    'Learners',tLearners,'FitPosterior',true);

CVMdl is a ClassificationPartitionedECOC cross-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 = 
  classreg.learning.classif.CompactClassificationECOC
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: {'setosa'  'versicolor'  'virginica'}
           ScoreTransform: 'none'
           BinaryLearners: {3x1 cell}
             CodingMatrix: [3x3 double]


  Properties, Methods

Each fold is a CompactClassificationECOC model 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 = 
  classreg.learning.classif.CompactClassificationSVM
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: [-1 1]
           ScoreTransform: '@(S)sigmoid(S,-4.016427e+00,-3.244999e-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%.

Algorithms

Random Coding Design Matrices

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

1. The software generates one of these matrices:

   1. Dense random — The software assigns 1 or –1 with equal probability to each element of the K-by-L_d coding design matrix, where $$L_d\approx \lceil 10{\log }_{2}K\rceil$$.

   2. Sparse random — The software assigns 1 to each element of the K-by-L_s coding design matrix with probability 0.25, –1 with probability 0.25, and 0 with probability 0.5, where $$L_s\approx \lceil 15{\log }_{2}K\rceil$$.

2. If a column does not contain at least one 1 and at least one –1, then the software removes that column.

3. 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 ([4]) 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] Fürnkranz, Johannes. “Round Robin Classification.” Journal of Machine Learning Research, 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 Recognition Letters, 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:

• The predict and update functions support code generation.

• When you train an ECOC model by using fitcecoc, the following restrictions apply.

  • You cannot fit posterior probabilities by using the 'FitPosterior' name-value pair argument.

  • All binary learners must be either SVM classifiers or linear classification models. For the 'Learners' name-value pair argument, you can specify:

    • 'svm' or 'linear'

    • An SVM template object or a cell array of such objects (see templateSVM)

    • A linear classification model template object or a cell array of such objects (see templateLinear)

  • When you generate code using a coder configurer for predict and update, the following additional restrictions apply for binary learners.

    • If you use a cell array of SVM template objects, the value of 'Standardize' for SVM learners must be consistent. For example, if you specify 'Standardize',true for 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',true for the learner with a linear kernel.

    For details, see ClassificationECOCCoderConfigurer. For information on name-value pair arguments that you cannot modify when you retrain a model, see Tips.

  • Code generation limitations for SVM classifiers and linear classification models also apply to ECOC classifiers, depending on the choice of binary learners. For more details, see Code Generation of the CompactClassificationSVM class and Code Generation of the ClassificationLinear class.

For more information, see Introduction to Code Generation.