fitcsvm
Train binary support vector machine classifiercollapse all in page
fitcsvm trains or cross-validates a support vector machine (SVM) model for two-class (binary) classification on a low- through moderate-dimensional predictor data set. fitcsvm supports mapping the predictor data using kernel functions, and supports SMO, ISDA, or L1 soft-margin minimization via quadratic programming for objective-function minimization.
To train a linear SVM model for binary classification on a high-dimensional data set, that is, data sets that include many predictor variables, use fitclinear instead.
For multiclass learning by combining binary SVM models, use error-correcting output codes (ECOC). For more details, see fitcecoc.
To train an SVM regression model, see fitrsvm for low- through moderate-dimensional predictor data sets, or fitrlinear for high-dimensional data sets.
Syntax
Mdl = fitcsvm(Tbl,ResponseVarName)
Mdl = fitcsvm(Tbl,formula)
Mdl = fitcsvm(Tbl,Y)
Mdl = fitcsvm(X,Y)
Mdl = fitcsvm(___,Name,Value)
Description
Mdl = fitcsvm(Tbl,ResponseVarName) returns a support vector machine classifier Mdl trained using the sample data contained in a table (Tbl). ResponseVarName is the name of the variable in Tbl that contains the class labels for one- or two-class classification.
Mdl = fitcsvm(Tbl,formula) returns an SVM classifer trained using the sample data contained in a table (Tbl). formula is an explanatory model of the response and a subset of predictor variables in Tbl used to fit Mdl.
Mdl = fitcsvm(Tbl,Y) returns an SVM classifer trained using the predictor variables in table Tbl and class labels in vector Y.
example
Mdl = fitcsvm(X,Y) returns an SVM classifier trained using the predictors in the matrix X and class labels in vector Y for one- or two-class classification.
example
Mdl = fitcsvm(___,Name,Value) returns a support vector machine classifier with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes. For example, you can specify the type of cross-validation, the cost for misclassification, or the type of score transformation function.
Examples
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Train a Support Vector Machine Classifier
Open Script
Load Fisher's iris data set. Remove the sepal lengths and widths, and all observed setosa irises.
load fisheriris
inds = ~strcmp(species,'setosa');
X = meas(inds,3:4);
y = species(inds);
Train an SVM classifier using the processed data set.
SVMModel = fitcsvm(X,y)
SVMModel =
ClassificationSVM
ResponseName: 'Y'
CategoricalPredictors: []
ClassNames: {'versicolor' 'virginica'}
ScoreTransform: 'none'
NumObservations: 100
Alpha: [24x1 double]
Bias: -14.4149
KernelParameters: [1x1 struct]
BoxConstraints: [100x1 double]
ConvergenceInfo: [1x1 struct]
IsSupportVector: [100x1 logical]
Solver: 'SMO'
The Command Window shows that SVMModel is a trained ClassificationSVM classifier and a property list. Display the properties of SVMModel, for example, to determine the class order, by using dot notation.
classOrder = SVMModel.ClassNames
classOrder =
2x1 cell array
{'versicolor'}
{'virginica' }
The first class ('versicolor') is the negative class, and the second ('virginica') is the positive class. You can change the class order during training by using the 'ClassNames' name-value pair argument.
Plot a scatter diagram of the data and circle the support vectors.
sv = SVMModel.SupportVectors;
figure
gscatter(X(:,1),X(:,2),y)
hold on
plot(sv(:,1),sv(:,2),'ko','MarkerSize',10)
legend('versicolor','virginica','Support Vector')
hold off
The support vectors are observations that occur on or beyond their estimated class boundaries.
You can adjust the boundaries (and therefore the number of support vectors) by setting a box constraint during training using the 'BoxConstraint' name-value pair argument.
Train and Cross Validate an SVM Classifier
Open Script
Load the ionosphere data set.
load ionosphere
rng(1); % For reproducibility
Train an SVM classifier using the radial basis kernel. Let the software find a scale value for the kernel function. It is good practice to standardize the predictors.
SVMModel = fitcsvm(X,Y,'Standardize',true,'KernelFunction','RBF',...
'KernelScale','auto');
SVMModel is a trained ClassificationSVM classifier.
Cross validate the SVM classifier. By default, the software uses 10-fold cross validation.
CVSVMModel = crossval(SVMModel);
CVSVMModel is a ClassificationPartitionedModel cross-validated classifier.
Estimate the out-of-sample misclassification rate.
classLoss = kfoldLoss(CVSVMModel)
classLoss =
0.0484
The generalization rate is approximately 5%.
Detect Outliers Using SVM and One-Class Learning
Open Script
Load Fisher's iris data set. Remove the petal lengths and widths. Treat all irises as coming from the same class.
load fisheriris
X = meas(:,1:2);
y = ones(size(X,1),1);
Train an SVM classifier using the processed data set. Assume that 5% of the observations are outliers. It is good practice to standardize the predictors.
rng(1);
SVMModel = fitcsvm(X,y,'KernelScale','auto','Standardize',true,...
'OutlierFraction',0.05);
SVMModel is a trained ClassificationSVM classifier. By default, the software uses the Gaussian kernel for one-class learning.
Plot the observations and the decision boundary. Flag the support vectors and potential outliers.
svInd = SVMModel.IsSupportVector;
h = 0.02; % Mesh grid step size
[X1,X2] = meshgrid(min(X(:,1)):h:max(X(:,1)),...
min(X(:,2)):h:max(X(:,2)));
[~,score] = predict(SVMModel,[X1(:),X2(:)]);
scoreGrid = reshape(score,size(X1,1),size(X2,2));
figure
plot(X(:,1),X(:,2),'k.')
hold on
plot(X(svInd,1),X(svInd,2),'ro','MarkerSize',10)
contour(X1,X2,scoreGrid)
colorbar;
title('{\bf Iris Outlier Detection via One-Class SVM}')
xlabel('Sepal Length (cm)')
ylabel('Sepal Width (cm)')
legend('Observation','Support Vector')
hold off
The boundary separating the outliers from the rest of the data occurs where the contour value is 0.
Verify that the fraction of observations with negative scores in the cross-validated data is close to 5%.
CVSVMModel = crossval(SVMModel);
[~,scorePred] = kfoldPredict(CVSVMModel);
outlierRate = mean(scorePred<0)
outlierRate =
0.0467
Find Multiple Class Boundaries Using Binary SVM
Open Script
Load Fisher's iris data set. Use the petal lengths and widths.
load fisheriris
X = meas(:,3:4);
Y = species;
Examine a scatter plot of the data.
figure
gscatter(X(:,1),X(:,2),Y);
h = gca;
lims = [h.XLim h.YLim]; % Extract the x and y axis limits
title('{\bf Scatter Diagram of Iris Measurements}');
xlabel('Petal Length (cm)');
ylabel('Petal Width (cm)');
legend('Location','Northwest');
There are three classes, one of which is linearly separable from the others.
For each class:
Create a logical vector (indx) indicating whether an observation is a member of the class.
Train an SVM classifier using the predictor data and indx.
Store the classifier in a cell of a cell array.
It is good practice to define the class order.
SVMModels = cell(3,1);
classes = unique(Y);
rng(1); % For reproducibility
for j = 1:numel(classes);
indx = strcmp(Y,classes(j)); % Create binary classes for each classifier
SVMModels{j} = fitcsvm(X,indx,'ClassNames',[false true],'Standardize',true,...
'KernelFunction','rbf','BoxConstraint',1);
end
SVMModels is a 3-by-1 cell array, with each cell containing a ClassificationSVM classifier. For each cell, the positive class is setosa, versicolor, and virginica, respectively.
Define a fine grid within the plot, and treat the coordinates as new observations from the distribution of the training data. Estimate the score of the new observations using each classifier.
d = 0.02;
[x1Grid,x2Grid] = meshgrid(min(X(:,1)):d:max(X(:,1)),...
min(X(:,2)):d:max(X(:,2)));
xGrid = [x1Grid(:),x2Grid(:)];
N = size(xGrid,1);
Scores = zeros(N,numel(classes));
for j = 1:numel(classes);
[~,score] = predict(SVMModels{j},xGrid);
Scores(:,j) = score(:,2); % Second column contains positive-class scores
end
Each row of Scores contains three scores. The index of the element with the largest score is the index of the class to which the new class observation most likely belongs.
Associate each new observation with the classifier that gives it the maximum score.
[~,maxScore] = max(Scores,[],2);
Color in the regions of the plot based on which class the corresponding new observation belongs.
figure
h(1:3) = gscatter(xGrid(:,1),xGrid(:,2),maxScore,...
[0.1 0.5 0.5; 0.5 0.1 0.5; 0.5 0.5 0.1]);
hold on
h(4:6) = gscatter(X(:,1),X(:,2),Y);
title('{\bf Iris Classification Regions}');
xlabel('Petal Length (cm)');
ylabel('Petal Width (cm)');
legend(h,{'setosa region','versicolor region','virginica region',...
'observed setosa','observed versicolor','observed virginica'},...
'Location','Northwest');
axis tight
hold off
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楼主
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