Class RDA

java.lang.Object

smile.classification.AbstractClassifier<double[]>

smile.classification.QDA

smile.classification.RDA

All Implemented Interfaces:

Serializable, ToDoubleFunction<double[]>, ToIntFunction<double[]>, Classifier<double[]>

public class RDA
extends QDA

Regularized discriminant analysis. RDA is a compromise between LDA and QDA, which allows one to shrink the separate covariances of QDA toward a common variance as in LDA. This method is very similar in flavor to ridge regression. The regularized covariance matrices of each class is Σ_k(α) = α Σ_k + (1 - α) Σ. The quadratic discriminant function is defined using the shrunken covariance matrices Σ_k(α). The parameter α in [0, 1] controls the complexity of the model. When α is one, RDA becomes QDA. While α is zero, RDA is equivalent to LDA. Therefore, the regularization factor α allows a continuum of models between LDA and QDA.

See Also:

• LDA
• QDA
• Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface Classifier

Classifier.Trainer<T,M>

Field Summary

Fields inherited from class AbstractClassifier

classes

Constructor Summary

Constructors

Constructor	Description
RDA(double[] priori, double[][] mu, Vector[] eigen, DenseMatrix[] scaling)	Constructor.
RDA(double[] priori, double[][] mu, Vector[] eigen, DenseMatrix[] scaling, IntSet labels)	Constructor.

Method Summary

Modifier and Type	Method	Description
static RDA	fit(double[][] x, int[] y, double alpha)	Fits regularized discriminant analysis.
static RDA	fit(double[][] x, int[] y, double alpha, double[] priori, double tol)	Fits regularized discriminant analysis.
static RDA	fit(double[][] x, int[] y, Properties params)	Fits regularized discriminant analysis.

Methods inherited from class QDA

fit, fit, predict, predict, priori, soft

Methods inherited from class AbstractClassifier

classes, numClasses

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface Classifier

applyAsDouble, applyAsInt, online, predict, predict, predict, predict, predict, predict, score, update, update, update

Constructor Details

RDA

public RDA(double[] priori,
 double[][] mu,
 Vector[] eigen,
 DenseMatrix[] scaling)

Constructor.

Parameters:

priori - a priori probabilities of each class.

mu - the mean vectors of each class.

eigen - the eigen values of each variance matrix.

scaling - the eigen vectors of each covariance matrix.

RDA

public RDA(double[] priori,
 double[][] mu,
 Vector[] eigen,
 DenseMatrix[] scaling,
 IntSet labels)

Constructor.

Parameters:

priori - a priori probabilities of each class.

mu - the mean vectors of each class.

eigen - the eigen values of each variance matrix.

scaling - the eigen vectors of each covariance matrix.

labels - the class label encoder.

Method Details

fit

public static RDA fit(double[][] x,
 int[] y,
 Properties params)

Fits regularized discriminant analysis.

Parameters:

x - training samples.

y - training labels.

params - the hyperparameters.

Returns:

the model.

fit

public static RDA fit(double[][] x,
 int[] y,
 double alpha)

Fits regularized discriminant analysis.

Parameters:

x - training samples.

y - training labels in [0, k), where k is the number of classes.

alpha - regularization factor in [0, 1] allows a continuum of models between LDA and QDA.

Returns:

the model.

fit

public static RDA fit(double[][] x,
 int[] y,
 double alpha,
 double[] priori,
 double tol)

Fits regularized discriminant analysis.

Parameters:

x - training samples.

y - training labels in [0, k), where k is the number of classes.

alpha - regularization factor in [0, 1] allows a continuum of models between LDA and QDA.

priori - the priori probability of each class. If null, it will be estimated from the training data.

tol - a tolerance to decide if a covariance matrix is singular; it will reject variables whose variance is less than tol².

Returns:

the model.