predict - Classify observations using support vector machine (SVM) classifier - MATLAB (original) (raw)

Classify observations using support vector machine (SVM) classifier

Syntax

Description

[label](#mw%5Fd348509d-3d30-409d-b889-d0ed859a842a) = predict([SVMModel](#bt74bzo%5Fsep%5Fshared-SVMModel),[X](#mw%5Fbde43cb9-51ab-4cbf-992b-8ac2b2877736)) returns a vector of predicted class labels for the predictor data in the table or matrix X, based on the trained support vector machine (SVM) classification model SVMModel. The trained SVM model can either be full or compact.

example

[[label](#mw%5Fd348509d-3d30-409d-b889-d0ed859a842a),[score](#mw%5F606ce41c-e0f0-42bb-91f5-f24e9fdc08f5)] = predict([SVMModel](#bt74bzo%5Fsep%5Fshared-SVMModel),[X](#mw%5Fbde43cb9-51ab-4cbf-992b-8ac2b2877736)) also returns a matrix of scores (score) indicating the likelihood that a label comes from a particular class. For SVM, likelihood measures are either classification scores or class posterior probabilities. For each observation in X, the predicted class label corresponds to the maximum score among all classes.

example

Examples

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Load the ionosphere data set.

load ionosphere rng(1); % For reproducibility

Train an SVM classifier. Specify a 15% holdout sample for testing, standardize the data, and specify that 'g' is the positive class.

CVSVMModel = fitcsvm(X,Y,'Holdout',0.15,'ClassNames',{'b','g'},... 'Standardize',true); CompactSVMModel = CVSVMModel.Trained{1}; % Extract trained, compact classifier testInds = test(CVSVMModel.Partition); % Extract the test indices XTest = X(testInds,:); YTest = Y(testInds,:);

CVSVMModel is a ClassificationPartitionedModel classifier. It contains the property Trained, which is a 1-by-1 cell array holding a CompactClassificationSVM classifier that the software trained using the training set.

Label the test sample observations. Display the results for the first 10 observations in the test sample.

[label,score] = predict(CompactSVMModel,XTest); table(YTest(1:10),label(1:10),score(1:10,2),'VariableNames',... {'TrueLabel','PredictedLabel','Score'})

ans=10×3 table TrueLabel PredictedLabel Score
_________ ______________ ________

  {'b'}          {'b'}          -1.7175
  {'g'}          {'g'}           2.0003
  {'b'}          {'b'}          -9.6836
  {'g'}          {'g'}           2.5616
  {'b'}          {'b'}           -1.548
  {'g'}          {'g'}           2.0983
  {'b'}          {'b'}          -2.7016
  {'b'}          {'b'}         -0.66331
  {'g'}          {'g'}           1.6047
  {'g'}          {'g'}            1.773

Label new observations using an SVM classifier.

Load the ionosphere data set. Assume that the last 10 observations become available after you train the SVM classifier.

load ionosphere rng(1); % For reproducibility n = size(X,1); % Training sample size isInds = 1:(n-10); % In-sample indices oosInds = (n-9):n; % Out-of-sample indices

Train an SVM classifier. Standardize the data and specify that 'g' is the positive class. Conserve memory by reducing the size of the trained SVM classifier.

SVMModel = fitcsvm(X(isInds,:),Y(isInds),'Standardize',true,... 'ClassNames',{'b','g'}); CompactSVMModel = compact(SVMModel); whos('SVMModel','CompactSVMModel')

Name Size Bytes Class Attributes

CompactSVMModel 1x1 30173 classreg.learning.classif.CompactClassificationSVM
SVMModel 1x1 136713 ClassificationSVM

The CompactClassificationSVM classifier (CompactSVMModel) uses less space than the ClassificationSVM classifier (SVMModel) because SVMModel stores the data.

Estimate the optimal score-to-posterior-probability transformation function.

CompactSVMModel = fitPosterior(CompactSVMModel,... X(isInds,:),Y(isInds))

CompactSVMModel = CompactClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: '@(S)sigmoid(S,-1.968371e+00,3.122227e-01)' Alpha: [88×1 double] Bias: -0.2142 KernelParameters: [1×1 struct] Mu: [0.8886 0 0.6365 0.0457 0.5933 0.1200 0.5414 0.1217 0.5020 0.1872 0.4659 0.1596 0.3889 0.0970 0.3308 0.0723 0.3685 -0.0039 0.3453 -0.0256 0.3231 0.0097 0.3490 -0.0596 0.3839 -0.0731 0.5343 -0.0718 0.3659 … ] (1×34 double) Sigma: [0.3151 0 0.5032 0.4476 0.5251 0.4668 0.4966 0.5275 0.5107 0.4896 0.5681 0.5011 0.6267 0.5009 0.6569 0.4639 0.6214 0.5035 0.6296 0.5265 0.6128 0.5250 0.6067 0.5349 0.5817 0.5157 0.5212 0.5577 0.5787 0.5151 … ] (1×34 double) SupportVectors: [88×34 double] SupportVectorLabels: [88×1 double]

Properties, Methods

The optimal score transformation function (CompactSVMModel.ScoreTransform) is the sigmoid function because the classes are inseparable.

Predict the out-of-sample labels and positive class posterior probabilities. Because true labels are available, compare them with the predicted labels.

[labels,PostProbs] = predict(CompactSVMModel,X(oosInds,:)); table(Y(oosInds),labels,PostProbs(:,2),'VariableNames',... {'TrueLabels','PredictedLabels','PosClassPosterior'})

ans=10×3 table TrueLabels PredictedLabels PosClassPosterior __________ _______________ _________________

  {'g'}            {'g'}              0.98418     
  {'g'}            {'g'}              0.95545     
  {'g'}            {'g'}              0.67793     
  {'g'}            {'g'}              0.94447     
  {'g'}            {'g'}              0.98744     
  {'g'}            {'g'}               0.9248     
  {'g'}            {'g'}               0.9711     
  {'g'}            {'g'}              0.96986     
  {'g'}            {'g'}              0.97802     
  {'g'}            {'g'}               0.9436     

PostProbs is a 10-by-2 matrix, where the first column is the negative class posterior probabilities, and the second column is the positive class posterior probabilities corresponding to the new observations.

Input Arguments

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Predictor data to be classified, specified as a numeric matrix or table.

Each row of X corresponds to one observation, and each column corresponds to one variable.

• For a numeric matrix:
  • The variables in the columns of X must have the same order as the predictor variables that trained SVMModel.
  • If you trained SVMModel using a table (for example, Tbl) andTbl contains all numeric predictor variables, then X can be a numeric matrix. To treat numeric predictors inTbl as categorical during training, identify categorical predictors by using theCategoricalPredictors name-value pair argument of fitcsvm. IfTbl contains heterogeneous predictor variables (for example, numeric and categorical data types) and X is a numeric matrix, then predict throws an error.
• For a table:
  • predict does not support multicolumn variables or cell arrays other than cell arrays of character vectors.
  • If you trained SVMModel using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as those that trained SVMModel (stored inSVMModel.PredictorNames). However, the column order of X does not need to correspond to the column order ofTbl. Also, Tbl and X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.
  • If you trained SVMModel using a numeric matrix, then the predictor names inSVMModel.PredictorNames and corresponding predictor variable names inX must be the same. To specify predictor names during training, see the PredictorNames name-value pair argument of fitcsvm. All predictor variables in X must be numeric vectors.X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

If you set 'Standardize',true infitcsvm to train SVMModel, then the software standardizes the columns of X using the corresponding means in SVMModel.Mu and the standard deviations in SVMModel.Sigma.

Data Types: table | double | single

Output Arguments

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

label has the same data type as the observed class labels (Y) that trained SVMModel, and its length is equal to the number of rows in X.(The software treats string arrays as cell arrays of character vectors.)

The predict function classifies an observation into the class yielding the highest score. For an observation with NaN scores, the function classifies the observation into the majority class, which makes up the largest proportion of the training labels.

For one-class learning, each value in label is the same—the one class in the training data. Use score to identify anomalies.

Predicted class scores or posterior probabilities, returned as a numeric column vector or numeric matrix.

• For one-class learning, score is a column vector with the same number of rows as the observations (X). The elements ofscore are anomaly scores for the corresponding observations. Negative score values indicate that the corresponding observations are outliers. You cannot obtain posterior probabilities for one-class learning.
• For two-class learning, score is a two-column matrix with the same number of rows asX.
  • If you fit the optimal score-to-posterior-probability transformation function using fitPosterior or fitSVMPosterior, thenscore contains class posterior probabilities. That is, if the value ofSVMModel.ScoreTransform is notnone, then the first and second columns of score contain the negative class (SVMModel.ClassNames{1}) and positive class (SVMModel.ClassNames{2}) posterior probabilities for the corresponding observations, respectively.
  • Otherwise, the first column contains the negative class scores and the second column contains the positive class scores for the corresponding observations.

IfSVMModel.KernelParameters.Function is 'linear', then the classification score for the observation x is

SVMModel stores_β_, b, and s in the properties Beta, Bias, andKernelParameters .Scale, respectively.

To estimate classification scores manually, you must first apply any transformations to the predictor data that were applied during training. Specifically, if you specify 'Standardize',true when using fitcsvm, then you must standardize the predictor data manually by using the mean SVMModel.Mu and standard deviation SVMModel.Sigma, and then divide the result by the kernel scale in SVMModel.KernelParameters.Scale.

All SVM functions, such as resubPredict and predict, apply any required transformation before estimation.

IfSVMModel .KernelParameters.Function is not 'linear', then Beta is empty ([]).

More About

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The SVM classification score for classifying observation x is the signed distance from x to the decision boundary ranging from -∞ to +∞. A positive score for a class indicates that x is predicted to be in that class. A negative score indicates otherwise.

The positive class classification score f(x) is the trained SVM classification function. f(x) is also the numerical predicted response for x, or the score for predicting x into the positive class.

where (α1,...,αn,b) are the estimated SVM parameters, G(xj,x) is the dot product in the predictor space between x and the support vectors, and the sum includes the training set observations. The negative class classification score for x, or the score for predicting_x_ into the negative class, is –f(x).

If G(xj,x) = xj_′_x (the linear kernel), then the score function reduces to

s is the kernel scale and β is the vector of fitted linear coefficients.

For more details, see Understanding Support Vector Machines.

The posterior probability is the probability that an observation belongs in a particular class, given the data.

For SVM, the posterior probability is a function of the score_P_(s) that observation j is in class k = {-1,1}.

• For separable classes, the posterior probability is the step function
  where:
  • sj is the score of observation j.
  • +1 and –1 denote the positive and negative classes, respectively.
  • π is the prior probability that an observation is in the positive class.
• For inseparable classes, the posterior probability is the sigmoid function
  where the parameters A and_B_ are the slope and intercept parameters, respectively.

The prior probability of a class is the assumed relative frequency with which observations from that class occur in a population.

Tips

• If you are using a linear SVM model for classification and the model has many support vectors, then using predict for the prediction method can be slow. To efficiently classify observations based on a linear SVM model, remove the support vectors from the model object by using discardSupportVectors.

Algorithms

• By default and irrespective of the model kernel function, MATLAB® uses the dual representation of the score function to classify observations based on trained SVM models, specifically
  This prediction method requires the trained support vectors and_α_ coefficients (see the SupportVectors andAlpha properties of the SVM model).
• By default, the software computes optimal posterior probabilities using Platt’s method [3]:
  1. Perform 10-fold cross-validation.
  2. Fit the sigmoid function parameters to the scores returned from the cross-validation.
  3. Estimate the posterior probabilities by entering the cross-validation scores into the fitted sigmoid function.
• The software incorporates prior probabilities in the SVM objective function during training.
• For SVM, predict and resubPredict classify observations into the class yielding the largest score (the largest posterior probability). The software accounts for misclassification costs by applying the average-cost correction before training the classifier. That is, given the class prior vector P, misclassification cost matrix C, and observation weight vector w, the software defines a new vector of observation weights (W) such that

Alternative Functionality

Simulink Block

To integrate the prediction of an SVM classification model into Simulink®, you can use the ClassificationSVM Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB Function block with the predict function. For examples, see Predict Class Labels Using ClassificationSVM Predict Block and Predict Class Labels Using MATLAB Function Block.

When deciding which approach to use, consider the following:

• If you use the Statistics and Machine Learning Toolbox library block, you can use the Fixed-Point Tool (Fixed-Point Designer) to convert a floating-point model to fixed point.
• Support for variable-size arrays must be enabled for a MATLAB Function block with the predict function.
• If you use a MATLAB Function block, you can use MATLAB functions for preprocessing or post-processing before or after predictions in the same MATLAB Function block.

References

[1] Christianini, N., and J. C. Shawe-Taylor.An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge, UK: Cambridge University Press, 2000.

[2] Hastie, T., R. Tibshirani, and J. Friedman.The Elements of Statistical Learning, Second Edition. NY: Springer, 2008.

[3] Platt, J. “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.” Advances in Large Margin Classifiers. MIT Press, 1999, pages 61–74.

Extended Capabilities

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Thepredict function fully supports tall arrays. For more information, see Tall Arrays.

Usage notes and limitations:

• You can generate C/C++ code for both predict andupdate by using a coder configurer. Or, generate code only forpredict by using saveLearnerForCoder,loadLearnerForCoder, and codegen.

  • Code generation for predict and update — Create a coder configurer by using learnerCoderConfigurer and then generate code by using generateCode. Then you can update model parameters in the generated code without having to regenerate the code.
  • Code generation for predict — Save a trained model by using saveLearnerForCoder. Define an entry-point function that loads the saved model by using loadLearnerForCoder and calls thepredict function. Then use codegen (MATLAB Coder) to generate code for the entry-point function.

• For single-precision code generation, use standardized data by specifying 'Standardize',true when you train the model. To generate single-precision C/C++ code forpredict, specify DataType="single" when you call the loadLearnerForCoder function.

• You can also generate fixed-point C/C++ code forpredict. Fixed-point code generation requires an additional step that defines the fixed-point data types of the variables required for prediction. Create a fixed-point data type structure by using the data type function generated by generateLearnerDataTypeFcn, and then use the structure as an input argument ofloadLearnerForCoder in an entry-point function. Generating fixed-point C/C++ code requires MATLAB Coder™ and Fixed-Point Designer™.

• This table contains notes about the arguments of predict. Arguments not included in this table are fully supported.

  Argument	Notes and Limitations
  SVMModel	If you usesaveLearnerForCoder to save a model that is equipped to predict posterior probabilities, and use loadLearnerForCoder to load the model, then loadLearnerForCoder cannot restore theScoreTransform property into the MATLAB Workspace. However, loadLearnerForCoder can load the model, including the ScoreTransform property, within an entry-point function at compile time for code generation. For the usage notes and limitations of the model object, see Code Generation of theCompactClassificationSVM object.
  X	For general code generation, X must be a single-precision or double-precision matrix or a table containing numeric variables, categorical variables, or both.In the coder configurer workflow, X must be a single-precision or double-precision matrix.For fixed-point code generation, X must be a fixed-point matrix.The number of rows, or observations, in X can be a variable size, but the number of columns in X must be fixed.If you want to specify X as a table, then your model must be trained using a table, and your entry-point function for prediction must do the following: Accept data as arrays.Create a table from the data input arguments and specify the variable names in the table.Pass the table to predict.For an example of this table workflow, see Generate Code to Classify Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder).

For more information, see Introduction to Code Generation.

Usage notes and limitations:

• The predict function does not support one-class classification models.

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

Version History

Introduced in R2014a