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# ClassificationDiscriminant class

Superclasses: `CompactClassificationDiscriminant`

Discriminant analysis classification

## Description

A `ClassificationDiscriminant` object encapsulates a discriminant analysis classifier, which is a Gaussian mixture model for data generation. A `ClassificationDiscriminant` object can predict responses for new data using the `predict` method. The object contains the data used for training, so can compute resubstitution predictions.

## Construction

Create a `ClassificationDiscriminant` object by using `fitcdiscr`.

## Properties

 `BetweenSigma` `p`-by-`p` matrix, the between-class covariance, where `p` is the number of predictors. `CategoricalPredictors` Categorical predictor indices, which is always empty (`[]`) . `ClassNames` List of the elements in the training data `Y` with duplicates removed. `ClassNames` can be a categorical array, cell array of character vectors, character array, logical vector, or a numeric vector. `ClassNames` has the same data type as the data in the argument `Y`. (The software treats string arrays as cell arrays of character vectors.) `Coeffs` `k`-by-`k` structure of coefficient matrices, where `k` is the number of classes. `Coeffs(i,j)` contains coefficients of the linear or quadratic boundaries between classes `i` and `j`. Fields in `Coeffs(i,j)`: `DiscrimType``Class1` — `ClassNames``(i)``Class2` — `ClassNames``(j)``Const` — A scalar`Linear` — A vector with `p` components, where `p` is the number of columns in `X``Quadratic` — `p`-by-`p` matrix, exists for quadratic `DiscrimType` The equation of the boundary between class `i` and class `j` is `Const` + `Linear` * `x` + `x'` * `Quadratic` * `x` = `0`, where `x` is a column vector of length `p`. If `fitcdiscr` had the `FillCoeffs` name-value pair set to `'off'` when constructing the classifier, `Coeffs` is empty (`[]`). `Cost` Square matrix, where `Cost(i,j)` is the cost of classifying a point into class `j` if its true class is `i` (i.e., the rows correspond to the true class and the columns correspond to the predicted class). The order of the rows and columns of `Cost` corresponds to the order of the classes in `ClassNames`. The number of rows and columns in `Cost` is the number of unique classes in the response. Change a `Cost` matrix using dot notation: ```obj.Cost = costMatrix```. `Delta` Value of the Delta threshold for a linear discriminant model, a nonnegative scalar. If a coefficient of `obj` has magnitude smaller than `Delta`, `obj` sets this coefficient to `0`, and so you can eliminate the corresponding predictor from the model. Set `Delta` to a higher value to eliminate more predictors. `Delta` must be `0` for quadratic discriminant models. Change `Delta` using dot notation: ```obj.Delta = newDelta```. `DeltaPredictor` Row vector of length equal to the number of predictors in `obj`. If `DeltaPredictor(i) < Delta` then coefficient `i` of the model is `0`. If `obj` is a quadratic discriminant model, all elements of `DeltaPredictor` are `0`. `DiscrimType` Character vector specifying the discriminant type. One of: `'linear'``'quadratic'``'diagLinear'``'diagQuadratic'``'pseudoLinear'``'pseudoQuadratic'` Change `DiscrimType` using dot notation: ```obj.DiscrimType = newDiscrimType```. You can change between linear types, or between quadratic types, but cannot change between linear and quadratic types. `Gamma` Value of the Gamma regularization parameter, a scalar from `0` to `1`. Change `Gamma` using dot notation: ```obj.Gamma = newGamma```. If you set `1` for linear discriminant, the discriminant sets its type to `'diagLinear'`.If you set a value between `MinGamma` and `1` for linear discriminant, the discriminant sets its type to `'linear'`.You cannot set values below the value of the `MinGamma` property.For quadratic discriminant, you can set either `0` (for `DiscrimType` `'quadratic'`) or `1` (for `DiscrimType` `'diagQuadratic'`). `HyperparameterOptimizationResults` Description of the cross-validation optimization of hyperparameters, stored as a `BayesianOptimization` object or a table of hyperparameters and associated values. Nonempty when the `OptimizeHyperparameters` name-value pair is nonempty at creation. Value depends on the setting of the `HyperparameterOptimizationOptions` name-value pair at creation: `'bayesopt'` (default) — Object of class `BayesianOptimization``'gridsearch'` or `'randomsearch'` — Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst) `LogDetSigma` Logarithm of the determinant of the within-class covariance matrix. The type of `LogDetSigma` depends on the discriminant type: Scalar for linear discriminant analysisVector of length `K` for quadratic discriminant analysis, where `K` is the number of classes `MinGamma` Nonnegative scalar, the minimal value of the Gamma parameter so that the correlation matrix is invertible. If the correlation matrix is not singular, `MinGamma` is `0`. `ModelParameters` Parameters used in training `obj`. `Mu` Class means, specified as a `K`-by-`p` matrix of scalar values class means of size. `K` is the number of classes, and `p` is the number of predictors. Each row of `Mu` represents the mean of the multivariate normal distribution of the corresponding class. The class indices are in the `ClassNames` attribute. `NumObservations` Number of observations in the training data, a numeric scalar. `NumObservations` can be less than the number of rows of input data `X` when there are missing values in `X` or response `Y`. `PredictorNames ` Cell array of names for the predictor variables, in the order in which they appear in the training data `X`. `Prior` Numeric vector of prior probabilities for each class. The order of the elements of `Prior` corresponds to the order of the classes in `ClassNames`. Add or change a `Prior` vector using dot notation: ```obj.Prior = priorVector```. `ResponseName` Character vector describing the response variable `Y`. `ScoreTransform` Character vector representing a built-in transformation function, or a function handle for transforming scores. `'none'` means no transformation; equivalently, `'none'` means `@(x)x`. For a list of built-in transformation functions and the syntax of custom transformation functions, see `fitcdiscr`. Implement dot notation to add or change a `ScoreTransform` function using one of the following: `cobj.ScoreTransform = 'function'``cobj.ScoreTransform = @function` `Sigma` Within-class covariance matrix or matrices. The dimensions depend on `DiscrimType`: `'linear'` (default) — Matrix of size `p`-by-`p`, where `p` is the number of predictors`'quadratic'` — Array of size `p`-by-`p`-by-`K`, where `K` is the number of classes`'diagLinear'` — Row vector of length `p``'diagQuadratic'` — Array of size `1`-by-`p`-by-`K``'pseudoLinear'` — Matrix of size `p`-by-`p``'pseudoQuadratic'` — Array of size `p`-by-`p`-by-`K` `W` Scaled `weights`, a vector with length `n`, the number of rows in `X`. `X` Matrix of predictor values. Each column of `X` represents one predictor (variable), and each row represents one observation. `Xcentered` `X` data with class means subtracted. If `Y(i)` is of class `j`, `Xcentered(i,:)` = `X(i,:)` – `Mu(j,:)`, where `Mu` is the class mean property. `Y` A categorical array, cell array of character vectors, character array, logical vector, or a numeric vector with the same number of rows as `X`. Each row of `Y` represents the classification of the corresponding row of `X`.

## Methods

 compact Compact discriminant analysis classifier crossval Cross-validated discriminant analysis classifier cvshrink Cross-validate regularization of linear discriminant resubEdge Classification edge by resubstitution resubLoss Classification error by resubstitution resubMargin Classification margins by resubstitution resubPredict Predict resubstitution labels of discriminant analysis classification model

### Inherited Methods

 edge Classification edge logP Log unconditional probability density for discriminant analysis classifier loss Classification error mahal Mahalanobis distance to class means margin Classification margins nLinearCoeffs Number of nonzero linear coefficients predict Predict labels using discriminant analysis classification model

## Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).

## Examples

collapse all

`load fisheriris`

Train a discriminant analysis model using the entire data set.

`Mdl = fitcdiscr(meas,species)`
```Mdl = ClassificationDiscriminant ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 DiscrimType: 'linear' Mu: [3x4 double] Coeffs: [3x3 struct] Properties, Methods ```

`Mdl` is a `ClassificationDiscriminant` model. To access its properties, use dot notation. For example, display the group means for each predictor.

`Mdl.Mu`
```ans = 3×4 5.0060 3.4280 1.4620 0.2460 5.9360 2.7700 4.2600 1.3260 6.5880 2.9740 5.5520 2.0260 ```

To predict labels for new observations, pass `Mdl` and predictor data to `predict`.

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## References

[1] Guo, Y., T. Hastie, and R. Tibshirani. Regularized linear discriminant analysis and its application in microarrays. Biostatistics, Vol. 8, No. 1, pp. 86–100, 2007.