fitrsvm

Fit a support vector machine regression model

collapse all in page

Syntax

Mdl = fitrsvm(Tbl,ResponseVarName)

Mdl = fitrsvm(Tbl,formula)

Mdl = fitrsvm(Tbl,Y)

Mdl = fitrsvm(X,Y)

Mdl = fitrsvm(___,Name,Value)

Description

fitrsvmtrains or cross-validates a support vector machine (SVM) regression model on a low- through moderate-dimensional predictor data set.fitrsvmsupports mapping the predictor data using kernel functions, and supports SMO, ISDA, orL1 soft-margin minimization via quadratic programming for objective-function minimization.

To train a linear SVM regression model on a high-dimensional data set, that is, data sets that include many predictor variables, usefitrlinearinstead.

To train an SVM model for binary classification, seefitcsvmfor low- through moderate-dimensional predictor data sets, orfitclinearfor high-dimensional data sets.

example

Mdl= fitrsvm(Tbl,ResponseVarName)再保险turns a full, trained support vector machine (SVM) regression modelMdltrained using the predictors values in the tableTbland the response values inTbl.ResponseVarName．

Mdl= fitrsvm(Tbl,formula)再保险turns a full SVM regression model trained using the predictors values in the tableTbl．formulais an explanatory model of the response and a subset of predictor variables inTblused to fitMdl．

Mdl= fitrsvm(Tbl,Y)再保险turns a full, trained SVM regression model trained using the predictors values in the tableTbland the response values in the vectorY．

Mdl= fitrsvm(X,Y)再保险turns a full, trained SVM regression model trained using the predictors values in the matrixXand the response values in the vectorY．

example

Mdl= fitrsvm(___,Name,Value)再保险turns an SVM regression model with additional options specified by one or more name-value pair arguments, using any of the previous syntaxes. For example, you can specify the kernel function or train a cross-validated model.

Examples

collapse all

Train Linear Support Vector Machine Regression Model

Open Live Script

Train a support vector machine (SVM) regression model using sample data stored in matrices.

Load thecarsmalldata set.

loadcarsmallrng'default'% For reproducibility

SpecifyHorsepowerandWeightas the predictor variables (X) andMPGas the response variable (Y).

X = [Horsepower,Weight]; Y = MPG;

Train a default SVM regression model.

Mdl = fitrsvm(X,Y)

Mdl = RegressionSVM ResponseName: 'Y' CategoricalPredictors: [] ResponseTransform: 'none' Alpha: [75x1 double] Bias: 57.3958 KernelParameters: [1x1 struct] NumObservations: 93 BoxConstraints: [93x1 double] ConvergenceInfo: [1x1 struct] IsSupportVector: [93x1 logical] Solver: 'SMO' Properties, Methods

Mdlis a trainedRegressionSVMmodel.

Check the model for convergence.

Mdl.ConvergenceInfo.Converged

ans =logical0

0indicates that the model did not converge.

Retrain the model using standardized data.

MdlStd = fitrsvm(X,Y,'Standardize',true)

MdlStd = RegressionSVM ResponseName:“Y”确定alPredictors: [] ResponseTransform: 'none' Alpha: [77x1 double] Bias: 22.9131 KernelParameters: [1x1 struct] Mu: [109.3441 2.9625e+03] Sigma: [45.3545 805.9668] NumObservations: 93 BoxConstraints: [93x1 double] ConvergenceInfo: [1x1 struct] IsSupportVector: [93x1 logical] Solver: 'SMO' Properties, Methods

Check the model for convergence.

MdlStd.ConvergenceInfo.Converged

ans =logical1

1indicates that the model did converge.

Compute the resubstitution (in-sample) mean-squared error for the new model.

lStd = resubLoss(MdlStd)

lStd = 17.0256

Train Support Vector Machine Regression Model

Open Live Script

Train a support vector machine regression model using the abalone data from the UCI Machine Learning Repository.

Download the data and save it in your current folder with the name'abalone.csv'．

url ='https://archive.ics.uci.edu/ml/machine-learning-databases/abalone/abalone.data'; websave('abalone.csv',url);

Read the data into a table. Specify the variable names.

varnames = {'Sex';'Length';'Diameter';'Height';'Whole_weight';．..'Shucked_weight';'Viscera_weight';'Shell_weight';'Rings'}; Tbl = readtable('abalone.csv','Filetype','text','ReadVariableNames',false); Tbl.Properties.VariableNames = varnames;

The sample data contains 4177 observations. All the predictor variables are continuous except forSex, which is a categorical variable with possible values'M'(for males),'F'(for females), and'I'(for infants). The goal is to predict the number of rings (stored inRings) on the abalone and determine its age using physical measurements.

Train an SVM regression model, using a Gaussian kernel function with an automatic kernel scale. Standardize the data.

rngdefault% For reproducibilityMdl = fitrsvm(Tbl,'Rings',“克恩elFunction','gaussian',“克恩elScale','auto',．..'Standardize',true)

Mdl = RegressionSVM PredictorNames: {'Sex' 'Length' 'Diameter' 'Height' 'Whole_weight' 'Shucked_weight' 'Viscera_weight' 'Shell_weight'} ResponseName: 'Rings' CategoricalPredictors: 1 ResponseTransform: 'none' Alpha: [3635×1 double] Bias: 10.8144 KernelParameters: [1×1 struct] Mu: [0 0 0 0.5240 0.4079 0.1395 0.8287 0.3594 0.1806 0.2388] Sigma: [1 1 1 0.1201 0.0992 0.0418 0.4904 0.2220 0.1096 0.1392] NumObservations: 4177 BoxConstraints: [4177×1 double] ConvergenceInfo: [1×1 struct] IsSupportVector: [4177×1 logical] Solver: 'SMO' Properties, Methods

The Command Window shows thatMdlis a trainedRegressionSVMmodel and displays a property list.

Display the properties ofMdlusing dot notation. For example, check to confirm whether the model converged and how many iterations it completed.

conv = Mdl.ConvergenceInfo.Converged

conv =logical1

它er = Mdl.NumIterations

它er = 2759

The returned results indicate that the model converged after 2759 iterations.

Cross-Validate SVM Regression Model

Open Live Script

Load thecarsmalldata set.

loadcarsmallrng'default'% For reproducibility

SpecifyHorsepowerandWeightas the predictor variables (X) andMPGas the response variable (Y).

X =(马力重量);Y = MPG;

Cross-validate two SVM regression models using 5-fold cross-validation. For both models, specify to standardize the predictors. For one of the models, specify to train using the default linear kernel, and the Gaussian kernel for the other model.

MdlLin = fitrsvm(X,Y,'Standardize',true,'KFold',5)

MdlLin = RegressionPartitionedSVM CrossValidatedModel: 'SVM' PredictorNames: {'x1' 'x2'} ResponseName: 'Y' NumObservations: 94 KFold: 5 Partition: [1x1 cvpartition] ResponseTransform: 'none' Properties, Methods

MdlGau = fitrsvm(X,Y,'Standardize',true,'KFold',5,“克恩elFunction','gaussian')

MdlGau = RegressionPartitionedSVM CrossValidatedModel: 'SVM' PredictorNames: {'x1' 'x2'} ResponseName: 'Y' NumObservations: 94 KFold: 5 Partition: [1x1 cvpartition] ResponseTransform: 'none' Properties, Methods

MdlLin.Trained

ans=5×1 cell array{1x1 classreg.learning.regr.CompactRegressionSVM} {1x1 classreg.learning.regr.CompactRegressionSVM} {1x1 classreg.learning.regr.CompactRegressionSVM} {1x1 classreg.learning.regr.CompactRegressionSVM} {1x1 classreg.learning.regr.CompactRegressionSVM}

MdlLinandMdlGauareRegressionPartitionedSVMcross-validated models. TheTrainedproperty of each model is a 5-by-1 cell array ofCompactRegressionSVMmodels. The models in the cell store the results of training on 4 folds of observations, and leaving one fold of observations out.

Compare the generalization error of the models. In this case, the generalization error is the out-of-sample mean-squared error.

mseLin = kfoldLoss(MdlLin)

mseLin = 17.4417

mseGau = kfoldLoss(MdlGau)

mseGau = 16.7355

The SVM regression model using the Gaussian kernel performs better than the one using the linear kernel.

Create a model suitable for making predictions by passing the entire data set tofitrsvm, and specify all name-value pair arguments that yielded the better-performing model. However, do not specify any cross-validation options.

MdlGau = fitrsvm(X,Y,'Standardize',true,“克恩elFunction','gaussian');

To predict the MPG of a set of cars, passMdland a table containing the horsepower and weight measurements of the cars topredict．

Optimize SVM Regression

Open Live Script

This example shows how to optimize hyperparameters automatically usingfitrsvm．The example uses thecarsmalldata.

Load thecarsmalldata set.

loadcarsmall

SpecifyHorsepowerandWeightas the predictor variables (X) andMPGas the response variable (Y).

X =(马力重量);Y = MPG;

Find hyperparameters that minimize five-fold cross-validation loss by using automatic hyperparameter optimization.

For reproducibility, set the random seed and use the'expected-improvement-plus'acquisition function.

rngdefaultMdl = fitrsvm(X,Y,'OptimizeHyperparameters','auto',．..'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName',．..'expected-improvement-plus'))

|====================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | BoxConstraint| KernelScale | Epsilon | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 1 | Best | 6.8077 | 8.9946 | 6.8077 | 6.8077 | 0.35664 | 0.043031 | 0.30396 | | 2 | Best | 2.9108 | 0.079288 | 2.9108 | 3.1259 | 70.67 | 710.65 | 1.6369 | | 3 | Accept | 4.1884 | 0.061383 | 2.9108 | 3.1211 | 14.367 | 0.0059144 | 442.64 | | 4 | Accept | 4.159 | 0.072431 | 2.9108 | 3.0773 | 0.0030879 | 715.31 | 2.6045 | | 5 | Best | 2.902 | 0.19692 | 2.902 | 2.9015 | 969.07 | 703.1 | 0.88614 | | 6 | Accept | 4.1884 | 0.063713 | 2.902 | 2.9017 | 993.93 | 919.26 | 22.16 | | 7 | Accept | 2.9307 | 0.09127 | 2.902 | 2.9018 | 219.88 | 613.28 | 0.015526 | | 8 | Accept | 2.9537 | 0.38273 | 2.902 | 2.9017 | 905.17 | 395.74 | 0.021914 | | 9 | Accept | 2.9073 | 0.13752 | 2.902 | 2.9017 | 24.242 | 647.2 | 0.17855 | | 10 | Accept | 2.9044 | 0.2345 | 2.902 | 2.9017 | 117.27 | 173.98 | 0.73387 | | 11 | Accept | 2.9035 | 0.084693 | 2.902 | 2.9016 | 1.3516 | 131.19 | 0.0093404 | | 12 | Accept | 4.0917 | 0.10013 | 2.902 | 2.902 | 0.012201 | 962.58 | 0.0092777 | | 13 | Accept | 2.9525 | 0.88983 | 2.902 | 2.902 | 77.38 | 65.508 | 0.0093299 | | 14 | Accept | 2.9352 | 0.10519 | 2.902 | 2.9019 | 21.591 | 166.43 | 0.035214 | | 15 | Accept | 2.9341 | 0.12667 | 2.902 | 2.9019 | 45.286 | 207.56 | 0.009379 | | 16 | Accept | 2.9104 | 0.072284 | 2.902 | 2.9018 | 0.064315 | 23.313 | 0.0093341 | | 17 | Accept | 2.9056 | 0.11728 | 2.902 | 2.9018 | 0.33909 | 40.311 | 0.053394 | | 18 | Accept | 2.9335 | 0.22476 | 2.902 | 2.8999 | 0.9904 | 41.169 | 0.0099688 | | 19 | Accept | 2.9929 | 0.1796 | 2.902 | 2.8995 | 0.0010811 | 33.401 | 0.017694 | | 20 | Accept | 4.1884 | 0.081198 | 2.902 | 2.9 | 0.0014524 | 1.9514 | 856.49 | |====================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | BoxConstraint| KernelScale | Epsilon | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 21 | Accept | 2.904 | 0.11233 | 2.902 | 2.8831 | 88.487 | 405.92 | 0.44372 | | 22 | Accept | 2.9107 | 0.096647 | 2.902 | 2.884 | 344.34 | 992 | 0.28418 | | 23 | Accept | 2.904 | 0.1051 | 2.902 | 2.8841 | 0.92028 | 70.985 | 0.52233 | | 24 | Best | 2.859 | 0.93928 | 2.859 | 2.8606 | 18.319 | 27.763 | 3.008 | | 25 | Accept | 2.9177 | 3.1086 | 2.859 | 2.8612 | 39.154 | 24.119 | 0.67121 | | 26 | Accept | 2.9059 | 0.14666 | 2.859 | 2.8609 | 0.067541 | 15.019 | 1.192 | | 27 | Accept | 4.1884 | 0.093034 | 2.859 | 2.8622 | 987.04 | 3.1666 | 70.752 | | 28 | Accept | 2.8936 | 0.17454 | 2.859 | 2.8744 | 2.2395 | 36.089 | 1.6775 | | 29 | Accept | 2.9156 | 0.067328 | 2.859 | 2.875 | 0.0027368 | 12.221 | 0.10637 | | 30 | Accept | 2.9105 | 0.074655 | 2.859 | 2.8757 | 0.05895 | 21.326 | 0.2563 |

Figure contains an axes object. The axes object with title Min objective vs. Number of function evaluations contains 2 objects of type line. These objects represent Min observed objective, Estimated min objective.

__________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 32.4033 seconds Total objective function evaluation time: 17.2141 Best observed feasible point: BoxConstraint KernelScale Epsilon _____________ ___________ _______ 18.319 27.763 3.008 Observed objective function value = 2.859 Estimated objective function value = 2.8727 Function evaluation time = 0.93928 Best estimated feasible point (according to models): BoxConstraint KernelScale Epsilon _____________ ___________ _______ 2.2395 36.089 1.6775 Estimated objective function value = 2.8757 Estimated function evaluation time = 0.20807

Mdl = RegressionSVM ResponseName: 'Y' CategoricalPredictors: [] ResponseTransform: 'none' Alpha: [62x1 double] Bias: 45.4806 KernelParameters: [1x1 struct] NumObservations: 93 HyperparameterOptimizationResults: [1x1 BayesianOptimization] BoxConstraints: [93x1 double] ConvergenceInfo: [1x1 struct] IsSupportVector: [93x1 logical] Solver: 'SMO' Properties, Methods

The optimization searched overBoxConstraint,KernelScale, andEpsilon．The output is the regression with the minimum estimated cross-validation loss.

Input Arguments

collapse all

`Tbl`—Predictor data
table

Sample data used to train the model, specified as a table. Each row ofTblcorresponds to one observation, and each column corresponds to one predictor variable. Optionally,Tblcan contain one additional column for the response variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

IfTblcontains the response variable, and you want to use all remaining variables inTblas predictors, then specify the response variable usingResponseVarName．

IfTblcontains the response variable, and you want to use only a subset of the remaining variables inTblas predictors, then specify a formula usingformula．

IfTbldoes not contain the response variable, then specify a response variable usingY．The length of response variable and the number of rows ofTblmust be equal.

If a row ofTblor an element ofYcontains at least oneNaN, thenfitrsvm再保险moves those rows and elements from both arguments when training the model.

To specify the names of the predictors in the order of their appearance inTbl, use thePredictorNamesname-value pair argument.

Data Types:table

`ResponseVarName`—Response variable name
name of variable in`Tbl`

响应变量名称,指定的名称variable inTbl．The response variable must be a numeric vector.

You must specifyResponseVarNameas a character vector or string scalar. For example, ifTblstores the response variableYasTbl.Y, then specify it as'Y'．否则,软件将所有列Tbl, includingY, as predictors when training the model.

Data Types:char|string

`formula`—Explanatory model of response variable and subset of predictor variables
character vector|string scalar

Explanatory model of the response variable and a subset of the predictor variables, specified as a character vector or string scalar in the form"Y~x1+x2+x3"．In this form,Y再保险presents the response variable, andx1,x2, andx3再保险present the predictor variables.

To specify a subset of variables inTblas predictors for training the model, use a formula. If you specify a formula, then the software does not use any variables inTblthat do not appear informula．

The variable names in the formula must be both variable names inTbl(Tbl.Properties.VariableNames) and valid MATLAB^®identifiers. You can verify the variable names inTblby using theisvarname功能ion. If the variable names are not valid, then you can convert them by using thematlab.lang.makeValidName功能ion.

Data Types:char|string

`Y`—Response data
numeric vector

Response data, specified as ann-by-1 numeric vector. The length ofYand the number of rows ofTblorXmust be equal.

If a row ofTblorX, or an element ofY, contains at least oneNaN, thenfitrsvm再保险moves those rows and elements from both arguments when training the model.

To specify the response variable name, use theResponseNamename-value pair argument.

Data Types:single|double

`X`—Predictor data
numeric matrix

Predictor data to which the SVM regression model is fit, specified as ann-by-pnumeric matrix.nis the number of observations andpis the number of predictor variables.

The length ofYand the number of rows ofXmust be equal.

If a row ofXor an element ofYcontains at least oneNaN, thenfitrsvm再保险moves those rows and elements from both arguments.

To specify the names of the predictors in the order of their appearance inX, use thePredictorNamesname-value pair argument.

Data Types:single|double

Name-Value Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN．

Example:“克恩elFunction','gaussian','Standardize',true,'CrossVal','on'trains a 10-fold cross-validated SVM regression model using a Gaussian kernel and standardized training data.

Note

You cannot use any cross-validation name-value argument together with the'OptimizeHyperparameters'name-value argument. You can modify the cross-validation for'OptimizeHyperparameters'only by using the'HyperparameterOptimizationOptions'name-value argument.

Support Vector Machine Options

collapse all

`BoxConstraint`—Box constraint
positive scalar value

Box constraint for the alpha coefficients, specified as the comma-separated pair consisting of'BoxConstraint'and a positive scalar value.

The absolute value of theAlphacoefficients cannot exceed the value ofBoxConstraint．

The defaultBoxConstraintvalue for the'gaussian'or'rbf'kernel function isiqr(Y)/1.349, whereiqr(Y)is the interquartile range of response variableY．For all other kernels, the defaultBoxConstraintvalue is 1.

Example:BoxConstraint,10

Data Types:single|double

`KernelFunction`—Kernel function
`'linear'`(default) |`'gaussian'`|`'rbf'`|`'polynomial'`|功能ion name

Kernel function used to compute theGram matrix, specified as the comma-separated pair consisting of“克恩elFunction'and a value in this table.

Value Description Formula

Value	Description	Formula
`'gaussian'`or`'rbf'`	Gaussian or Radial Basis Function (RBF) kernel	$G (x_{j}, x_{k}) = \exp (- {‖ x_{j} - x_{k} ‖}^{2})$
`'linear'`	Linear kernel	$G (x_{j}, x_{k}) = x_{j}' x_{k}$
`'polynomial'`	Polynomial kernel. Use`'PolynomialOrder',q`to specify a polynomial kernel of order`q`．	$G (x_{j}, x_{k}) = {(1 + x_{j}' x_{k})}^{q}$

'gaussian'or'rbf'

Gaussian or Radial Basis Function (RBF) kernel

$G (x_{j}, x_{k}) = \exp (- {‖ x_{j} - x_{k} ‖}^{2})$

'linear'

Linear kernel

$G (x_{j}, x_{k}) = x_{j}' x_{k}$

'polynomial'

Polynomial kernel. Use'PolynomialOrder',qto specify a polynomial kernel of orderq．

$G (x_{j}, x_{k}) = {(1 + x_{j}' x_{k})}^{q}$

You can set your own kernel function, for example,kernel, by setting“克恩elFunction','kernel'．kernelmust have the following form:

功能ionG = kernel(U,V)

where:

Uis anm-by-pmatrix.
Vis ann-by-pmatrix.
Gis anm-by-nGram matrix of the rows ofUandV．

Andkernel.mmust be on the MATLAB path.

It is good practice to avoid using generic names for kernel functions. For example, call a sigmoid kernel function'mysigmoid'rather than'sigmoid'．

Example:“克恩elFunction','gaussian'

Data Types:char|string

`KernelScale`—Kernel scale parameter
`1`(default) |`'auto'`|positive scalar

Kernel scale parameter, specified as the comma-separated pair consisting of“克恩elScale'and'auto'or a positive scalar. The software divides all elements of the predictor matrixXby the value ofKernelScale．Then, the software applies the appropriate kernel norm to compute the Gram matrix.

If you specify'auto', then the software selects an appropriate scale factor using a heuristic procedure. This heuristic procedure uses subsampling, so estimates can vary from one call to another. Therefore, to reproduce results, set a random number seed usingrngbefore training.
If you specifyKernelScaleand your own kernel function, for example,“克恩elFunction','kernel', then the software throws an error. You must apply scaling withinkernel．

Example:“克恩elScale','auto'

Data Types:double|single|char|string

`PolynomialOrder`—Polynomial kernel function order
`3`(default) |positive integer

Polynomial kernel function order, specified as the comma-separated pair consisting of'PolynomialOrder'and a positive integer.

If you set'PolynomialOrder'andKernelFunctionis not'polynomial', then the software throws an error.

Example:'PolynomialOrder',2

Data Types:double|single

`KernelOffset`—Kernel offset parameter
nonnegative scalar

Kernel offset parameter, specified as the comma-separated pair consisting of“克恩elOffset'and a nonnegative scalar.

The software addsKernelOffsetto each element of the Gram matrix.

The defaults are:

0if the solver is SMO (that is, you set'Solver','SMO')
0.1if the solver is ISDA (that is, you set'Solver','ISDA')

Example:“克恩elOffset',0

Data Types:double|single

`Epsilon`—Half the width of epsilon-insensitive band
`iqr(Y)/13.49`(default) |nonnegative scalar value

Half the width of the epsilon-insensitive band, specified as the comma-separated pair consisting of'Epsilon'and a nonnegative scalar value.

The defaultEpsilonvalue isiqr(Y)/13.49, which is an estimate of a tenth of the standard deviation using the interquartile range of the response variableY．Ifiqr(Y)is equal to zero, then the defaultEpsilonvalue is 0.1.

Example:'Epsilon',0.3

Data Types:single|double

`Standardize`—Flag to standardize predictor data
`false`(default) |`true`

Flag to standardize the predictor data, specified as the comma-separated pair consisting of'Standardize'andtrue(1) orfalse(0)．

If you set'Standardize',true:

The software centers and scales each column of the predictor data (X) by the weighted column mean and standard deviation, respectively (for details on weighted standardizing, seeAlgorithms). MATLAB does not standardize the data contained in the dummy variable columns generated for categorical predictors.
The software trains the model using the standardized predictor matrix, but stores the unstandardized data in the model propertyX．

Example:'Standardize',true

Data Types:logical

`Solver`—Optimization routine
`'ISDA'`|`'L1QP'`|`'SMO'`

Optimization routine, specified as the comma-separated pair consisting of'Solver'and a value in this table.

Value	Description
`'ISDA'`	Iterative Single Data Algorithm (see[30])
`'L1QP'`	Uses`quadprog`(Optimization Toolbox)to implementL1通过二次programmin soft-margin最小化g. This option requires an Optimization Toolbox™ license. For more details, seeQuadratic Programming Definition(Optimization Toolbox)．
`'SMO'`	Sequential Minimal Optimization (see[17])

The defaults are:

'ISDA'if you set'OutlierFraction'to a positive value
'SMO'otherwise

Example:'Solver','ISDA'

`Alpha`—Initial estimates of alpha coefficients
numeric vector

Initial estimates of alpha coefficients, specified as the comma-separated pair consisting of'Alpha'and a numeric vector. The length ofAlphamust be equal to the number of rows ofX．

Each element ofAlphacorresponds to an observation inX．
Alphacannot contain anyNaNs.
If you specifyAlphaand any one of the cross-validation name-value pair arguments ('CrossVal','CVPartition','Holdout','KFold', or'Leaveout'), then the software returns an error.

IfYcontains any missing values, then remove all rows ofY,X, andAlphathat correspond to the missing values. That is, enter:

idx = ~isnan(Y); Y = Y(idx); X = X(idx,:); alpha = alpha(idx);

Then, passY,X, andalphaas the response, predictors, and initial alpha estimates, respectively.

The default iszeros(size(Y,1))．

Example:'Alpha',0.1*ones(size(X,1),1)

Data Types:single|double

`CacheSize`—缓存大小
`1000`(default) |`'maximal'`|positive scalar

缓存大小, specified as the comma-separated pair consisting of'CacheSize'and'maximal'or a positive scalar.

IfCacheSizeis'maximal', then the software reserves enough memory to hold the entiren-by-nGram matrix．

IfCacheSizeis a positive scalar, then the software reservesCacheSizemegabytes of memory for training the model.

Example:'CacheSize','maximal'

Data Types:double|single|char|string

`ClipAlphas`—Flag to clip alpha coefficients
`true`(default) |`false`

Flag to clip alpha coefficients, specified as the comma-separated pair consisting of'ClipAlphas'and eithertrueorfalse．

Suppose that the alpha coefficient for observationjisα_jand the box constraint of observationjisC_j,j= 1,...,n, wherenis the training sample size.

Value	Description
`true`	At each iteration, ifα_jis near 0 or nearC_j, then MATLAB setsα_jto 0 or toC_j, respectively.
`false`	MATLAB does not change the alpha coefficients during optimization.

MATLAB stores the final values ofαin theAlphaproperty of the trained SVM model object.

ClipAlphascan affect SMO and ISDA convergence.

Example:'ClipAlphas',false

Data Types:logical

`NumPrint`—Number of iterations between optimization diagnostic message output
`1000`(default) |nonnegative integer

Number of iterations between optimization diagnostic message output, specified as the comma-separated pair consisting of'NumPrint'和一个非负整数。

If you specify'Verbose',1and'NumPrint',numprint, then the software displays all optimization diagnostic messages from SMO and ISDA everynumprint它erations in the Command Window.

Example:'NumPrint',500

Data Types:double|single

`OutlierFraction`—Expected proportion of outliers in training data
0(default) |numeric scalar in the interval [0,1)

Expected proportion of outliers in training data, specified as the comma-separated pair consisting of'OutlierFraction'and a numeric scalar in the interval [0,1).fitrsvm再保险moves observations with large gradients, ensuring thatfitrsvm再保险moves the fraction of observations specified byOutlierFractionby the time convergence is reached. This name-value pair is only valid when'Solver'is'ISDA'．

Example:'OutlierFraction',0.1

Data Types:single|double

`RemoveDuplicates`—Flag to replace duplicate observations with single observations
`false`(default) |`true`

Flag to replace duplicate observations with single observations in the training data, specified as the comma-separated pair consisting of'RemoveDuplicates'andtrueorfalse．

IfRemoveDuplicatesistrue, thenfitrsvm再保险places duplicate observations in the training data with a single observation of the same value. The weight of the single observation is equal to the sum of the weights of the corresponding removed duplicates (seeWeights).

Tip

If your data set contains many duplicate observations, then specifying'RemoveDuplicates',truecan decrease convergence time considerably.

Data Types:logical

`Verbose`—Verbosity level
`0`(default) |`1`|`2`

Verbosity level, specified as the comma-separated pair consisting of'Verbose'and0,1, or2．The value ofVerbosecontrols the amount of optimization information that the software displays in the Command Window and saves the information as a structure toMdl.ConvergenceInfo.History．

This table summarizes the available verbosity level options.

Value	Description
`0`	The software does not display or save convergence information.
`1`	The software displays diagnostic messages and saves convergence criteria every`numprint`它erations, where`numprint`is the value of the name-value pair argument`'NumPrint'`．
`2`	The software displays diagnostic messages and saves convergence criteria at every iteration.

Example:'Verbose',1

Data Types:double|single

Other Regression Options

collapse all

`CategoricalPredictors`—Categorical predictors list
vector of positive integers|logical vector|character matrix|string array|cell array of character vectors|`'all'`

Categorical predictors list, specified as one of the values in this table.

Value	Description
Vector of positive integers	Each entry in the vector is an index value indicating that the corresponding predictor is categorical. The index values are between 1 and`p`, where`p`is the number of predictors used to train the model. If`fitrsvm`uses a subset of input variables as predictors, then the function indexes the predictors using only the subset. The`CategoricalPredictors`values do not count the response variable, observation weight variable, or any other variables that the function does not use.
逻辑向量	A`true`entry means that the corresponding predictor is categorical. The length of the vector is`p`．
Character matrix	Each row of the matrix is the name of a predictor variable. The names must match the entries in`PredictorNames`．Pad the names with extra blanks so each row of the character matrix has the same length.
String array or cell array of character vectors	Each element in the array is the name of a predictor variable. The names must match the entries in`PredictorNames`．
`"all"`	All predictors are categorical.

By default, if the predictor data is in a table (Tbl),fitrsvmassumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If the predictor data is a matrix (X),fitrsvmassumes that all predictors are continuous. To identify any other predictors as categorical predictors, specify them by using the'CategoricalPredictors'name-value argument.

For the identified categorical predictors,fitrsvmcreates dummy variables using two different schemes, depending on whether a categorical variable is unordered or ordered. For an unordered categorical variable,fitrsvmcreates one dummy variable for each level of the categorical variable. For an ordered categorical variable,fitrsvmcreates one less dummy variable than the number of categories. For details, seeAutomatic Creation of Dummy Variables．

Example:'CategoricalPredictors','all'

`PredictorNames`—Predictor variable names
string array of unique names|cell array of unique character vectors

Predictor variable names, specified as a string array of unique names or cell array of unique character vectors. The functionality ofPredictorNamesdepends on the way you supply the training data.

If you supplyXandY, then you can usePredictorNamesto assign names to the predictor variables inX．
- The order of the names inPredictorNamesmust correspond to the column order ofX．That is,PredictorNames{1}is the name ofX(:,1),PredictorNames{2}is the name ofX(:,2), and so on. Also,size(X,2)andnumel(PredictorNames)must be equal.
- By default,PredictorNamesis{'x1','x2',...}．
If you supplyTbl, then you can usePredictorNamesto choose which predictor variables to use in training. That is,fitrsvmuses only the predictor variables inPredictorNamesand the response variable during training.
- PredictorNamesmust be a subset ofTbl.Properties.VariableNamesand cannot include the name of the response variable.
- By default,PredictorNamescontains the names of all predictor variables.
- A good practice is to specify the predictors for training using eitherPredictorNamesorformula, but not both.

Example:"PredictorNames",["SepalLength","SepalWidth","PetalLength","PetalWidth"]

Data Types:string|cell

`ResponseName`—Response variable name
`"Y"`(default) |character vector|string scalar

Response variable name, specified as a character vector or string scalar.

If you supplyY, then you can useResponseNameto specify a name for the response variable.
If you supplyResponseVarNameorformula, then you cannot useResponseName．

Example:"ResponseName","response"

Data Types:char|string

`ResponseTransform`—Response transformation
`'none'`(default) |功能ion handle

Response transformation, specified as either'none'or a function handle. The default is'none', which means@(y)y, or no transformation. For a MATLAB function or a function you define, use its function handle for the response transformation. The function handle must accept a vector (the original response values) and return a vector of the same size (the transformed response values).

Example:Suppose you create a function handle that applies an exponential transformation to an input vector by usingmyfunction = @(y)exp(y)．Then, you can specify the response transformation as'ResponseTransform',myfunction．

Data Types:char|string|功能ion_handle

`Weights`—Observation weights
`ones(size(X,1),1)`(default) |vector of numeric values

Observation weights, specified as the comma-separated pair consisting of'Weights'and a vector of numeric values. The size ofWeightsmust equal the number of rows inX．fitrsvmnormalizes the values ofWeightsto sum to 1.

Data Types:single|double

Cross-Validation Options

collapse all

`CrossVal`—Cross-validation flag
`'off'`(default) |`'on'`

Cross-validation flag, specified as the comma-separated pair consisting of'CrossVal'and either'on'or'off'．

If you specify'on', then the software implements 10-fold cross-validation.

To override this cross-validation setting, use one of these name-value pair arguments:CVPartition,Holdout,KFold, orLeaveout．To create a cross-validated model, you can use one cross-validation name-value pair argument at a time only.

Alternatively, you can cross-validate the model later using thecrossvalmethod.

Example:'CrossVal','on'

`CVPartition`—Cross-validation partition
`[]`(default) |`cvpartition`partition object

Cross-validation partition, specified as acvpartitionpartition object created bycvpartition．The partition object specifies the type of cross-validation and the indexing for the training and validation sets.

To create a cross-validated model, you can specify only one of these four name-value arguments:CVPartition,Holdout,KFold, orLeaveout．

Example:Suppose you create a random partition for 5-fold cross-validation on 500 observations by usingcvp = cvpartition(500,'KFold',5)．Then, you can specify the cross-validated model by using'CVPartition',cvp．

`Holdout`—Fraction of data for holdout validation
scalar value in the range (0,1)

Fraction of the data used for holdout validation, specified as a scalar value in the range (0,1). If you specify'Holdout',p, then the software completes these steps:

Randomly select and reservep*100% of the data as validation data, and train the model using the rest of the data.
Store the compact, trained model in theTrainedproperty of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments:CVPartition,Holdout,KFold, orLeaveout．

Example:'Holdout',0.1

Data Types:double|single

`KFold`—Number of folds
`10`(default) |positive integer value greater than 1

Number of folds to use in a cross-validated model, specified as a positive integer value greater than 1. If you specify'KFold',k, then the software completes these steps:

Randomly partition the data intoksets.
For each set, reserve the set as validation data, and train the model using the otherk– 1sets.
Store thekcompact, trained models in ak-by-1 cell vector in theTrainedproperty of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments:CVPartition,Holdout,KFold, orLeaveout．

Example:'KFold',5

Data Types:single|double

`Leaveout`—Leave-one-out cross-validation flag
`'off'`(default) |`'on'`

Leave-one-out cross-validation flag, specified as'on'or'off'．If you specify'Leaveout','on', then for each of thenobservations (wherenis the number of observations, excluding missing observations, specified in theNumObservationsproperty of the model), the software completes these steps:

Reserve the one observation as validation data, and train the model using the othern– 1 observations.
Store thencompact, trained models in ann-by-1 cell vector in theTrainedproperty of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments:CVPartition,Holdout,KFold, orLeaveout．

Example:'Leaveout','on'

Convergence Controls

collapse all

`DeltaGradientTolerance`—对梯度差异
0(default) |nonnegative scalar

对梯度差异between upper and lower violators obtained by SMO or ISDA, specified as the comma-separated pair consisting of'DeltaGradientTolerance'and a nonnegative scalar.

Example:'DeltaGradientTolerance',1e-4

Data Types:single|double

`GapTolerance`—Feasibility gap tolerance
`1e-3`(default) |nonnegative scalar

Feasibility gap tolerance obtained by SMO or ISDA, specified as the comma-separated pair consisting of'GapTolerance'and a nonnegative scalar.

IfGapToleranceis0, thenfitrsvmdoes not use this parameter to check convergence.

Example:'GapTolerance',1e-4

Data Types:single|double

`IterationLimit`—Maximal number of numerical optimization iterations
`1e6`(default) |positive integer

Maximal number of numerical optimization iterations, specified as the comma-separated pair consisting of'IterationLimit'and a positive integer.

The software returns a trained model regardless of whether the optimization routine successfully converges.Mdl.ConvergenceInfocontains convergence information.

Example:'IterationLimit',1e8

Data Types:double|single

`KKTTolerance`—Tolerance for KKT violation
0|nonnegative scalar value

Tolerance for Karush-Kuhn-Tucker (KKT) violation, specified as the comma-separated pair consisting of'KKTTolerance'and a nonnegative scalar value.

This name-value pair applies only if'Solver'is'SMO'or'ISDA'．

IfKKTToleranceis0, thenfitrsvmdoes not use this parameter to check convergence.

Example:'KKTTolerance',1e-4

Data Types:single|double

`ShrinkagePeriod`—Number of iterations between reductions of active set
`0`(default) |nonnegative integer

Number of iterations between reductions of the active set, specified as the comma-separated pair consisting of'ShrinkagePeriod'和一个非负整数。

If you set'ShrinkagePeriod',0, then the software does not shrink the active set.

Example:'ShrinkagePeriod',1000

Data Types:double|single

Hyperparameter Optimization

collapse all

`OptimizeHyperparameters`—Parameters to optimize
`'none'`(default) |`'auto'`|`'all'`|string array or cell array of eligible parameter names|vector of`optimizableVariable`objects

Parameters to optimize, specified as the comma-separated pair consisting of'OptimizeHyperparameters'and one of the following:

'none'— Do not optimize.
'auto'— Use{'BoxConstraint','KernelScale','Epsilon'}．
'all'— Optimize all eligible parameters.
String array or cell array of eligible parameter names.
Vector ofoptimizableVariableobjects, typically the output ofhyperparameters．

The optimization attempts to minimize the cross-validation loss (error) forfitrsvmby varying the parameters. To control the cross-validation type and other aspects of the optimization, use theHyperparameterOptimizationOptionsname-value pair.

Note

The values of'OptimizeHyperparameters'override any values you specify using other name-value arguments. For example, setting'OptimizeHyperparameters'to'auto'causesfitrsvmto optimize hyperparameters corresponding to the'auto'option and to ignore any specified values for the hyperparameters.

The eligible parameters forfitrsvmare:

BoxConstraint—fitrsvmsearches among positive values, by default log-scaled in the range[1e-3,1e3]．
KernelScale—fitrsvmsearches among positive values, by default log-scaled in the range[1e-3,1e3]．
Epsilon—fitrsvmsearches among positive values, by default log-scaled in the range[1e-3,1e2]*iqr(Y)/1.349．
KernelFunction—fitrsvmsearches among'gaussian','linear', and'polynomial'．
PolynomialOrder—fitrsvmsearches among integers in the range[2,4]．
Standardize—fitrsvmsearches among'true'and'false'．

Set nondefault parameters by passing a vector ofoptimizableVariableobjects that have nondefault values. For example,

loadcarsmallparams = hyperparameters('fitrsvm',[Horsepower,Weight],MPG); params(1).Range = [1e-4,1e6];

Passparamsas the value ofOptimizeHyperparameters．

By default, the iterative display appears at the command line, and plots appear according to the number of hyperparameters in the optimization. For the optimization and plots, the objective function islog(1 + cross-validation loss)．To control the iterative display, set theVerbosefield of the'HyperparameterOptimizationOptions'name-value argument. To control the plots, set theShowPlotsfield of the'HyperparameterOptimizationOptions'name-value argument.

For an example, seeOptimize SVM Regression．

Example:'OptimizeHyperparameters','auto'

`HyperparameterOptimizationOptions`—Options for optimization
structure

Options for optimization, specified as a structure. This argument modifies the effect of theOptimizeHyperparametersname-value argument. All fields in the structure are optional.

Field Name	Values	Default
`Optimizer`	`'bayesopt'`— Use Bayesian optimization. Internally, this setting calls`bayesopt`． `'gridsearch'`— Use grid search with`NumGridDivisions`values per dimension. `'randomsearch'`— Search at random among`MaxObjectiveEvaluations`points. `'gridsearch'`searches in a random order, using uniform sampling without replacement from the grid. After optimization, you can get a table in grid order by using the command`sortrows(Mdl.HyperparameterOptimizationResults)`．	`'bayesopt'`
`AcquisitionFunctionName`	`'expected-improvement-per-second-plus'` `'expected-improvement'` `'expected-improvement-plus'` `'expected-improvement-per-second'` `'lower-confidence-bound'` `'probability-of-improvement'` Acquisition functions whose names include`per-second`do not yield reproducible results because the optimization depends on the runtime of the objective function. Acquisition functions whose names include`plus`modify their behavior when they are overexploiting an area. For more details, seeAcquisition Function Types．	`'expected-improvement-per-second-plus'`
`MaxObjectiveEvaluations`	Maximum number of objective function evaluations.	`30`for`'bayesopt'`and`'randomsearch'`, and the entire grid for`'gridsearch'`
`MaxTime`	Time limit, specified as a positive real scalar. The time limit is in seconds, as measured by`tic`and`toc`．The run time can exceed`MaxTime`because`MaxTime`does not interrupt function evaluations.	`Inf`
`NumGridDivisions`	For`'gridsearch'`, the number of values in each dimension. The value can be a vector of positive integers giving the number of values for each dimension, or a scalar that applies to all dimensions. This field is ignored for categorical variables.	`10`
`ShowPlots`	Logical value indicating whether to show plots. If`true`, this field plots the best observed objective function value against the iteration number. If you use Bayesian optimization (`Optimizer`is`'bayesopt'`), then this field also plots the best estimated objective function value. The best observed objective function values and best estimated objective function values correspond to the values in the`BestSoFar (observed)`and`BestSoFar (estim.)`columns of the iterative display, respectively. You can find these values in the properties`ObjectiveMinimumTrace`and`EstimatedObjectiveMinimumTrace`of`Mdl.HyperparameterOptimizationResults`．If the problem includes one or two optimization parameters for Bayesian optimization, then`ShowPlots`also plots a model of the objective function against the parameters.	`true`
`SaveIntermediateResults`	Logical value indicating whether to save results when`Optimizer`is`'bayesopt'`．If`true`, this field overwrites a workspace variable named`'BayesoptResults'`at each iteration. The variable is a`BayesianOptimization`object.	`false`
`Verbose`	Display at the command line: `0`— No iterative display `1`— Iterative display `2`— Iterative display with extra information For details, see the`bayesoptVerbose`name-value argument and the exampleOptimize Classifier Fit Using Bayesian Optimization．	`1`
`UseParallel`	Logical value indicating whether to run Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, seeParallel Bayesian Optimization．	`false`
`Repartition`	Logical value indicating whether to repartition the cross-validation at every iteration. If this field is`false`, the optimizer uses a single partition for the optimization. The setting`true`usually gives the most robust results because it takes partitioning noise into account. However, for good results,`true`再保险quires at least twice as many function evaluations.	`false`
Use no more than one of the following three options.
`CVPartition`	A`cvpartition`object, as created by`cvpartition`	`'Kfold',5`if you do not specify a cross-validation field
`Holdout`	A scalar in the range`(0,1)`再保险presenting the holdout fraction
`Kfold`	An integer greater than 1

Example:'HyperparameterOptimizationOptions',struct('MaxObjectiveEvaluations',60)

Data Types:struct

Output Arguments

collapse all

`Mdl`— Trained SVM regression model
`RegressionSVM`model |`RegressionPartitionedSVM`cross-validated model

Trained SVM regression model, returned as aRegressionSVMmodel orRegressionPartitionedSVMcross-validated model.

If you set any of the name-value pair argumentsKFold,Holdout,Leaveout,CrossVal, orCVPartition, thenMdlis aRegressionPartitionedSVMcross-validated model. Otherwise,Mdlis aRegressionSVMmodel.

Limitations

fitrsvmsupports low- through moderate-dimensional data sets. For high-dimensional data set, usefitrlinearinstead.

Tips

Unless your data set is large, always try to standardize the predictors (seeStandardize). Standardization makes predictors insensitive to the scales on which they are measured.
It is good practice to cross-validate using theKFoldname-value pair argument. The cross-validation results determine how well the SVM model generalizes.
Sparsity in support vectors is a desirable property of an SVM model. To decrease the number of support vectors, set theBoxConstraintname-value pair argument to a large value. This action also increases the training time.
For optimal training time, setCacheSizeas high as the memory limit on your computer allows.
If you expect many fewer support vectors than observations in the training set, then you can significantly speed up convergence by shrinking the active-set using the name-value pair argument'ShrinkagePeriod'．It is good practice to use'ShrinkagePeriod',1000．
Duplicate observations that are far from the regression line do not affect convergence. However, just a few duplicate observations that occur near the regression line can slow down convergence considerably. To speed up convergence, specify'RemoveDuplicates',trueif:
- Your data set contains many duplicate observations.
- You suspect that a few duplicate observations can fall near the regression line.
However, to maintain the original data set during training,fitrsvmmust temporarily store separate data sets: the original and one without the duplicate observations. Therefore, if you specifytruefor data sets containing few duplicates, thenfitrsvmconsumes close to double the memory of the original data.
After training a model, you can generate C/C++ code that predicts responses for new data. Generating C/C++ code requiresMATLAB Coder™．For details, seeIntroduction to Code Generation．

Algorithms

For the mathematical formulation of linear and nonlinear SVM regression problems and the solver algorithms, see理解支持矢量金宝apptor Machine Regression．
NaN,, empty character vector (''), empty string (""), andvalues indicate missing data values.fitrsvm再保险moves entire rows of data corresponding to a missing response. When normalizing weights,fitrsvmignores any weight corresponding to an observation with at least one missing predictor. Consequently, observation box constraints might not equalBoxConstraint．
fitrsvm再保险moves observations that have zero weight.
If you set'Standardize',trueand'Weights', thenfitrsvmstandardizes the predictors using their corresponding weighted means and weighted standard deviations. That is,fitrsvmstandardizes predictorj(x_j) using

$x_{j}^{*} = \frac{x_{j} - μ_{j}^{*}}{σ_{j}^{*}} ．$
- $μ_{j}^{*} = \frac{1}{\sum_{k} w_{k}} \sum_{k} w_{k} x_{j k} ．$
- x_jkis observationk(row) of predictorj(column).
- ${(σ_{j}^{*})}^{2} = \frac{v_{1}}{v_{1}^{2} - v_{2}} \sum_{k} w_{k} {(x_{j k} - μ_{j}^{*})}^{2} ．$
- $v_{1} = \sum_{j} w_{j} ．$
- $v_{2} = \sum_{j} {(w_{j})}^{2} ．$
If your predictor data contains categorical variables, then the software generally uses full dummy encoding for these variables. The software creates one dummy variable for each level of each categorical variable.
- ThePredictorNamesproperty stores one element for each of the original predictor variable names. For example, assume that there are three predictors, one of which is a categorical variable with three levels. ThenPredictorNamesis a 1-by-3 cell array of character vectors containing the original names of the predictor variables.
- TheExpandedPredictorNamesproperty stores one element for each of the predictor variables, including the dummy variables. For example, assume that there are three predictors, one of which is a categorical variable with three levels. ThenExpandedPredictorNamesis a 1-by-5 cell array of character vectors containing the names of the predictor variables and the new dummy variables.
- Similarly, theBetaproperty stores one beta coefficient for each predictor, including the dummy variables.
- TheSupportVectorsproperty stores the predictor values for the support vectors, including the dummy variables. For example, assume that there aremsupport vectors and three predictors, one of which is a categorical variable with three levels. ThenSupportVectorsis anm-by-5 matrix.
- TheXproperty stores the training data as originally input. It does not include the dummy variables. When the input is a table,Xcontains only the columns used as predictors.
For predictors specified in a table, if any of the variables contain ordered (ordinal) categories, the software uses ordinal encoding for these variables.
- For a variable havingkordered levels, the software createsk– 1dummy variables. Thejth dummy variable is-1for levels up toj, and+1for levelsj+ 1throughk．
- The names of the dummy variables stored in theExpandedPredictorNamesproperty indicate the first level with the value+1．The software storesk– 1additional predictor names for the dummy variables, including the names of levels 2, 3, ...,k．

All solvers implementL1 soft-margin minimization.
Letpbe the proportion of outliers that you expect in the training data. If you set'OutlierFraction',p, then the software implementsrobust learning．In other words, the software attempts to remove 100p% of the observations when the optimization algorithm converges. The removed observations correspond to gradients that are large in magnitude.

References

[1] Clark, D., Z. Schreter, A. Adams. "A Quantitative Comparison of Dystal and Backpropagation." submitted to the Australian Conference on Neural Networks, 1996.

[2] Fan, R.-E., P.-H. Chen, and C.-J. Lin. “Working set selection using second order information for training support vector machines.”Journal of Machine Learning Research, Vol 6, 2005, pp. 1889–1918.

[3] Kecman V., T. -M. Huang, and M. Vogt. “Iterative Single Data Algorithm for Training Kernel Machines from Huge Data Sets: Theory and Performance.” InSupport Vector Machines: Theory and Applications．Edited by Lipo Wang, 255–274. Berlin: Springer-Verlag, 2005.

[4] Lichman, M.UCI Machine Learning Repository, [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

[5] Nash, W.J., T. L. Sellers, S. R. Talbot, A. J. Cawthorn, and W. B. Ford. "The Population Biology of Abalone (Haliotisspecies) in Tasmania. I. Blacklip Abalone (H. rubra) from the North Coast and Islands of Bass Strait." Sea Fisheries Division, Technical Report No. 48, 1994.

[6] Waugh, S. "Extending and Benchmarking Cascade-Correlation: Extensions to the Cascade-Correlation Architecture and Benchmarking of Feed-forward Supervised Artificial Neural Networks."University of Tasmania Department of Computer Science thesis, 1995.

Extended Capabilities

Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To perform parallel hyperparameter optimization, use the'HyperparameterOptimizationOptions', struct('UseParallel',true)name-value argument in the call to thefitrsvm功能ion.

For more information on parallel hyperparameter optimization, seeParallel Bayesian Optimization．

For general information about parallel computing, seeRun MATLAB Functions with Automatic Parallel Support(Parallel Computing Toolbox)．

fitrsvm

Syntax

Description

Examples

Train Linear Support Vector Machine Regression Model

Train Support Vector Machine Regression Model

Cross-Validate SVM Regression Model

Optimize SVM Regression

Input Arguments

Tbl—Predictor datatable

ResponseVarName—Response variable namename of variable inTbl

formula—Explanatory model of response variable and subset of predictor variablescharacter vector|string scalar

Y—Response datanumeric vector

X—Predictor datanumeric matrix

Name-Value Arguments

BoxConstraint—Box constraintpositive scalar value

KernelFunction—Kernel function'linear'(default) |'gaussian'|'rbf'|'polynomial'|功能ion name

KernelScale—Kernel scale parameter1(default) |'auto'|positive scalar

PolynomialOrder—Polynomial kernel function order3(default) |positive integer

KernelOffset—Kernel offset parameternonnegative scalar

Epsilon—Half the width of epsilon-insensitive bandiqr(Y)/13.49(default) |nonnegative scalar value

Standardize—Flag to standardize predictor datafalse(default) |true

Solver—Optimization routine'ISDA'|'L1QP'|'SMO'

Alpha—Initial estimates of alpha coefficientsnumeric vector

CacheSize—缓存大小1000(default) |'maximal'|positive scalar

ClipAlphas—Flag to clip alpha coefficientstrue(default) |false

NumPrint—Number of iterations between optimization diagnostic message output1000(default) |nonnegative integer

OutlierFraction—Expected proportion of outliers in training data0(default) |numeric scalar in the interval [0,1)

RemoveDuplicates—Flag to replace duplicate observations with single observationsfalse(default) |true

Verbose—Verbosity level0(default) |1|2

CategoricalPredictors—Categorical predictors listvector of positive integers|logical vector|character matrix|string array|cell array of character vectors|'all'

PredictorNames—Predictor variable namesstring array of unique names|cell array of unique character vectors

ResponseName—Response variable name"Y"(default) |character vector|string scalar

ResponseTransform—Response transformation'none'(default) |功能ion handle

Weights—Observation weightsones(size(X,1),1)(default) |vector of numeric values

CrossVal—Cross-validation flag'off'(default) |'on'

CVPartition—Cross-validation partition[](default) |cvpartitionpartition object

Holdout—Fraction of data for holdout validationscalar value in the range (0,1)

KFold—Number of folds10(default) |positive integer value greater than 1

Leaveout—Leave-one-out cross-validation flag'off'(default) |'on'

DeltaGradientTolerance—对梯度差异0(default) |nonnegative scalar

GapTolerance—Feasibility gap tolerance1e-3(default) |nonnegative scalar

IterationLimit—Maximal number of numerical optimization iterations1e6(default) |positive integer

KKTTolerance—Tolerance for KKT violation0|nonnegative scalar value

ShrinkagePeriod—Number of iterations between reductions of active set0(default) |nonnegative integer

OptimizeHyperparameters—Parameters to optimize'none'(default) |'auto'|'all'|string array or cell array of eligible parameter names|vector ofoptimizableVariableobjects

HyperparameterOptimizationOptions—Options for optimizationstructure

Output Arguments

Mdl— Trained SVM regression modelRegressionSVMmodel |RegressionPartitionedSVMcross-validated model

Limitations

Tips

Algorithms

References

Extended Capabilities

Automatic Parallel SupportAccelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

See Also

Topics

Statistics and Machine Learning Toolbox Documentation

金宝app

Mastering Machine Learning: A Step-by-Step Guide with MATLAB

`Tbl`—Predictor data
table

`ResponseVarName`—Response variable name
name of variable in`Tbl`

`formula`—Explanatory model of response variable and subset of predictor variables
character vector|string scalar

`Y`—Response data
numeric vector

`X`—Predictor data
numeric matrix

`BoxConstraint`—Box constraint
positive scalar value

`KernelFunction`—Kernel function
`'linear'`(default) |`'gaussian'`|`'rbf'`|`'polynomial'`|功能ion name

`KernelScale`—Kernel scale parameter
`1`(default) |`'auto'`|positive scalar

`PolynomialOrder`—Polynomial kernel function order
`3`(default) |positive integer

`KernelOffset`—Kernel offset parameter
nonnegative scalar

`Epsilon`—Half the width of epsilon-insensitive band
`iqr(Y)/13.49`(default) |nonnegative scalar value

`Standardize`—Flag to standardize predictor data
`false`(default) |`true`

`Solver`—Optimization routine
`'ISDA'`|`'L1QP'`|`'SMO'`

`Alpha`—Initial estimates of alpha coefficients
numeric vector

`CacheSize`—缓存大小
`1000`(default) |`'maximal'`|positive scalar

`ClipAlphas`—Flag to clip alpha coefficients
`true`(default) |`false`

`NumPrint`—Number of iterations between optimization diagnostic message output
`1000`(default) |nonnegative integer

`OutlierFraction`—Expected proportion of outliers in training data
0(default) |numeric scalar in the interval [0,1)

`RemoveDuplicates`—Flag to replace duplicate observations with single observations
`false`(default) |`true`

`Verbose`—Verbosity level
`0`(default) |`1`|`2`

`CategoricalPredictors`—Categorical predictors list
vector of positive integers|logical vector|character matrix|string array|cell array of character vectors|`'all'`

`PredictorNames`—Predictor variable names
string array of unique names|cell array of unique character vectors

`ResponseName`—Response variable name
`"Y"`(default) |character vector|string scalar

`ResponseTransform`—Response transformation
`'none'`(default) |功能ion handle

`Weights`—Observation weights
`ones(size(X,1),1)`(default) |vector of numeric values

`CrossVal`—Cross-validation flag
`'off'`(default) |`'on'`

`CVPartition`—Cross-validation partition
`[]`(default) |`cvpartition`partition object

`Holdout`—Fraction of data for holdout validation
scalar value in the range (0,1)

`KFold`—Number of folds
`10`(default) |positive integer value greater than 1

`Leaveout`—Leave-one-out cross-validation flag
`'off'`(default) |`'on'`

`DeltaGradientTolerance`—对梯度差异
0(default) |nonnegative scalar

`GapTolerance`—Feasibility gap tolerance
`1e-3`(default) |nonnegative scalar

`IterationLimit`—Maximal number of numerical optimization iterations
`1e6`(default) |positive integer

`KKTTolerance`—Tolerance for KKT violation
0|nonnegative scalar value

`ShrinkagePeriod`—Number of iterations between reductions of active set
`0`(default) |nonnegative integer

`OptimizeHyperparameters`—Parameters to optimize
`'none'`(default) |`'auto'`|`'all'`|string array or cell array of eligible parameter names|vector of`optimizableVariable`objects

`HyperparameterOptimizationOptions`—Options for optimization
structure

`Mdl`— Trained SVM regression model
`RegressionSVM`model |`RegressionPartitionedSVM`cross-validated model

Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.