margin - Classification margins for neural network classifier - MATLAB (original) (raw)

Classification margins for neural network classifier

Since R2021a

Syntax

Description

`m` = margin([Mdl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F401b4373-f245-41e6-965a-a6ce03891d5b),[Tbl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5Ff28bc064-2113-4915-ba44-719ed8f6c4ea),[ResponseVarName](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F37cee4f7-3101-4991-b3e7-7ec414dff94d)) returns the classification margins for the trained neural network classifier Mdl using the predictor data in table Tbl and the class labels in theResponseVarName table variable.

m is returned as a numeric vector, whose _i_th entry corresponds to the _i_th observation inTbl.

example

`m` = margin([Mdl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F401b4373-f245-41e6-965a-a6ce03891d5b),[Tbl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5Ff28bc064-2113-4915-ba44-719ed8f6c4ea),[Y](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fshared-Y)) returns the classification margins for the classifier Mdl using the predictor data in table Tbl and the class labels in vectorY.

`m` = margin([Mdl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F401b4373-f245-41e6-965a-a6ce03891d5b),[X](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F50ef4366-758a-48ab-b9a1-12ac24d79ac0),[Y](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fshared-Y)) returns the classification margins for the trained neural network classifierMdl using the predictor data X and the corresponding class labels in Y.

m is returned as a numeric vector, whose _i_th entry corresponds to the _i_th observation inX.

`m` = margin([Mdl](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F401b4373-f245-41e6-965a-a6ce03891d5b),[X](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fmw%5F50ef4366-758a-48ab-b9a1-12ac24d79ac0),[Y](#mw%5Fd013a1f3-de1d-437b-ae5d-d91d9792387e%5Fsep%5Fshared-Y),'ObservationsIn',[dimension](#mw%5Fecfc3509-8885-4fac-8d02-b4731aeb7fc9)) specifies the predictor data observation dimension, either 'rows' (default) or 'column'. For example, specify'ObservationsIn','columns' to indicate that columns in the predictor data correspond to observations.

Examples

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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")

Figure contains an axes object. The axes object with title Test Set Margins, xlabel Observation, ylabel Margin contains an object of type bar.

Only the sixth and twenty-eighth observations have negative margins, which indicates that the model performs well overall.

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")

Figure contains 2 axes objects. Axes object 1 with title All Predictors, xlabel Observation, ylabel Margin contains an object of type bar. Axes object 2 with title Subset of Predictors, xlabel Observation, ylabel Margin contains an object of type bar.

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

allEdge = edge(allMdl,testTbl)

subsetEdge = edge(subsetMdl,testTbl)

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

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

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")

Figure contains an object of type ConfusionMatrixChart. The chart of type ConfusionMatrixChart has title All Predictors.

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

Figure contains an object of type ConfusionMatrixChart. The chart of type ConfusionMatrixChart has 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

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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 margin 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

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 asTbl.Y, then specify ResponseVarName as'Y'. Otherwise, the software treats all columns ofTbl, 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

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

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

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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.

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

Version History

Introduced in R2021a

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margin fully supports GPU arrays.