edge

Classification edge for Gaussian kernel classification model

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年代yntax

e = edge(Mdl,X,Y)

e = edge(Mdl,Tbl,ResponseVarName)

e = edge(Mdl,Tbl,Y)

e = edge(___,'Weights',weights)

Description

example

e= edge(Mdl,X,Y)returns theclassification edgefor the binary Gaussian kernel classification modelMdlusing the predictor data inXand the corresponding class labels inY.

e= edge(Mdl,Tbl,ResponseVarName)returns the classification edge for the trained kernel classifierMdlusing the predictor data in tableTbland the class labels inTbl.ResponseVarName.

e= edge(Mdl,Tbl,Y)returns the classification edge for the classifierMdlusing the predictor data in tableTbland the class labels in vectorY.

e= edge(___,“重量”,weights)returns the weighted classification edge using the observation weights supplied inweights. Specify the weights after any of the input argument combinations in previous syntaxes.

Note

If the predictor dataXor the predictor variables inTblcontain any missing values, theedgefunction can return NaN. For more details, seeedge can return NaN for predictor data with missing values.

Examples

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Estimate Test-Set Edge

Open Live Script

Load theionospheredata set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

loadionosphere

Partition the data set into training and test sets. Specify a 15% holdout sample for the test set.

rng('default')% For reproducibility分区= cvpartition (Y,'Holdout',0.15); trainingInds = training(Partition);% Indices for the training settestInds = test(Partition);% Indices for the test set

Train a binary kernel classification model using the training set.

Mdl = fitckernel(X(trainingInds,:),Y(trainingInds));

Estimate the training-set edge and the test-set edge.

eTrain = edge(Mdl,X(trainingInds,:),Y(trainingInds))

eTrain = 2.1703

eTest = edge(Mdl,X(testInds,:),Y(testInds))

eTest = 1.5643

Feature Selection Using Test-Set Edges

Open Live Script

Perform feature selection by comparing test-set edges from multiple models. Based solely on this criterion, the classifier with the highest edge is the best classifier.

Load theionospheredata set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b') or good ('g').

loadionosphere

Partition the data set into training and test sets. Specify a 15% holdout sample for the test set.

rng('default')% For reproducibility分区= cvpartition (Y,'Holdout',0.15); trainingInds = training(Partition);% Indices for the training setXTrain = X(trainingInds,:); YTrain = Y(trainingInds); testInds = test(Partition);% Indices for the test setXTest = X(testInds,:); YTest = Y(testInds);

Randomly choose half of the predictor variables.

p = size(X,2);% Number of predictorsidxPart = randsample(p,ceil(0.5*p));

Train two binary kernel classification models: one that uses all of the predictors, and one that uses half of the predictors.

Mdl = fitckernel(XTrain,YTrain); PMdl = fitckernel(XTrain(:,idxPart),YTrain);

MdlandPMdlareClassificationKernelmodels.

Estimate the test-set edge for each classifier.

fullEdge = edge(Mdl,XTest,YTest)

fullEdge = 1.6335

partEdge = edge(PMdl,XTest(:,idxPart),YTest)

partEdge = 2.0205

Based on the test-set edges, the classifier that uses half of the predictors is the better model.

Input Arguments

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`Mdl`—Binary kernel classification model
`ClassificationKernel`model object

Binary kernel classification model, specified as aClassificationKernelmodel object. You can create aClassificationKernelmodel object usingfitckernel.

`X`—Predictor data
n-by-pnumeric matrix

Predictor data, specified as ann-by-pnumeric matrix, wherenis the number of observations andpis the number of predictors used to trainMdl.

The length ofYand the number of observations inXmust be equal.

Data Types:single|double

`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.

The data type ofYmust be the same as the data type ofMdl.ClassNames.(The software treats string arrays as cell arrays of character vectors.)
The distinct classes inYmust be a subset ofMdl.ClassNames.
IfYis a character array, then each element must correspond to one row of the array.
The length ofYmust be equal to the number of observations inXorTbl.

`Tbl`—年代ample data
table

年代ample 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 additional columns for the response variable and observation weights.Tblmust contain all the predictors used to trainMdl. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

IfTblcontains the response variable used to trainMdl, then you do not need to specifyResponseVarNameorY.

If you trainMdlusing sample data contained in a table, then the input data foredgemust also be in a table.

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

Response variable name, specified as the name of a variable inTbl. IfTblcontains the response variable used to trainMdl, then you do not need to specifyResponseVarName.

If you specifyResponseVarName, then you must specify it as a character vector or string scalar. For example, if the response variable is stored asTbl.Y, then specifyResponseVarNameas'Y'. Otherwise, the software treats all columns ofTbl, includingTbl.Y, as predictors.

The response variable must be a categorical, character, or string array; a logical or numeric vector; or a 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

`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 inTbl.

Ifweightsis a numeric vector, then the size ofweights必须等于中的行数XorTbl.
Ifweightsis the name of a variable inTbl, you must specifyweightsas a character vector or string scalar. For example, if the weights are stored asTbl.W, then specifyweightsas'W'. Otherwise, the software treats all columns ofTbl, includingTbl.W, as predictors.

If you supply weights,edgecomputes the weightedclassification edge. The software weights the observations in each row ofXorTblwith the corresponding weights inweights.

edgenormalizesweightsto sum up to the value of the prior probability in the respective class.

Data Types:single|double|char|string

Output Arguments

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`e`— Classification edge
numeric scalar

Classification edge, returned as a numeric scalar.

More About

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Classification Edge

Theclassification edgeis the weighted mean of the classification margins.

One way to choose among multiple classifiers, for example to perform feature selection, is to choose the classifier that yields the greatest edge.

Classification Margin

Theclassification marginfor 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

$m = 2 y f (x) .$

xis an observation. If the true label ofxis the positive class, thenyis 1, and –1 otherwise.f(x) is the positive-class classification score for the observationx. The classification margin is commonly defined asm=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

For kernel classification models, the rawclassification scorefor classifying the observationx, a row vector, into the positive class is defined by

$f (x) = T (x) β + b .$

$T (\cdot)$ is a transformation of an observation for feature expansion.
βis the estimated column vector of coefficients.
bis the estimated scalar bias.

The raw classification score for classifyingxinto the negative class is−f(x). The software classifies observations into the class that yields a positive score.

If the kernel classification model consists of logistic regression learners, then the software applies the'logit'score transformation to the raw classification scores (see年代coreTransform).

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

edgedoes not support talltabledata.

For more information, seeTall Arrays.

Version History

Introduced in R2017b

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R2022a:`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, theedgefunction returns a different value compared to previous releases.

Theedgefunction uses the prior probabilities stored in thePriorproperty to normalize the observation weights of the input data. The way the function uses thePriorproperty 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, seeCost property stores the user-specified cost matrix.

If you want the software to handle the cost matrix, prior probabilities, and observation weights as in previous releases, adjust the prior probabilities and observation weights for the nondefault cost matrix, as described inAdjust 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 thePriorandWeightsname-value arguments, respectively, and use the default cost matrix.

R2022a:`edge`can return NaN for predictor data with missing values

Theedgefunction no longer omits an observation with a NaN score when computing the weighted mean of the classification margins. Therefore,edgecan now return NaN when the predictor dataXor the predictor variables inTblcontain any missing values. In most cases, if the test set observations do not contain missing predictors, theedgefunction does not return NaN.

This change improves the automatic selection of a classification model when you usefitcauto. Before this change, the software might select a model (expected to best classify new data) with few non-NaN predictors.

Ifedgein your code returns NaN, you can update your code to avoid this result. Remove or replace the missing values by usingrmmissingorfillmissing, respectively.

The following table shows the classification models for which theedgeobject function might return NaN. For more details, see the Compatibility Considerations for eachedgefunction.

Model Type	Full or Compact Model Object	`edge`Object Function
判别分析分类模el	`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`
年代upport vector machine (SVM) classification model	`ClassificationSVM`,`CompactClassificationSVM`	`edge`

年代ee Also

ClassificationKernel|fitckernel|margin|predict

edge

年代yntax

Description

Examples

Estimate Test-Set Edge

Feature Selection Using Test-Set Edges

Input Arguments

Mdl—Binary kernel classification modelClassificationKernelmodel object

X—Predictor datan-by-pnumeric matrix

Y—Class labelscategorical array|character array|string array|logical vector|numeric vector|cell array of character vectors

Tbl—年代ample datatable

ResponseVarName—Response variable namename of variable inTbl

weights—Observation weightsones(size(X,1),1)(default) |numeric vector|name of variable inTbl

Output Arguments

e— Classification edgenumeric scalar

More About

Classification Edge

Classification Margin

Classification Score

Extended Capabilities

Tall ArraysCalculate with arrays that have more rows than fit in memory.

Version History

R2022a:edgereturns a different value for a model with a nondefault cost matrix

R2022a:edgecan return NaN for predictor data with missing values

年代ee Also

`Mdl`—Binary kernel classification model
`ClassificationKernel`model object

`X`—Predictor data
n-by-pnumeric matrix

`Y`—Class labels
categorical array|character array|string array|logical vector|numeric vector|cell array of character vectors

`Tbl`—年代ample data
table

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

`weights`—Observation weights
`ones(size(X,1),1)`(default) |numeric vector|name of variable in`Tbl`

`e`— Classification edge
numeric scalar

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

R2022a:`edge`returns a different value for a model with a nondefault cost matrix

R2022a:`edge`can return NaN for predictor data with missing values