Classification edge for neural network classifier
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.
e = edge(___,
Calculate the test set classification edge of a neural network classifier.
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.
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
Mdl— Trained neural network classifier
ClassificationNeuralNetworkmodel object |
Tbl— Sample data
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 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
fitcnet when training
Mdl, then the
software standardizes the numeric columns of the predictor data using the
corresponding means and standard deviations.
ResponseVarName— Response variable name
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
'Y'. Otherwise, the software treats all columns of
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.
X— Predictor data
Predictor data, specified as a numeric matrix. By default,
edge assumes that each row of
corresponds to one observation, and each column corresponds to one predictor
If you orient your predictor matrix so that observations correspond to columns and
'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.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
edge(Mdl,Tbl,"Response","Weights","W")specifies to use the
Wvariables in the table
Tblas the class labels and observation weights, respectively.
Weights— Observation weights
Observation weights, specified as a nonnegative numeric vector or the name of a
Tbl. The software weights each observation in
Tbl with the corresponding value in
Weights. The length of
Weights must equal
the number of observations in
If you specify the input data as a table
Weights can be the name of a variable in
Tbl that contains a numeric vector. In this case, you must
Weights as a character vector or string scalar. For
example, if the weights vector
W is stored as
Tbl.W, then specify it as
n is the number of observations in
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.
The classification edge is the mean of the
classification margins, or the weighted mean of the
classification margins when you specify
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.