edge

Classification edge for neural network classifier

Since R2021a

Syntax

e = edge(Mdl,Tbl,ResponseVarName)

e = edge(Mdl,Tbl,Y)

e = edge(Mdl,X,Y)

e = edge(___,Name,Value)

Description

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

e is returned as a scalar value that represents the mean of the classification margins.

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(Mdl,X,Y) returns the classification edge for the trained neural network classifier Mdl using the predictor data X and the corresponding class labels in Y.

e = edge(___,Name,Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. For example, you can specify that columns in the predictor data correspond to observations or supply observation weights.

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

Test Set Classification Edge of Neural Network

Calculate the test set classification edge of a neural network classifier.

Load the patients data set. Create a table from the data set. Each row corresponds to one patient, and each column corresponds to a diagnostic variable. Use the Smoker variable as the response variable, and the rest of the variables as predictors.

load patients
tbl = table(Diastolic,Systolic,Gender,Height,Weight,Age,Smoker);

Separate the data into a training set tblTrain and a test set tblTest by using a stratified holdout partition. The software reserves approximately 30% of the observations for the test data set and uses the rest of the observations for the training data set.

rng("default") % For reproducibility of the partition
c = cvpartition(tbl.Smoker,"Holdout",0.30);
trainingIndices = training(c);
testIndices = test(c);
tblTrain = tbl(trainingIndices,:);
tblTest = tbl(testIndices,:);

Train a neural network classifier using the training set. Specify the Smoker column of tblTrain as the response variable. Specify to standardize the numeric predictors.

Mdl = fitcnet(tblTrain,"Smoker", ...
    "Standardize",true);

Calculate the test set classification edge.

e = edge(Mdl,tblTest,"Smoker")

e = 
0.8657

The mean of the classification margins is close to 1, which indicates that the model performs well overall.

Select Features to Include in Neural Network Classifier

Perform feature selection by comparing test set classification margins, edges, errors, and predictions. Compare the test set metrics for a model trained using all the predictors to the test set metrics for a model trained using only a subset of the predictors.

Load the sample file fisheriris.csv, which contains iris data including sepal length, sepal width, petal length, petal width, and species type. Read the file into a table.

fishertable = readtable('fisheriris.csv');

Separate the data into a training set trainTbl and a test set testTbl by using a stratified holdout partition. The software reserves approximately 30% of the observations for the test data set and uses the rest of the observations for the training data set.

rng("default")
c = cvpartition(fishertable.Species,"Holdout",0.3);
trainTbl = fishertable(training(c),:);
testTbl = fishertable(test(c),:);

Train one neural network classifier using all the predictors in the training set, and train another classifier using all the predictors except PetalWidth. For both models, specify Species as the response variable, and standardize the predictors.

allMdl = fitcnet(trainTbl,"Species","Standardize",true);
subsetMdl = fitcnet(trainTbl,"Species ~ SepalLength + SepalWidth + PetalLength", ...
    "Standardize",true);

Calculate the test set classification margins for the two models. Because the test set includes only 45 observations, display the margins using bar graphs.

For each observation, the classification margin is the difference between the classification score for the true class and the maximal score for the false classes. Because neural network classifiers return classification scores that are posterior probabilities, margin values close to 1 indicate confident classifications and negative margin values indicate misclassifications.

tiledlayout(2,1)

% Top axes
ax1 = nexttile;
allMargins = margin(allMdl,testTbl);
bar(ax1,allMargins)
xlabel(ax1,"Observation")
ylabel(ax1,"Margin")
title(ax1,"All Predictors")

% Bottom axes
ax2 = nexttile;
subsetMargins = margin(subsetMdl,testTbl);
bar(ax2,subsetMargins)
xlabel(ax2,"Observation")
ylabel(ax2,"Margin")
title(ax2,"Subset of Predictors")

Compare the test set classification edge, or mean of the classification margins, of the two models.

allEdge = edge(allMdl,testTbl)

allEdge = 
0.8198

subsetEdge = edge(subsetMdl,testTbl)

subsetEdge = 
0.9556

Based on the test set classification margins and edges, the model trained on a subset of the predictors seems to outperform the model trained on all the predictors.

Compare the test set classification error of the two models.

allError = loss(allMdl,testTbl);
allAccuracy = 1-allError

allAccuracy = 
0.9111

subsetError = loss(subsetMdl,testTbl);
subsetAccuracy = 1-subsetError

subsetAccuracy = 
0.9778

Again, the model trained using only a subset of the predictors seems to perform better than the model trained using all the predictors.

Visualize the test set classification results using confusion matrices.

allLabels = predict(allMdl,testTbl);
figure
confusionchart(testTbl.Species,allLabels)
title("All Predictors")

subsetLabels = predict(subsetMdl,testTbl);
figure
confusionchart(testTbl.Species,subsetLabels)
title("Subset of Predictors")

The model trained using all the predictors misclassifies four of the test set observations. The model trained using a subset of the predictors misclassifies only one of the test set observations.

Given the test set performance of the two models, consider using the model trained using all the predictors except PetalWidth.

Input Arguments

Mdl — Trained neural network classifier

ClassificationNeuralNetwork model object | CompactClassificationNeuralNetwork model object

Trained neural network classifier, specified as a ClassificationNeuralNetwork model object or CompactClassificationNeuralNetwork model object returned by fitcnet or compact, respectively.

Tbl — Sample data

table

Sample data, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, Tbl can contain an additional column for the response variable. Tbl must contain all of 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 trained Mdl 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 fitcnet when training Mdl, then the software standardizes the numeric columns of the predictor data using the corresponding means and standard deviations.

Data Types: 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

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

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. By default, edge assumes that each row of X corresponds to one observation, and each column corresponds to one predictor variable.

Note

If you orient your predictor matrix so that observations correspond to columns and specify 'ObservationsIn','columns', then you might experience a significant reduction in computation time.

The length of Y and the number of observations in X must be equal.

If you set 'Standardize',true in fitcnet when training Mdl, then the software standardizes the numeric columns of the predictor data using the corresponding means and standard deviations.

Data Types: single | double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: edge(Mdl,Tbl,"Response","Weights","W") specifies to use the Response and W variables in the table Tbl as the class labels and observation weights, respectively.

ObservationsIn — Predictor data observation dimension

'rows' (default) | 'columns'

Predictor data observation dimension, specified as 'rows' or 'columns'.

Note

If you orient your predictor matrix so that observations correspond to columns and specify 'ObservationsIn','columns', then you might experience a significant reduction in computation time. You cannot specify 'ObservationsIn','columns' for predictor data in a table.

Data Types: char | string

Weights — Observation weights

nonnegative numeric vector | name of variable in Tbl

Observation weights, specified as a nonnegative numeric vector or the name of a variable in Tbl. The software weights each observation in X or Tbl with the corresponding value in Weights. The length of Weights must equal the number of observations in X or Tbl.

If you specify the input data as a table Tbl, then Weights can be the name of a variable in Tbl that contains a numeric vector. In this case, you must specify Weights as a character vector or string scalar. For example, if the weights vector W is stored as Tbl.W, then specify it as 'W'.

By default, Weights is ones(n,1), where n is the number of observations in X or Tbl.

If you supply weights, then edge computes the weighted classification edge and normalizes weights to sum to the value of the prior probability in the respective class.

Data Types: single | double | char | string

More About

Classification Edge

The classification edge is the mean of the classification margins, or the weighted mean of the classification margins when you specify Weights.

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 classification margin for multiclass classification is the difference between the classification score for the true class and the maximal score for the false classes.

If the margins are on the same scale (that is, the score values are based on the same score transformation), then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™. (since R2024b)

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2021a

R2024b: Specify GPU arrays (requires Parallel Computing Toolbox)

edge fully supports GPU arrays.

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