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loss

Classification loss for multiclass, error-correcting output codes model

Sintaxis

L = loss(Mdl,tbl,ResponseVarName)
L = loss(Mdl,tbl,Y)
L = loss(Mdl,X,Y)
L = loss(___,Name,Value)

Description

L = loss(Mdl,tbl,ResponseVarName) returns the classification loss (L), a scalar representing how well the trained, multiclass, error-correcting output code (ECOC) model Mdl classifies the predictor data (tbl) as compared to the true class labels (ResponseVarName). Each row of tbl and ResponseVarName is an observation.

L = loss(Mdl,tbl,Y) returns the classification loss (L), a scalar representing how well the trained error-correcting output code (ECOC) multiclass classifier Mdl classifies the predictor data (tbl) as compared to the true class labels (Y). Each row of tbl and Y is an observation.

ejemplo

L = loss(Mdl,X,Y) returns the classification loss (L), a scalar representing how well the trained error-correcting output code (ECOC) multiclass classifier Mdl classifies the predictor data (X) as compared to the true class labels (Y). Each row of X and Y is an observation.

ejemplo

L = loss(___,Name,Value) returns the classification loss with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes. For example, you can specify a decoding scheme, classification loss function, or verbosity level.

Argumentos de entrada

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Full or compact, multiclass ECOC model, specified as a ClassificationECOC or CompactClassificationECOC model object.

To create a full or compact ECOC model, see ClassificationECOC or CompactClassificationECOC.

Sample data, specified as a table. Each row of tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, tbl can contain additional columns for the response variable and observation weights. tbl must contain all the predictors used to train Mdl. Multi-column variables and cell arrays other than cell arrays of character vectors are not allowed.

If you trained Mdl using sample data contained in a table, then the input data for this method must also be in a table.

Nota

If Mdl.BinaryLearners contains linear or kernel classification models (that is, ClassificationLinear or ClassificationKernel model objects), then you cannot specify sample data in a table. Instead, pass a matrix (X) and class labels (Y).

Tipos de datos: table

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, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.

Tipos de datos: char | string

Predictor data, specified as a numeric matrix.

Each row of X corresponds to one observation, and each column corresponds to one variable. The variables composing the columns of X should be the same as the variables that trained the Mdl classifier.

The length of Y and the number of rows of X must be equal.

Tipos de datos: double | single

Class labels, specified as a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. Y must be the same as the data type of Mdl.ClassNames. (The software treats string arrays as cell arrays of character vectors.)

The length of Y and the number of rows of X must be equal.

Tipos de datos: categorical | char | string | logical | single | double | cell

Argumentos de par nombre-valor

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

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

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

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

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

    customFunction has this form:

    bLoss = customFunction(M,s)
    where:

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

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

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

    • K is the number of classes.

    • L is the number of binary learners.

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

By default, if all binary learners are:

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

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

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

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

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

Ejemplo: 'BinaryLoss','binodeviance'

Tipos de datos: char | string | function_handle

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

Ejemplo: 'Decoding','lossbased'

Loss function, specified as the comma-separated pair consisting of 'LossFun' and 'classiferror' or a function handle.

You can:

  • Specify the built-in function 'classiferror' for classification error, i.e., the proportion of misclassified observations.

  • Specify your own function using function handle notation.

    Suppose that n = size(X,1) is the sample size and k is the number of classes. Your function must have the signature lossvalue = lossfun(C,S,W,Cost), where:

    • The output argument lossvalue is a scalar.

    • You choose the function name (lossfun).

    • C is an n-by-k logical matrix with rows indicating which class the corresponding observation belongs. The column order corresponds to the class order in Mdl.ClassNames.

      Construct C by setting C(p,q) = 1 if observation p is in class q, for each row. Set all other elements of row p to 0.

    • S is an n-by-k numeric matrix of negated loss values for classes. Each row corresponds to an observation. The column order corresponds to the class order in Mdl.ClassNames. S resembles the output argument NegLoss of predict.

    • W is an n-by-1 numeric vector of observation weights. If you pass W, the software normalizes its elements to sum to 1.

    • Cost is a k-by-k numeric matrix of misclassification costs. For example, Cost = ones(K) -eye(K) specifies a cost of 0 for correct classification, and 1 for misclassification.

    Specify your function using 'LossFun',@lossfun.

Tipos de datos: char | string | function_handle

Predictor data observation dimension, specified as the comma-separated pair consisting of 'ObservationsIn' and 'columns' or 'rows'. Mdl.BinaryLearners must contain linear classification models.

Nota

If you orient your predictor matrix so that observations correspond to columns and specify 'ObservationsIn','columns', you can experience a significant reduction in execution time.

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

To invoke parallel computing:

  • You need a Parallel Computing Toolbox™ license.

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

Verbosity level, specified as the comma-separated pair consisting of 'Verbose' and 0 or 1. Verbose controls the number of diagnostic messages that the software displays in the Command Window.

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

Ejemplo: 'Verbose',1

Tipos de datos: single | double

Observation weights, specified as the comma-separated pair consisting of 'Weights' and a numeric vector or the name of a variable in tbl. If you supply weights, then loss computes the weighted loss.

Weights requires the same length as the number of observations in X or tbl.

If you specify Weights as the name of a variable in tbl, you must do so as a character vector or string scalar. For example, if the weights are stored as tbl.w, then specify it as 'w'. Otherwise, the software treats all columns of tbl, including tbl.w, as predictors.

If you do not specify your own loss function (using LossFun), then the software normalizes Weights to sum up to the value of the prior probability in the respective class.

If Mdl.BinaryLearners contains linear classification models, then you must specify a vector.

Tipos de datos: single | double | char | string

Output Arguments

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Classification loss, returned as a numeric scalar or row vector. L is a generalization or resubstitution quality measure. Its interpretation depends on the loss function and weighting scheme, but, in general, better classifiers yield smaller loss values.

If Mdl.BinaryLearners contains linear classification models, then L is a 1-by- vector, where is the number of regularization strengths in the linear classification models (i.e., numel(Mdl.BinaryLearners{1}.Lambda)). L(j) is the loss for the model trained using regularization strength Mdl.BinaryLearners{1}.Lambda(j).

Otherwise, L is a scalar.

Ejemplos

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Load Fisher's iris data set.

load fisheriris
X = meas;
Y = categorical(species);
classOrder = unique(Y); % Class order
rng(1); % For reproducibility

Train an ECOC model using SVM binary classifiers, and specify a 15% holdout sample. It is good practice to standardize the predictors and define the class order. Specify to standardize the predictors using an SVM template.

t = templateSVM('Standardize',1);
CVMdl = fitcecoc(X,Y,'Holdout',0.15,'Learners',t,'ClassNames',classOrder);
CMdl = CVMdl.Trained{1};           % Extract trained, compact classifier
testInds = test(CVMdl.Partition);  % Extract the test indices
XTest = X(testInds,:);
YTest = Y(testInds,:);

CVMdl is a ClassificationPartitionedECOC model. It contains the property Trained, which is a 1-by-1 cell array holding a CompactClassificationECOC model that the software trained using the training set.

Estimate the test-sample loss.

L = loss(CMdl,XTest,YTest)
L = 0

The ECOC model correctly classifies all out-of-sample irises.

Suppose that it is interesting to know how well a model classifies a particular class. This example shows how to pass such a custom loss function to loss.

Load Fisher's iris data set.

load fisheriris
X = meas;
Y = categorical(species);
n = numel(Y);           % Sample size
classOrder = unique(Y)  % Class order
classOrder = 3x1 categorical array
     setosa 
     versicolor 
     virginica 

K = numel(classOrder);  % Number of classes
rng(1) % For reproducibility

Train an ECOC model using SVM binary classifiers and specifying a 15% holdout sample. It is good practice to define the class order. Specify to standardize the predictors using an SVM template.

t = templateSVM('Standardize',1);
CVMdl = fitcecoc(X,Y,'Holdout',0.15,'Learners',t,'ClassNames',classOrder);
CMdl = CVMdl.Trained{1};           % Extract trained, compact classifier
testInds = test(CVMdl.Partition);  % Extract the test indices
XTest = X(testInds,:);
YTest = Y(testInds,:);

CVMdl is a ClassificationPartitionedECOC model. It contains the property Trained, which is a 1-by-1 cell array holding a CompactClassificationECOC model that the software trained using the training set.

Compute the negated losses for the test-sample observations.

[~,negLoss] = predict(CMdl,XTest);

Create a function that takes the minimal loss for each observation, and then averages the minimal losses across all observations.

lossfun = @(~,S,~,~)mean(min(-S,[],2));

Compute the test-sample custom loss.

loss(CMdl,XTest,YTest,'LossFun',lossfun)
ans = 0.0033

The average, minimal, binary loss in the test sample is 0.0033.

Más acerca de

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Algoritmos

If you trained Mdl specifying to standardize the predictor data, then the software standardizes the columns of X using the corresponding means and standard deviations that the software stored in Mdl.BinaryLearner{j}.Mu and Mdl.BinaryLearner{j}.Sigma for learner j.

References

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

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

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

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