# edge

Classification edge for neural network classifier

## Description

returns the classification edge
for the trained neural network classifier `e`

= edge(`Mdl`

,`Tbl`

,`ResponseVarName`

)`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.

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(___,`Name,Value`

)

**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.

## Version History

**Introduced in R2021a**

### 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 | `edge` |

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