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# edge

Classification edge for Gaussian kernel classification model

## Syntax

``e = edge(Mdl,X,Y)``
``e = edge(Mdl,Tbl,ResponseVarName)``
``e = edge(Mdl,Tbl,Y)``
``e = edge(___,'Weights',weights)``

## Description

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````e = edge(Mdl,X,Y)` returns the classification edge for the binary Gaussian kernel classification model `Mdl` using the predictor data in `X` and the corresponding class labels in `Y`.```
````e = edge(Mdl,Tbl,ResponseVarName)` returns the classification edge for the trained kernel classifier `Mdl` using the predictor data in table `Tbl` and the class labels in `Tbl.ResponseVarName`.```
````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(___,'Weights',weights)` returns the weighted classification edge using the observation weights supplied in `weights`. Specify the weights after any of the input argument combinations in previous syntaxes. NoteIf 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

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Load the `ionosphere` data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad (`'b'`) or good (`'g'`).

`load ionosphere`

Partition the data set into training and test sets. Specify a 15% holdout sample for the test set.

```rng('default') % For reproducibility Partition = cvpartition(Y,'Holdout',0.15); trainingInds = training(Partition); % Indices for the training set testInds = test(Partition); % Indices for the test set```

Train a binary kernel classification model using the training set.

`Mdl = fitckernel(X(trainingInds,:),Y(trainingInds));`

Estimate the training-set edge and the test-set edge.

`eTrain = edge(Mdl,X(trainingInds,:),Y(trainingInds))`
```eTrain = 2.1703 ```
`eTest = edge(Mdl,X(testInds,:),Y(testInds))`
```eTest = 1.5643 ```

Perform feature selection by comparing test-set edges from multiple models. Based solely on this criterion, the classifier with the highest edge is the best classifier.

Load the `ionosphere` data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad (`'b'`) or good (`'g'`).

`load ionosphere`

Partition the data set into training and test sets. Specify a 15% holdout sample for the test set.

```rng('default') % For reproducibility Partition = cvpartition(Y,'Holdout',0.15); trainingInds = training(Partition); % Indices for the training set XTrain = X(trainingInds,:); YTrain = Y(trainingInds); testInds = test(Partition); % Indices for the test set XTest = X(testInds,:); YTest = Y(testInds);```

Randomly choose half of the predictor variables.

```p = size(X,2); % Number of predictors idxPart = randsample(p,ceil(0.5*p));```

Train two binary kernel classification models: one that uses all of the predictors, and one that uses half of the predictors.

```Mdl = fitckernel(XTrain,YTrain); PMdl = fitckernel(XTrain(:,idxPart),YTrain);```

`Mdl` and `PMdl` are `ClassificationKernel` models.

Estimate the test-set edge for each classifier.

`fullEdge = edge(Mdl,XTest,YTest)`
```fullEdge = 1.6335 ```
`partEdge = edge(PMdl,XTest(:,idxPart),YTest)`
```partEdge = 2.0205 ```

Based on the test-set edges, the classifier that uses half of the predictors is the better model.

## Input Arguments

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Binary kernel classification model, specified as a `ClassificationKernel` model object. You can create a `ClassificationKernel` model object using `fitckernel`.

Predictor data, specified as an n-by-p numeric matrix, where n is the number of observations and p is the number of predictors used to train `Mdl`.

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

Data Types: `single` | `double`

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`

Sample data used to train the model, specified as a table. Each row of `Tbl` corresponds to one observation, and each column corresponds to one predictor variable. Optionally, `Tbl` can contain additional columns for the response variable and observation weights. `Tbl` must contain all 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 train `Mdl` using sample data contained in a table, then the input data for `edge` must also be in a 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 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`

Observation weights, specified as a numeric vector or the name of a variable in `Tbl`.

• If `weights` is a numeric vector, then the size of `weights` must be equal to the number of rows in `X` or `Tbl`.

• If `weights` is the name of a variable in `Tbl`, you must specify `weights` as a character vector or string scalar. For example, if the weights are stored as `Tbl.W`, then specify `weights` as `'W'`. Otherwise, the software treats all columns of `Tbl`, including `Tbl.W`, as predictors.

If you supply weights, `edge` computes the weighted classification edge. The software weights the observations in each row of `X` or `Tbl` with the corresponding weights in `weights`.

`edge` normalizes `weights` to sum up to the value of the prior probability in the respective class.

Data Types: `single` | `double` | `char` | `string`

## Output Arguments

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Classification edge, returned as a numeric scalar.

## More About

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### Classification Edge

The classification edge is the weighted 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 software defines the classification margin for binary classification as

`$m=2yf\left(x\right).$`

x is an observation. If the true label of x is the positive class, then y is 1, and –1 otherwise. f(x) is the positive-class classification score for the observation x. The classification margin is commonly defined as m = yf(x).

If the margins are on the same scale, then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.

### Classification Score

For kernel classification models, the raw classification score for classifying the observation x, a row vector, into the positive class is defined by

`$f\left(x\right)=T\left(x\right)\beta +b.$`

• $T\left(·\right)$ is a transformation of an observation for feature expansion.

• β is the estimated column vector of coefficients.

• b is the estimated scalar bias.

The raw classification score for classifying x into the negative class is f(x). The software classifies observations into the class that yields a positive score.

If the kernel classification model consists of logistic regression learners, then the software applies the `'logit'` score transformation to the raw classification scores (see `ScoreTransform`).

## Version History

Introduced in R2017b

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Behavior changed in R2022a

Behavior changed in R2022a