smile.classification

Class RDA

java.lang.Object

smile.classification.RDA

All Implemented Interfaces:

Classifier<double[]>

public class RDA
extends Object
implements Classifier<double[]>

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.

Author:

Haifeng Li

See Also:

LDA, QDA

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	RDA.Trainer Trainer for regularized discriminant analysis.

Constructor Summary

Constructors

Constructor and Description
RDA(double[][] x, int[] y, double alpha) Constructor.
RDA(double[][] x, int[] y, double[] priori, double alpha) Constructor.
RDA(double[][] x, int[] y, double[] priori, double alpha, double tol) Constructor.

Method Summary

Modifier and Type	Method and Description
double[]	getPriori() Returns a priori probabilities.
int	predict(double[] x) Predicts the class label of an instance.
int	predict(double[] x, double[] posteriori) Predicts the class label of an instance and also calculate a posteriori probabilities.

Methods inherited from class java.lang.Object

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

Constructor Detail

RDA

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

Constructor. Learn 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.

RDA

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

Constructor. Learn 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.

RDA

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

Constructor. Learn 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.

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

Method Detail

getPriori

public double[] getPriori()

Returns a priori probabilities.

predict

public int predict(double[] x)

Description copied from interface: Classifier

Predicts the class label of an instance.

Specified by:

predict in interface Classifier<double[]>

Parameters:

x - the instance to be classified.

Returns:

the predicted class label

predict

public int predict(double[] x,
                   double[] posteriori)

Description copied from interface: Classifier

Predicts the class label of an instance and also calculate a posteriori probabilities. Classifiers may NOT support this method since not all classification algorithms are able to calculate such a posteriori probabilities.

Specified by:

predict in interface Classifier<double[]>

Parameters:

x - the instance to be classified.

posteriori - the array to store a posteriori probabilities on output.

Returns:

the predicted class label