margin
Syntax
Description
returns the classification
margins for the trained neural network classifier m
= margin(Mdl
,Tbl
,ResponseVarName
)Mdl
using
the predictor data in table Tbl
and the class labels in the
ResponseVarName
table variable.
m
is returned as a numeric vector, whose ith
entry corresponds to the ith observation in
Tbl
.
Examples
Test Set Classification Margins of Neural Network
Calculate the test set classification margins 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 margins. Because the test set includes only 30 observations, display the margins using a bar graph.
m = margin(Mdl,tblTest,"Smoker"); bar(m) xlabel("Observation") ylabel("Margin") title("Test Set Margins")
Only the sixth and twenty-eighth observations have negative margins, 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 trainMdl
, then you do not need to specifyResponseVarName
orY
.If you trained
Mdl
using sample data contained in a table, then the input data formargin
must also be in a table.If you set
'Standardize',true
infitcnet
when trainingMdl
, 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 ofMdl.ClassNames
. (The software treats string arrays as cell arrays of character vectors.)The distinct classes in
Y
must be a subset ofMdl.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 inX
orTbl
.
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix. By default,
margin
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
dimension
— 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
More About
Classification Edge
The classification edge is the 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 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 R2021aR2024b: Specify GPU arrays (requires Parallel Computing Toolbox)
margin
fully supports GPU arrays.
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