smile.classification

Class RDA

java.lang.Object

smile.classification.QDA

smile.classification.RDA

All Implemented Interfaces:

java.io.Serializable, java.util.function.ToDoubleFunction<double[]>, java.util.function.ToIntFunction<double[]>, Classifier<double[]>, SoftClassifier<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

Constructor Summary

Constructors

Constructor and Description
RDA(double[] priori, double[][] mu, double[][] eigen, smile.math.matrix.DenseMatrix[] scaling) Constructor.
RDA(double[] priori, double[][] mu, double[][] eigen, smile.math.matrix.DenseMatrix[] scaling, smile.util.IntSet labels) Constructor.

Method Summary

Modifier and Type	Method and Description
static RDA	fit(double[][] x, int[] y, double alpha) Learn regularized discriminant analysis.
static RDA	fit(double[][] x, int[] y, double alpha, double[] priori, double tol) Learn regularized discriminant analysis.
static RDA	fit(double[][] x, int[] y, java.util.Properties prop) Learns regularized discriminant analysis.
static RDA	fit(smile.data.formula.Formula formula, smile.data.DataFrame data) Learns regularized discriminant analysis.
static RDA	fit(smile.data.formula.Formula formula, smile.data.DataFrame data, java.util.Properties prop) Learns regularized discriminant analysis.

Methods inherited from class smile.classification.QDA

fit, fit, predict, predict, priori

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.classification.Classifier

applyAsDouble, applyAsInt, f, predict

Constructor Detail

RDA

public RDA(double[] priori,
           double[][] mu,
           double[][] eigen,
           smile.math.matrix.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,
           double[][] eigen,
           smile.math.matrix.DenseMatrix[] scaling,
           smile.util.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 - class labels

Method Detail

fit

public static RDA fit(smile.data.formula.Formula formula,
                      smile.data.DataFrame data)

Learns regularized discriminant analysis.

Parameters:

formula - a symbolic description of the model to be fitted.

data - the data frame of the explanatory and response variables.

fit

public static RDA fit(smile.data.formula.Formula formula,
                      smile.data.DataFrame data,
                      java.util.Properties prop)

Learns regularized discriminant analysis.

Parameters:

formula - a symbolic description of the model to be fitted.

data - the data frame of the explanatory and response variables.

fit

public static RDA fit(double[][] x,
                      int[] y,
                      java.util.Properties prop)

Learns regularized discriminant analysis.

Parameters:

x - training samples.

y - training labels.

fit

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

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.

fit

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

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. 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.