edge

Classification edge for Gaussian kernel classification model

Syntax

e = edge(Mdl,X,Y)

e = edge(Mdl,Tbl,ResponseVarName)

e = edge(Mdl,Tbl,Y)

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

Description

e = edge(Mdl,X,Y) returns the classification edge for the binary Gaussian kernel classification model Mdl using the predictor data in X and the corresponding class labels in Y.

e = edge(Mdl,Tbl,ResponseVarName) returns the classification edge for the trained kernel classifier Mdl using the predictor data in table Tbl and the class labels in Tbl.ResponseVarName.

e = edge(Mdl,Tbl,Y) returns the classification edge for the classifier Mdl using the predictor data in table Tbl and the class labels in vector Y.

e = edge(___,'Weights',weights) returns the weighted classification edge using the observation weights supplied in weights. Specify the weights after any of the input argument combinations in 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-Set Edge

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

load ionosphere

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

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

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

load ionosphere

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

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

Randomly choose half of the predictor variables.

p = size(X,2); % Number of predictors
idxPart = 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);

Mdl and PMdl are ClassificationKernel models.

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

Mdl — Binary kernel classification model

ClassificationKernel model object

Binary kernel classification model, specified as a ClassificationKernel model object. You can create a ClassificationKernel model object using fitckernel.

X — Predictor data

n-by-p numeric matrix

Predictor data, specified as an n-by-p numeric matrix, where n is the number of observations and p is the number of predictors used to train Mdl.

The length of Y and the number of observations in X must 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 of Y must be the same as the data type of Mdl.ClassNames. (The software treats string arrays as cell arrays of character vectors.)

• The distinct classes in Y must be a subset of Mdl.ClassNames.

• If Y is a character array, then each element must correspond to one row of the array.

• The length of Y must be equal to the number of observations in X or Tbl.

Data Types: categorical | char | string | logical | single | double | cell

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 the predictors used to train Mdl. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

If Tbl contains the response variable used to train Mdl, then you do not need to specify ResponseVarName or Y.

If you train Mdl using sample data contained in a table, then the input data for edge must also be in a table.

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 Mdl, then you do not need to specify ResponseVarName.

If you specify ResponseVarName, then you must specify it as a character vector or string scalar. For example, if the response variable is stored as Tbl.Y, then specify ResponseVarName as 'Y'. Otherwise, the software treats all columns of Tbl, including Tbl.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 in Tbl.

• If weights is a numeric vector, then the size of weights must be equal to the number of rows in X or Tbl.

• If weights is the name of a variable in Tbl, you must specify weights 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 weights in weights.

edge normalizes weights to sum up to the value of the prior probability in the respective class.

Data Types: single | double | char | string

Output Arguments

e — Classification edge

numeric scalar

Classification edge, returned as a numeric scalar.

More About

Classification Edge

The classification edge is 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

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

$$m=2yf\left(x\right).$$

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

For kernel classification models, the raw classification score for classifying the observation x, a row vector, into the positive class is defined by

$$f\left(x\right)=T(x)\beta +b.$$

• $$T(·)$$ is a transformation of an observation for feature expansion.

• β is the estimated column vector of coefficients.

• b is the estimated scalar bias.

The raw classification score for classifying x into 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 ScoreTransform).

Extended Capabilities

Tall Arrays

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

The edge function supports tall arrays with the following usage notes and limitations:

• edge does not support tall table data.

For more information, see Tall Arrays.

Version History

Introduced in R2017b

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, 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	ClassificationSVM, CompactClassificationSVM	edge