# Documentation

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# Statistics and Machine Learning Toolbox Classes

## Descriptive Statistics and Visualization

### Managing Data

#### Data Types

 `nominal` Arrays for nominal data `ordinal` Arrays for ordinal data `dataset` Arrays for statistical data

## Probability Distributions

### Discrete Distributions

#### Binomial Distribution

 `BinomialDistribution` Binomial probability distribution object

#### Multinomial Distribution

 `MultinomialDistribution` Multinomial probability distribution object

#### Negative Binomial Distribution

 `NegativeBinomialDistribution` Negative binomial distribution object

#### Poisson Distribution

 `PoissonDistribution` Poisson probability distribution object

### Continuous Distributions

#### Beta Distribution

 `BetaDistribution` Beta probability distribution object

#### Birnbaum-Saunders Distribution

 `BirnbaumSaundersDistribution` Birnbaum-Saunders probability distribution object

#### Burr Type XII Distribution

 `BurrDistribution` Burr probability distribution object

#### Exponential Distribution

 `ExponentialDistribution` Exponential probability distribution object

#### Extreme Value Distribution

 `ExtremeValueDistribution` Extreme value probability distribution object

#### Gamma Distribution

 `GammaDistribution` Gamma probability distribution object

#### Gaussian Mixture Distribution

 `gmdistribution` Construct Gaussian mixture distribution

#### Generalized Extreme Value Distribution

 `GeneralizedExtremeValueDistribution` Generalized extreme value probability distribution object

#### Generalized Pareto Distribution

 `GeneralizedParetoDistribution` Generalized Pareto probability distribution object

#### Half-Normal Distribution

 `HalfNormalDistribution` Half-normal probability distribution object

#### Inverse Gaussian Distribution

 `InverseGaussianDistribution` Inverse Gaussian probability distribution object

#### Kernel Distribution

 `KernelDistribution` Kernel probability distribution object

#### Logistic Distribution

 `LogisticDistribution` Logistic probability distribution object

#### Loglogistic Distribution

 `LoglogisticDistribution` Loglogistic probability distribution object

#### Lognormal Distribution

 `LognormalDistribution` Lognormal probability distribution object

#### Nakagami Distribution

 `NakagamiDistribution` Nakagami probability distribution object

#### Normal Distribution

 `NormalDistribution` Normal probability distribution object

#### Piecewise Linear Distribution

 `PiecewiseLinearDistribution` Piecewise linear probability distribution object

#### Rayleigh Distribution

 `RayleighDistribution` Rayleigh probability distribution object

#### Rician Distribution

 `RicianDistribution` Rician probability distribution object

#### Stable Distribution

 `StableDistribution` Stable probability distribution object

#### t Location-Scale Distribution

 `tLocationScaleDistribution` t Location-Scale probability distribution object

#### Triangular Distribution

 `TriangularDistribution` Triangular probability distribution object

#### Uniform Distribution (Continuous)

 `UniformDistribution` Uniform probability distribution object

#### Weibull Distribution

 `WeibullDistribution` Weibull probability distribution object

### Pseudorandom and Quasirandom Number Generation

 `haltonset` Construct Halton quasi-random point set `qrandset` Abstract quasi-random point set class `qrandstream` Construct quasi-random number stream `sobolset` Construct Sobol quasi-random point set `HamiltonianSampler` Hamiltonian Monte Carlo (HMC) sampler

## Cluster Analysis

### Gaussian Mixture Models

 `gmdistribution` Construct Gaussian mixture distribution

### Nearest Neighbors

 `ExhaustiveSearcher` Exhaustive nearest neighbor searcher `KDTreeSearcher` Nearest neighbor search using Kd-tree

### Cluster Visualization and Evaluation

 `CalinskiHarabaszEvaluation` Calinski-Harabasz criterion clustering evaluation object `DaviesBouldinEvaluation` Davies-Bouldin criterion clustering evaluation object `GapEvaluation` Gap criterion clustering evaluation object `SilhouetteEvaluation` Silhouette criterion clustering evaluation object

## ANOVA

### Repeated Measures and MANOVA

 `RepeatedMeasuresModel` Repeated measures model class

## Regression

### Linear Regression

#### Multiple Linear Regression

 `LinearModel` Linear regression model class `CompactLinearModel` Compact linear regression model class `RegressionLinear` Linear regression model for high-dimensional data `RegressionPartitionedLinear` Cross-validated linear regression model for high-dimensional data

#### Stepwise Regression

 `LinearModel` Linear regression model class

#### Regularization

 `RegressionLinear` Linear regression model for high-dimensional data `RegressionPartitionedLinear` Cross-validated linear regression model for high-dimensional data

#### Mixed Effects

 `LinearMixedModel` Linear mixed-effects model class

### Generalized Linear Models

#### Generalized Linear Regression

 `GeneralizedLinearModel` Generalized linear regression model class `CompactGeneralizedLinearModel` Compact generalized linear regression model class `ClassificationLinear` Linear model for binary classification of high-dimensional data `ClassificationECOC` Multiclass model for support vector machines or other classifiers `ClassificationKernel` Gaussian kernel classification model using feature expansion for big data `ClassificationPartitionedLinear` Cross-validated linear model for binary classification of high-dimensional data `ClassificationPartitionedLinearECOC` Cross-validated linear error-correcting output codes model for multiclass classification of high-dimensional data

#### Stepwise Regression

 `GeneralizedLinearModel` Generalized linear regression model class

#### Regularization

 `ClassificationLinear` Linear model for binary classification of high-dimensional data `ClassificationECOC` Multiclass model for support vector machines or other classifiers `ClassificationKernel` Gaussian kernel classification model using feature expansion for big data `ClassificationPartitionedLinear` Cross-validated linear model for binary classification of high-dimensional data `ClassificationPartitionedLinearECOC` Cross-validated linear error-correcting output codes model for multiclass classification of high-dimensional data

#### Mixed Effects

 `GeneralizedLinearMixedModel` Generalized linear mixed-effects model class

### Nonlinear Regression

#### Nonlinear Models

 `NonLinearModel` Nonlinear regression model class

### Support Vector Machine Regression

 `RegressionSVM` Support vector machine regression model `CompactRegressionSVM` Compact support vector machine regression model `RegressionLinear` Linear regression model for high-dimensional data `RegressionPartitionedLinear` Cross-validated linear regression model for high-dimensional data

### Gaussian Process Regression

 `RegressionGP` Gaussian process regression model class `CompactRegressionGP` Compact Gaussian process regression model class

### Regression Trees

 `RegressionTree` Regression tree `CompactRegressionTree` Compact regression tree `RegressionPartitionedModel` Cross-validated regression model

### Regression Tree Ensembles

 `RegressionEnsemble` Ensemble regression `CompactRegressionEnsemble` Compact regression ensemble class `RegressionPartitionedEnsemble` Cross-validated regression ensemble `TreeBagger` Bag of decision trees `CompactTreeBagger` Compact ensemble of decision trees grown by bootstrap aggregation `RegressionBaggedEnsemble` Regression ensemble grown by resampling

### Model Building and Assessment

 `BayesianOptimization` Bayesian optimization results `optimizableVariable` Variable description for bayesopt or other optimizers `cvpartition` Data partitions for cross validation

## Classification

### Classification Trees

 `ClassificationTree` Binary decision tree for classification `CompactClassificationTree` Compact classification tree `ClassificationPartitionedModel` Cross-validated classification model

### Discriminant Analysis

 `ClassificationDiscriminant` Discriminant analysis classification `CompactClassificationDiscriminant` Compact discriminant analysis class `ClassificationPartitionedModel` Cross-validated classification model

### Naive Bayes

 `ClassificationNaiveBayes` Naive Bayes classification `CompactClassificationNaiveBayes` Compact naive Bayes classifier `ClassificationPartitionedModel` Cross-validated classification model

### Nearest Neighbors

 `ClassificationKNN` k-nearest neighbor classification `ClassificationPartitionedModel` Cross-validated classification model `ExhaustiveSearcher` Exhaustive nearest neighbor searcher `KDTreeSearcher` Nearest neighbor search using Kd-tree

### Support Vector Machine Classification

 `ClassificationSVM` Support vector machine for binary classification `CompactClassificationSVM` Compact support vector machine for binary classification `ClassificationPartitionedModel` Cross-validated classification model `ClassificationLinear` Linear model for binary classification of high-dimensional data `ClassificationPartitionedLinear` Cross-validated linear model for binary classification of high-dimensional data `ClassificationKernel` Gaussian kernel classification model using feature expansion for big data `ClassificationECOC` Multiclass model for support vector machines or other classifiers `CompactClassificationECOC` Compact multiclass model for support vector machines or other classifiers `ClassificationPartitionedECOC` Cross-validated multiclass model for support vector machines or other classifiers `ClassificationPartitionedLinearECOC` Cross-validated linear error-correcting output codes model for multiclass classification of high-dimensional data

### Classification Ensembles

 `ClassificationEnsemble` Ensemble classifier `CompactClassificationEnsemble` Compact classification ensemble class `ClassificationPartitionedEnsemble` Cross-validated classification ensemble `TreeBagger` Bag of decision trees `CompactTreeBagger` Compact ensemble of decision trees grown by bootstrap aggregation `ClassificationBaggedEnsemble` Classification ensemble grown by resampling `ClassificationECOC` Multiclass model for support vector machines or other classifiers `CompactClassificationECOC` Compact multiclass model for support vector machines or other classifiers `ClassificationPartitionedECOC` Cross-validated multiclass model for support vector machines or other classifiers

### Model Building and Assessment

 `BayesianOptimization` Bayesian optimization results `optimizableVariable` Variable description for bayesopt or other optimizers `cvpartition` Data partitions for cross validation

## Dimensionality Reduction and Feature Extraction

 `FeatureSelectionNCAClassification` Feature selection for classification using neighborhood component analysis (NCA) `FeatureSelectionNCARegression` Feature selection for regression using neighborhood component analysis (NCA) `ReconstructionICA` Feature extraction by reconstruction ICA `SparseFiltering` Feature extraction by sparse filtering

## Industrial Statistics

### Design of Experiments (DOE)

#### Quasi-Random Designs

 `haltonset` Construct Halton quasi-random point set `qrandstream` Construct quasi-random number stream `sobolset` Construct Sobol quasi-random point set