de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions

Class GaussianKernelDensityFunction

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions.GaussianKernelDensityFunction

All Implemented Interfaces:

KernelDensityFunction

public final class GaussianKernelDensityFunction
extends Object
implements KernelDensityFunction

Gaussian kernel density estimator.

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GaussianKernelDensityFunction.Parameterizer Parameterization stub.

Field Summary

Fields

Modifier and Type	Field and Description
static double	CANONICAL_BANDWIDTH Canonical bandwidth: (1./(4*pi))^(1/10)
static GaussianKernelDensityFunction	KERNEL Static instance.
static double	R R constant.

Constructor Summary

Constructors

Modifier	Constructor and Description
private	GaussianKernelDensityFunction() Private, empty constructor.

Method Summary

Methods

Modifier and Type	Method and Description
double	canonicalBandwidth() Get the canonical bandwidth for this kernel.
double	density(double delta) Density contribution of a point at the given relative distance delta >= 0.
double	getR() Get the R integral of the kernel, \int K^2(x) dx TODO: any better name for this?
double	standardDeviation() Get the standard deviation of the kernel function.

Methods inherited from class java.lang.Object

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

Field Detail

KERNEL

public static final GaussianKernelDensityFunction KERNEL

Static instance.

CANONICAL_BANDWIDTH

@Reference(authors="J.S. Marron, D. Nolan",
           title="Canonical kernels for density estimation",
           booktitle="Statistics & Probability Letters, Volume 7, Issue 3",
           url="http://dx.doi.org/10.1016/0167-7152(88)90050-8")
public static final double CANONICAL_BANDWIDTH

Canonical bandwidth: (1./(4*pi))^(1/10)

R

public static final double R

R constant.

Constructor Detail

GaussianKernelDensityFunction

private GaussianKernelDensityFunction()

Private, empty constructor. Use the static instance!

Method Detail

density

public double density(double delta)

Description copied from interface: KernelDensityFunction

Density contribution of a point at the given relative distance delta >= 0. Note that for delta < 0, in particular for delta < 1, the results may become invalid. So usually, you will want to invoke this as: kernel.density(Math.abs(delta))

Specified by:

density in interface KernelDensityFunction

Parameters:

delta - Relative distance

Returns:

density contribution

canonicalBandwidth

public double canonicalBandwidth()

Description copied from interface: KernelDensityFunction

Get the canonical bandwidth for this kernel. Note: R uses a different definition of "canonical bandwidth", and also uses differently scaled kernels.

Specified by:

canonicalBandwidth in interface KernelDensityFunction

Returns:

Canonical bandwidth

standardDeviation

public double standardDeviation()

Description copied from interface: KernelDensityFunction

Get the standard deviation of the kernel function.

Specified by:

standardDeviation in interface KernelDensityFunction

Returns:

Standard deviation

getR

public double getR()

Description copied from interface: KernelDensityFunction

Get the R integral of the kernel, \int K^2(x) dx TODO: any better name for this?

Specified by:

getR in interface KernelDensityFunction

Returns:

R value