# margin

Classification margins for discriminant analysis classifier

## Syntax

``m = margin(Mdl,Tbl,ResponseVarName)``
``m = margin(Mdl,Tbl,Y)``
``m = margin(Mdl,X,Y)``

## Description

````m = margin(Mdl,Tbl,ResponseVarName)` returns the Classification Margin (`m`) for the trained discriminant analysis classifier `Mdl` using the predictor data in table `Tbl` and the class labels in `Tbl.ResponseVarName`.```
````m = margin(Mdl,Tbl,Y)` returns the classification margins for `Mdl` using the predictor data in table `Tbl` and the class labels in `Y`.```

example

````m = margin(Mdl,X,Y)` returns the classification margins for `Mdl` using the predictor data in matrix `X` and the class labels in `Y`.The classification margin is the difference between the classification score for the true class and the maximal classification score for the false classes. `m` is returned as a numeric vector with the same length as `Y`.```

## Examples

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Compute the classification margin for the Fisher iris data.

Compute the classification margin for the Fisher iris data, trained on its first two columns of data, and view the last 10 entries:

```load fisheriris X = meas(:,1:2); obj = fitcdiscr(X,species); M = margin(obj,X,species); M(end-10:end)```
```ans = 0.6551 0.4838 0.6551 -0.5127 0.5659 0.4611 0.4949 0.1024 0.2787 -0.1439 -0.4444```

Compute the classification margin for the Fisher iris data, trained on its first two columns of data, and view the last 10 entries:

```obj = fitcdiscr(meas,species); M = margin(obj,meas,species); M(end-10:end)```
```ans = 0.9983 1.0000 0.9991 0.9978 1.0000 1.0000 0.9999 0.9882 0.9937 1.0000 0.9649```

## Input Arguments

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Trained discriminant analysis classifier, specified as a `ClassificationDiscriminant` model object trained with `fitcdiscr`, or a `CompactClassificationDiscriminant` model object created with `compact`.

Sample data, specified as a table. Each row of `Tbl` corresponds to one observation, and each column corresponds to one predictor variable. Categorical predictor variables are not supported. Optionally, `Tbl` can contain an additional columns for the response variable, which can be categorical. `Tbl` must contain all of the predictors used to train the model. 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 `margin` must also be in a table.

Data Types: `table`

Predictor data, specified as a numeric matrix. Each row of `X` corresponds to one observation, and each column corresponds to one predictor variable. Categorical predictor variables are not supported. The variables in the columns of `X` must be the same as the variables used to train `Mdl`. The number of rows in `X` must equal the number of rows in `Y`.

If you trained `Mdl` using sample data contained in a matrix, then the input data for `margin` must also be in a matrix.

Data Types: `single` | `double`

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`, you must specify it as a character vector or string scalar. For example, if the response variable `Y` is stored as `Tbl.Y`, then specify it as `"Y"`. Otherwise, the software treats all columns of `Tbl`, including `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`

Class labels, specified as a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. `Y` must be of the same type as the classification used to train `Mdl`. (The software treats string arrays as cell arrays of character vectors.)

The length of `Y` must equal the number of rows in `Tbl` or `X`.

Data Types: `categorical` | `char` | `string` | `logical` | `single` | `double` | `cell`

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### Classification Margin

The classification margin is the difference between the classification score for the true class and maximal classification score for the false classes.

The classification margin is a column vector with the same number of rows as in the matrix `X`. A high value of margin indicates a more reliable prediction than a low value.

### Score (discriminant analysis)

For discriminant analysis, the score of a classification is the posterior probability of the classification. For the definition of posterior probability in discriminant analysis, see Posterior Probability.

## Version History

Introduced in R2011b