edge
Find classification edge for support vector machine (SVM) classifier
Syntax
Description
returns the classification edge
(e
= edge(SVMModel
,Tbl
,ResponseVarName
)e
) for the support vector machine (SVM) classifier
SVMModel
using the predictor data in table
Tbl
and the class labels in
Tbl.ResponseVarName
.
The classification edge (e
) is a scalar value that
represents the weighted mean of the classification
margins.
returns the classification edge
(e
= edge(SVMModel
,Tbl
,Y
)e
) for the SVM classifier SVMModel
using the predictor data in table Tbl
and the class labels
in Y
.
computes the classification edge for the observation weights supplied in
e
= edge(___,'Weights'
,weights
)weights
using any of the input arguments in the
previous syntaxes.
Note
If the predictor data X
or the predictor variables in
Tbl
contain any missing values, the
edge
function can return NaN. For more
details, see edge can return NaN for predictor data with missing values.
Examples
Estimate Test Sample Edge of SVM Classifiers
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.
Estimate the test sample edge.
e = edge(CompactSVMModel,XTest,YTest)
e = 5.0766
The margin average of the test sample is approximately 5.
Estimate Test Sample Weighted Margin Mean of SVM Classifiers
Suppose that the observations in a data set are measured sequentially, and that the last 150 observations have better quality due to a technology upgrade. Incorporate this advancement by weighing the better quality observations more than the other observations.
Load the ionosphere
data set.
load ionosphere rng(1); % For reproducibility
Define a weight vector that weighs the better quality observations two times the other observations.
n = size(X,1); weights = [ones(n-150,1);2*ones(150,1)];
Train an SVM classifier. Specify the weighting scheme and a 15% holdout sample for testing. Also, standardize the data and specify that 'g'
is the positive class.
CVSVMModel = fitcsvm(X,Y,'Weights',weights,'Holdout',0.15,... 'ClassNames',{'b','g'},'Standardize',true); CompactSVMModel = CVSVMModel.Trained{1}; testInds = test(CVSVMModel.Partition); % Extract the test indices XTest = X(testInds,:); YTest = Y(testInds,:); wTest = weights(testInds,:);
CVSVMModel
is a trained 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.
Estimate the test sample weighted edge using the weighting scheme.
e = edge(CompactSVMModel,XTest,YTest,'Weights',wTest)
e = 4.8340
The weighted average margin of the test sample is approximately 5.
Select SVM Classifier Features by Comparing Test Sample Edges
Perform feature selection by comparing test sample edges from multiple models. Based solely on this comparison, the classifier with the highest edge is the best classifier.
Load the ionosphere
data set.
load ionosphere rng(1); % For reproducibility
Partition the data set into training and test sets. Specify a 15% holdout sample for testing.
Partition = cvpartition(Y,'Holdout',0.15); testInds = test(Partition); % Indices for the test set XTest = X(testInds,:); YTest = Y(testInds,:);
Partition
defines the data set partition.
Define these two data sets:
fullX
contains all predictors (except the removed column of 0s).partX
contains the last 20 predictors.
fullX = X; partX = X(:,end-20:end);
Train SVM classifiers for each predictor set. Specify the partition definition.
FullCVSVMModel = fitcsvm(fullX,Y,'CVPartition',Partition); PartCVSVMModel = fitcsvm(partX,Y,'CVPartition',Partition); FCSVMModel = FullCVSVMModel.Trained{1}; PCSVMModel = PartCVSVMModel.Trained{1};
FullCVSVMModel
and PartCVSVMModel
are ClassificationPartitionedModel
classifiers. They contain the property Trained
, which is a 1-by-1 cell array holding a CompactClassificationSVM
classifier that the software trained using the training set.
Estimate the test sample edge for each classifier.
fullEdge = edge(FCSVMModel,XTest,YTest)
fullEdge = 2.8319
partEdge = edge(PCSVMModel,XTest(:,end-20:end),YTest)
partEdge = 1.5542
The edge for the classifier trained on the complete data set is greater, suggesting that the classifier trained with all the predictors is better.
Input Arguments
SVMModel
— SVM classification model
ClassificationSVM
model object | CompactClassificationSVM
model object
SVM classification model, specified as a ClassificationSVM
model object or CompactClassificationSVM
model object returned by fitcsvm
or compact
,
respectively.
Tbl
— Sample data
table
Sample data used to train the model, 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 of the
predictors used to train SVMModel
.
Multicolumn variables and cell arrays other than cell arrays of
character vectors are not allowed.
If Tbl
contains the response variable used to
train SVMModel
, then you do not need to
specify ResponseVarName
or
Y
.
If you trained SVMModel
using sample data
contained in a table, then the input data for
edge
must also be in a
table.
If you set 'Standardize',true
in fitcsvm
when training SVMModel
, then the software
standardizes the columns of the predictor data using the
corresponding means in SVMModel.Mu
and the
standard deviations in SVMModel.Sigma
.
Data Types: table
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix.
Each row of X
corresponds to one observation (also known as an instance
or example), and each column corresponds to one variable (also known as a feature). The
variables in the columns of X
must be the same as the variables
that trained the SVMModel
classifier.
The length of Y
and the number of rows in X
must be
equal.
If you set 'Standardize',true
in fitcsvm
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: double
| single
ResponseVarName
— Response variable name
name of variable in Tbl
Response variable name, specified as the name of a variable in
Tbl
. If Tbl
contains the response variable
used to train SVMModel
, then you do not need to specify
ResponseVarName
.
If you specify ResponseVarName
, then you must do so as a character vector
or string scalar. For example, if the response variable is stored as
Tbl.Response
, then specify ResponseVarName
as
'Response'
. Otherwise, the software treats all columns of
Tbl
, including Tbl.Response
, as
predictors.
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.
Data Types: char
| string
Y
— Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
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
SVMModel.ClassNames
. (The software treats string arrays as cell arrays of character
vectors.)
The length of Y
must equal the number of rows in Tbl
or the number of rows in X
.
weights
— Observation weights
ones(size(X,1),1)
(default) | numeric vector | name of variable in Tbl
Observation weights, specified as a numeric vector or the name of a
variable in Tbl
.
If you specify weights
as a numeric vector, then the
size of weights
must be equal to the number of rows 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 weights
as 'W'
.
Otherwise, the software treats all columns of Tbl
,
including Tbl.W
, as predictors.
If you supply weights, edge
computes the weighted classification
edge. The software weights the observations in each row of
X
or Tbl
with the
corresponding weight in weights
.
Example: 'Weights','W'
Data Types: single
| double
| char
| string
More About
Classification Edge
The edge is the weighted mean of the classification margins.
The weights are the prior class probabilities. If you supply weights, then the software normalizes them to sum to the prior probabilities in the respective classes. The software uses the renormalized weights to compute the weighted mean.
One way to choose among multiple classifiers, for example, to perform feature selection, is to choose the classifier that yields the highest edge.
Classification Margin
The classification margin for binary classification is, for each observation, the difference between the classification score for the true class and the classification score for the false class.
The software defines the classification margin for binary classification as
x is an observation. If the true label of x is the positive class, then y is 1, and –1 otherwise. f(x) is the positive-class classification score for the observation x. The classification margin is commonly defined as m = yf(x).
If the margins are on the same scale, then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.
Classification Score
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 is the trained SVM classification function. is also the numerical predicted response for x, or the score for predicting x into the positive class.
where are the estimated SVM parameters, 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.
Algorithms
For binary classification, the software defines the margin for observation j, mj, as
where yj ∊ {-1,1}, and f(xj) is the predicted score of observation j for the positive class. However, mj = yjf(xj) is commonly used to define the margin.
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.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
edge
function fully supports tall arrays. For more information,
see Tall Arrays.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
The
edge
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 R2014aR2022a: edge
returns a different value for
a model with a nondefault cost matrix
If you specify a nondefault cost matrix when you train the input model object, the edge
function returns a different value compared to previous releases.
The edge
function uses the prior
probabilities stored in the Prior
property to normalize the observation
weights of the input data. The way the function uses the Prior
property
value has not changed. However, the property value stored in the input model object has changed
for a model with a nondefault cost matrix, so the function can return a different value.
For details about the property value change, see Cost property stores the user-specified cost matrix.
If you want the software to handle the cost matrix, prior
probabilities, and observation weights in the same way as in previous releases, adjust the prior
probabilities and observation weights for the nondefault cost matrix, as described in Adjust Prior Probabilities and Observation Weights for Misclassification Cost Matrix. Then, when you train a
classification model, specify the adjusted prior probabilities and observation weights by using
the Prior
and Weights
name-value arguments, respectively,
and use the default cost matrix.
R2022a: edge
can return NaN for predictor data with missing values
The edge
function no longer omits an observation with a
NaN score when computing the weighted mean of the classification margins. Therefore,
edge
can now return NaN when the predictor data
X
or the predictor variables in Tbl
contain any missing values. In most cases, if the test set observations do not contain
missing predictors, the edge
function does not return
NaN.
This change improves the automatic selection of a classification model when you use
fitcauto
.
Before this change, the software might select a model (expected to best classify new
data) with few non-NaN predictors.
If edge
in your code returns NaN, you can update your code
to avoid this result. Remove or replace the missing values by using rmmissing
or fillmissing
, respectively.
The following table shows the classification models for which the
edge
object function might return NaN. For more details,
see the Compatibility Considerations for each edge
function.
Model Type | Full or Compact Model Object | edge Object Function |
---|---|---|
Discriminant analysis classification model | ClassificationDiscriminant , CompactClassificationDiscriminant | edge |
Ensemble of learners for classification | ClassificationEnsemble , CompactClassificationEnsemble | edge |
Gaussian kernel classification model | ClassificationKernel | edge |
k-nearest neighbor classification model | ClassificationKNN | edge |
Linear classification model | ClassificationLinear | edge |
Neural network classification model | ClassificationNeuralNetwork , CompactClassificationNeuralNetwork | edge |
Support vector machine (SVM) classification model | edge |
See Also
ClassificationSVM
| CompactClassificationSVM
| loss
| predict
| margin
| resubEdge
| kfoldEdge
| fitcsvm
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