# margin

Classification margins for Gaussian kernel classification model

## Description

returns the classification margins for the trained kernel classifier
`m`

= margin(`Mdl`

,`Tbl`

,`ResponseVarName`

)`Mdl`

using the predictor data in table
`Tbl`

and the class labels in
`Tbl.ResponseVarName`

.

## Examples

### Estimate Test-Set Margins

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 30% holdout sample for the test set.

rng('default') % For reproducibility Partition = cvpartition(Y,'Holdout',0.30); 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 margins and test-set margins.

mTrain = margin(Mdl,X(trainingInds,:),Y(trainingInds)); mTest = margin(Mdl,X(testInds,:),Y(testInds));

Plot both sets of margins using box plots.

boxplot([mTrain; mTest],[zeros(size(mTrain,1),1); ones(size(mTest,1),1)], ... 'Labels',{'Training set','Test set'}); title('Training-Set and Test-Set Margins')

The margin distribution of the training set is situated higher than the margin distribution of the test set.

### Feature Selection Using Test-Set Margins

Perform feature selection by comparing test-set margins from multiple models. Based solely on this criterion, the classifier with the larger margins is the better 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 10% of the predictor variables.

```
p = size(X,2); % Number of predictors
idxPart = randsample(p,ceil(0.1*p));
```

Train two binary kernel classification models: one that uses all of the predictors, and one that uses the random 10%.

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

`Mdl`

and `PMdl`

are `ClassificationKernel`

models.

Estimate the test-set margins for each classifier.

fullMargins = margin(Mdl,XTest,YTest); partMargins = margin(PMdl,XTest(:,idxPart),YTest);

Plot the distribution of the margin sets using box plots.

boxplot([fullMargins partMargins], ... 'Labels',{'All Predictors','10% of the Predictors'}); title('Test-Set Margins')

The margin distribution of `PMdl`

is situated higher than the margin distribution of `Mdl`

. Therefore, the `PMdl`

model is the better classifier.

## Input Arguments

`Mdl`

— Binary kernel classification model

`ClassificationKernel`

model object

Binary kernel classification model, specified as a `ClassificationKernel`

model object. You can create a
`ClassificationKernel`

model object using `fitckernel`

.

`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`

`Tbl`

— Sample data

table

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 `margin`

must also be in a 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`

## Output Arguments

`m`

— Classification margins

numeric column vector

Classification margins, returned as an *n*-by-1
numeric column vector, where *n* is the number of
observations in `X`

.

## More About

### 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* =
*y**f*(*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

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

$$T(\xb7)$$ 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`

).

## Extended Capabilities

### Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

`margin`

does not support tall`table`

data.

For more information, see Tall Arrays.

## Version History

**Introduced in R2017b**

## See Also

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