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# loss

Classification error

## Syntax

```L = loss(obj,X,Y) L = loss(obj,X,Y,Name,Value) ```

## Description

`L = loss(obj,X,Y)` returns the classification loss, which is a scalar representing how well `obj` classifies the data in `X`, when `Y` contains the true classifications.

When computing the loss, `loss` normalizes the class probabilities in `Y` to the class probabilities used for training, stored in the `Prior` property of `obj`.

`L = loss(obj,X,Y,Name,Value)` returns the loss with additional options specified by one or more `Name,Value` pair arguments.

## Input Arguments

 `obj` Discriminant analysis classifier of class `ClassificationDiscriminant` or `CompactClassificationDiscriminant`, typically constructed with `fitcdiscr`. `X` Matrix where each row represents an observation, and each column represents a predictor. The number of columns in `X` must equal the number of predictors in `obj`. `Y` Class labels, with the same data type as exists in `obj`. The number of elements of `Y` must equal the number of rows of `X`.

### 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`.

`LossFun`

Built-in, loss-function name (character vector or string scalar in the table) or function handle.

• The following table lists the available loss functions. Specify one using the corresponding value.

ValueDescription
`'binodeviance'`Binomial deviance
`'classiferror'`Misclassified rate in decimal
`'exponential'`Exponential loss
`'hinge'`Hinge loss
`'logit'`Logistic loss
`'mincost'`Minimal expected misclassification cost (for classification scores that are posterior probabilities)
`'quadratic'`Quadratic loss

`'mincost'` is appropriate for classification scores that are posterior probabilities. Discriminant analysis models return posterior probabilities as classification scores by default (see `predict`).

• Specify your own function using function handle notation.

Suppose that n be the number of observations in `X` and K be the number of distinct classes (`numel(Mdl.ClassNames)`). Your function must have this signature

``lossvalue = lossfun(C,S,W,Cost)``
where:

• The output argument `lossvalue` is a scalar.

• You choose the function name (`lossfun`).

• `C` is an n-by-K logical matrix with rows indicating which class the corresponding observation belongs. The column order corresponds to the class order in `Mdl.ClassNames`.

Construct `C` by setting `C(p,q) = 1` if observation `p` is in class `q`, for each row. Set all other elements of row `p` to `0`.

• `S` is an n-by-K numeric matrix of classification scores. The column order corresponds to the class order in `Mdl.ClassNames`. `S` is a matrix of classification scores, similar to the output of `predict`.

• `W` is an n-by-1 numeric vector of observation weights. If you pass `W`, the software normalizes them to sum to `1`.

• `Cost` is a K-by-K numeric matrix of misclassification costs. For example, `Cost = ones(K) - eye(K)` specifies a cost of `0` for correct classification, and `1` for misclassification.

Specify your function using `'LossFun',@lossfun`.

For more details on loss functions, see Classification Loss.

Default: `'mincost'`

`Weights`

Numeric vector of length `N`, where `N` is the number of rows of `X`. `weights` are nonnegative. `loss` normalizes the weights so that observation weights in each class sum to the prior probability of that class. When you supply `weights`, `loss` computes weighted classification loss.

Default: `ones(N,1)`

## Output Arguments

 `L` Classification loss, a scalar. The interpretation of `L` depends on the values in `weights` and `lossfun`.

## Examples

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Load Fisher's iris data set.

`load fisheriris`

Train a discriminant analysis model using all observations in the data.

`Mdl = fitcdiscr(meas,species);`

Estimate the classification error of the model using the training observations.

`L = loss(Mdl,meas,species)`
```L = 0.0200 ```

Alternatively, if `Mdl` is not compact, then you can estimate the training-sample classification error by passing `Mdl` to `resubLoss`.

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