# kfoldEdge

Classification edge for cross-validated kernel classification model

## Syntax

``edge = kfoldEdge(CVMdl)``
``edge = kfoldEdge(CVMdl,Name,Value)``

## Description

example

````edge = kfoldEdge(CVMdl)` returns the classification edge obtained by the cross-validated, binary kernel model (`ClassificationPartitionedKernel`) `CVMdl`. For every fold, `kfoldEdge` computes the classification edge for validation-fold observations using a model trained on training-fold observations.```
````edge = kfoldEdge(CVMdl,Name,Value)` returns the classification edge with additional options specified by one or more name-value pair arguments. For example, specify the number of folds or the aggregation level.```

## Examples

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

`load ionosphere`

Cross-validate a binary kernel classification model using the data.

`CVMdl = fitckernel(X,Y,'Crossval','on')`
```CVMdl = ClassificationPartitionedKernel CrossValidatedModel: 'Kernel' ResponseName: 'Y' NumObservations: 351 KFold: 10 Partition: [1x1 cvpartition] ClassNames: {'b' 'g'} ScoreTransform: 'none' Properties, Methods ```

`CVMdl` is a `ClassificationPartitionedKernel` model. By default, the software implements 10-fold cross-validation. To specify a different number of folds, use the `'KFold'` name-value pair argument instead of `'Crossval'`.

Estimate the cross-validated classification edge.

`edge = kfoldEdge(CVMdl)`
```edge = 1.5585 ```

Alternatively, you can obtain the per-fold edges by specifying the name-value pair `'Mode','individual'` in `kfoldEdge`.

Perform feature selection by comparing k-fold edges from multiple models. Based solely on this criterion, the classifier with the greatest edge is the best classifier.

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

`load ionosphere`

Randomly choose half of the predictor variables.

```rng(1); % For reproducibility p = size(X,2); % Number of predictors idxPart = randsample(p,ceil(0.5*p));```

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

```CVMdl = fitckernel(X,Y,'CrossVal','on'); PCVMdl = fitckernel(X(:,idxPart),Y,'CrossVal','on');```

`CVMdl` and `PCVMdl` are `ClassificationPartitionedKernel` models. By default, the software implements 10-fold cross-validation. To specify a different number of folds, use the `'KFold'` name-value pair argument instead of `'Crossval'`.

Estimate the k-fold edge for each classifier.

`fullEdge = kfoldEdge(CVMdl)`
```fullEdge = 1.5142 ```
`partEdge = kfoldEdge(PCVMdl)`
```partEdge = 1.8910 ```

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

## Input Arguments

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Cross-validated, binary kernel classification model, specified as a `ClassificationPartitionedKernel` model object. You can create a `ClassificationPartitionedKernel` model by using `fitckernel` and specifying any one of the cross-validation name-value pair arguments.

To obtain estimates, `kfoldEdge` applies the same data used to cross-validate the kernel classification model (`X` and `Y`).

### Name-Value Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is 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 `Name1,Value1,...,NameN,ValueN`.

Example: `kfoldEdge(CVMdl,'Mode','individual')` returns the classification edge for each fold.

Fold indices for prediction, specified as the comma-separated pair consisting of `'Folds'` and a numeric vector of positive integers. The elements of `Folds` must be within the range from `1` to `CVMdl.KFold`.

The software uses only the folds specified in `Folds` for prediction.

Example: `'Folds',[1 4 10]`

Data Types: `single` | `double`

Aggregation level for the output, specified as the comma-separated pair consisting of `'Mode'` and `'average'` or `'individual'`.

This table describes the values.

ValueDescription
`'average'`The output is a scalar average over all folds.
`'individual'`The output is a vector of length k containing one value per fold, where k is the number of folds.

Example: `'Mode','individual'`

## Output Arguments

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Classification edge, returned as a numeric scalar or numeric column vector.

If `Mode` is `'average'`, then `edge` is the average classification edge over all folds. Otherwise, `edge` is a k-by-1 numeric column vector containing the classification edge for each fold, where k is the number of folds.

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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`).