Beta Distribution with implementation of the regularized incomplete beta
function

###### Cauchy Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.CauchyDistribution

Cauchy distribution.

###### Chi Distribution

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ChiDistribution

Chi distribution.

###### Chi Squared Distribution

[BR75] (since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ChiSquaredDistribution

Chi-Squared distribution (a specialization of the Gamma distribution).

###### Constant Distribution

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ConstantDistribution

Pseudo distribution, that has a unique constant value.

###### Exp Gamma Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ExpGammaDistribution

Exp-Gamma Distribution, with random generation and density functions.

This distribution can be outlined as Y log[Gamma] distributed, or equivalently
exp(Y) Gamma.

Note: this matches the loggamma of SciPy, whereas Wolfram calls this the
Exponential Gamma Distribution "at times confused with the
LogGammaDistribution".

###### Exponential Distribution

(since 0.5.5)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ExponentialDistribution

Exponential distribution.

###### Exponentially Modified Gaussian Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.ExponentiallyModifiedGaussianDistribution

Exponentially modified Gaussian (EMG) distribution (ExGaussian distribution)
is a combination of a normal distribution and an exponential distribution.

Note that scipy uses a subtly different parameterization.

###### Gamma Distribution

[BR75, Ber76, AD74, AD82] (since 0.4.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution

Gamma Distribution, with random generation and density functions.

###### Generalized Extreme Value Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedExtremeValueDistribution

Generalized Extreme Value (GEV) distribution, also known as Fisher–Tippett
distribution.

This is a generalization of the Frechnet, Gumbel and (reversed) Weibull
distributions.

Implementation notice: In ELKI 0.8.0, the sign of the shape was negated.

###### Generalized Logistic Alternate Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedLogisticAlternateDistribution

Generalized logistic distribution.

One of multiple ways of generalizing the logistic distribution.

Where shape=0 yields the regular logistic distribution.

###### Generalized Logistic Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedLogisticDistribution

Generalized logistic distribution. (Type I, Skew-logistic distribution)

One of multiple ways of generalizing the logistic distribution.
pdf(x) = shape * exp(-x) / (1 + exp(-x))**(shape+1)
cdf(x) = pow(1+exp(-x), -shape)
Where shape=1 yields the regular logistic distribution.

###### Generalized Pareto Distribution

(since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedParetoDistribution

Generalized Pareto Distribution (GPD), popular for modeling long tail
distributions.

###### Gumbel Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.GumbelDistribution

Gumbel distribution, also known as Log-Weibull distribution.

###### Halton Uniform Distribution

[WH00] (since 0.5.5)

de.lmu.ifi.dbs.elki.math.statistics.distribution.HaltonUniformDistribution

Halton sequences are a pseudo-uniform distribution. The data is actually too
regular for a true uniform distribution, but as such will of course often
appear to be uniform.

Technically, they are based on Van der Corput sequence and the Von Neumann
Katutani transformation. These produce a series of integers which then are
converted to floating point values.

To randomize, we just choose a random starting position, as indicated by

###### Inverse Gaussian Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.InverseGaussianDistribution

Inverse Gaussian distribution aka Wald distribution.

Beware that SciPy uses a different location parameter.

InverseGaussian(a, x) scipy.stats.invgauss(a/x, x) Our parameter scheme is in
line with common literature. SciPy naming scheme has comparable notion of
location and scale across distributions. So both have their benefits.

###### Kappa Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.KappaDistribution

Kappa distribution, by Hosking.

###### Laplace Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.LaplaceDistribution

Laplace distribution also known as double exponential distribution

###### Log Gamma Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.LogGammaDistribution

Log-Gamma Distribution, with random generation and density functions.

This distribution can be outlined as Y exp(Gamma) or equivalently Log(Y)
Gamma.

Note: this is a different loggamma than scipy uses, but corresponds to the Log
Gamma Distribution of Wolfram, who notes that it is "at times confused with
ExpGammaDistribution".

###### Log Logistic Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.LogLogisticDistribution

Log-Logistic distribution also known as Fisk distribution.

###### Log Normal Distribution

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.LogNormalDistribution

Log-Normal distribution.

The parameterization of this class is somewhere inbetween of GNU R and SciPy.
Similar to GNU R we use the logmean and logstddev. Similar to Scipy, we also
have a location parameter that shifts the distribution.

Our implementation maps to SciPy’s as follows: scipy.stats.lognorm(logstddev,
shift, FastMath.exp(logmean))

###### Logistic Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.LogisticDistribution

Logistic distribution.

###### Normal Distribution

[Mar04, Oou96] (since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.NormalDistribution

Gaussian distribution aka normal distribution

###### Poisson Distribution

[Loa00] (since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.PoissonDistribution

INCOMPLETE implementation of the poisson distribution.

###### Rayleigh Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.RayleighDistribution

Rayleigh distribution, a special case of the Weibull distribution.

###### Skew Generalized Normal Distribution

[HW97] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.SkewGeneralizedNormalDistribution

Generalized normal distribution by adding a skew term, similar to lognormal
distributions.

This is one kind of generalized normal distributions. Note that there are
multiple that go by the name of a "Generalized Normal Distribution"; this is
what is currently called "version 2" in English Wikipedia.

###### Students T Distribution

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.StudentsTDistribution

Student’s t distribution.

###### Uniform Distribution

(since 0.2)

de.lmu.ifi.dbs.elki.math.statistics.distribution.UniformDistribution

Uniform distribution.

###### Weibull Distribution

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.WeibullDistribution

Weibull distribution.

######  AJ.2.1 Distribution Estimator

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator package:

Estimators for statistical distributions.

###### Cauchy MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.CauchyMADEstimator

Estimate Cauchy distribution parameters using Median and MAD.

###### EMG Olivier Norberg Estimator

[ON10] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.EMGOlivierNorbergEstimator

Naive distribution estimation using mean and sample variance.

###### Exp Gamma Exp MOM Estimator

(since 0.7.5)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.ExpGammaExpMOMEstimator

Simple parameter estimation for the ExpGamma distribution.

This is a very naive estimation, based on the mean and variance only,
sometimes referred to as the "Method of Moments" (MOM).

This estimator based on the GammaMOMEstimator and a simple exp data
transformation.

###### Exponential LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.ExponentialLMMEstimator

Estimate the parameters of a Gamma Distribution, using the methods of
L-Moments (LMM).

###### Exponential MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.ExponentialMADEstimator

Estimate Exponential distribution parameters using Median and MAD.

###### Exponential MOM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.ExponentialMOMEstimator

Estimate Exponential distribution parameters using the mean, which is the
maximum-likelihood estimate (MLE), but not very robust.

###### Exponential Median Estimator

[Oli06] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.ExponentialMedianEstimator

Estimate Exponential distribution parameters using Median and MAD.

###### Gamma Choi Wette Estimator

[CW69] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GammaChoiWetteEstimator

Estimate distribution parameters using the method by Choi and Wette.

###### Gamma LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GammaLMMEstimator

Estimate the parameters of a Gamma Distribution, using the methods of
L-Moments (LMM).

J. R. M. Hosking
Fortran routines for use with the method of L-moments Version 3.03
IBM Research.

###### Gamma MOM Estimator

[CB90] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GammaMOMEstimator

Simple parameter estimation for the Gamma distribution.

This is a very naive estimation, based on the mean and variance only,
sometimes referred to as the "Method of Moments" (MOM).

###### Generalized Extreme Value LMM Estimator

[HWW85] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GeneralizedExtremeValueLMMEstimator

Estimate the parameters of a Generalized Extreme Value Distribution, using the
methods of L-Moments (LMM).

###### Generalized Logistic Alternate LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GeneralizedLogisticAlternateLMMEstimator

Estimate the parameters of a Generalized Logistic Distribution, using the
methods of L-Moments (LMM).

###### Generalized Pareto LMM Estimator

[HWW85] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GeneralizedParetoLMMEstimator

Estimate the parameters of a Generalized Pareto Distribution (GPD), using the
methods of L-Moments (LMM).

###### Gumbel LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GumbelLMMEstimator

Estimate the parameters of a Gumbel Distribution, using the methods of
L-Moments (LMM).

###### Gumbel MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.GumbelMADEstimator

Parameter estimation via median and median absolute deviation from median
(MAD).

###### Inverse Gaussian ML Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.InverseGaussianMLEstimator

Estimate parameter of the inverse Gaussian (Wald) distribution.

###### Inverse Gaussian MOM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.InverseGaussianMOMEstimator

Estimate parameter of the inverse Gaussian (Wald) distribution.

###### Laplace LMM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LaplaceLMMEstimator

Estimate Laplace distribution parameters using the method of L-Moments (LMM).

###### Laplace MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LaplaceMADEstimator

Estimate Laplace distribution parameters using Median and MAD.

###### Laplace MLE Estimator

[Nor84] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LaplaceMLEEstimator

Estimate Laplace distribution parameters using Median and mean deviation from
median.

###### Log Gamma Log MOM Estimator

(since 0.7.5)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogGammaLogMOMEstimator

Simple parameter estimation for the LogGamma distribution.

This is a very naive estimation, based on the mean and variance only,
sometimes referred to as the "Method of Moments" (MOM).

This estimator based on the GammaMOMEstimator and a simple log data
transformation.

###### Log Logistic MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogLogisticMADEstimator

Estimate Logistic distribution parameters using Median and MAD.

###### Log Normal Bilkova LMM Estimator

[Bí12] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogNormalBilkovaLMMEstimator

Alternate estimate the parameters of a log Gamma Distribution, using the
methods of L-Moments (LMM) for the Generalized Normal Distribution.

###### Log Normal LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogNormalLMMEstimator

Estimate the parameters of a log Normal Distribution, using the methods of
L-Moments (LMM) for the Generalized Normal Distribution.

###### Log Normal Levenberg Marquardt KDE Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogNormalLevenbergMarquardtKDEEstimator

Distribution parameter estimation using Levenberg-Marquardt iterative
optimization and a kernel density estimation.

Note: this estimator is rather expensive, and needs optimization in the KDE
phase, which currently is O(n²)!

This estimator is primarily attractive when only part of the distribution was
observed.

###### Log Normal Log MAD Estimator

[Ham74] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogNormalLogMADEstimator

Estimator using Medians. More robust to outliers, and just slightly more
expensive (needs to copy the data for partial sorting to find the median).

###### Log Normal Log MOM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogNormalLogMOMEstimator

Naive distribution estimation using mean and sample variance.

This is a maximum-likelihood-estimator (MLE).

###### Logistic LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogisticLMMEstimator

Estimate the parameters of a Logistic Distribution, using the methods of
L-Moments (LMM).

###### Logistic MAD Estimator

[Oli06] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.LogisticMADEstimator

Estimate Logistic distribution parameters using Median and MAD.

###### Normal LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.NormalLMMEstimator

Estimate the parameters of a normal distribution using the method of L-Moments
(LMM).

###### Normal Levenberg Marquardt KDE Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.NormalLevenbergMarquardtKDEEstimator

Distribution parameter estimation using Levenberg-Marquardt iterative
optimization and a kernel density estimation.

Note: this estimator is rather expensive, and needs optimization in the KDE
phase, which currently is O(n²)!

This estimator is primarily attractive when only part of the distribution was
observed.

###### Normal MAD Estimator

[Ham74] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.NormalMADEstimator

Estimator using Medians. More robust to outliers, and just slightly more
expensive (needs to copy the data for partial sorting to find the median).

###### Normal MOM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.NormalMOMEstimator

Naive maximum-likelihood estimations for the normal distribution using mean
and sample variance.

While this is the most commonly used estimator, it is not very robust against
extreme values.

###### Rayleigh LMM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.RayleighLMMEstimator

Estimate the scale parameter of a (non-shifted) RayleighDistribution using the
method of L-Moments (LMM).

###### Rayleigh MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.RayleighMADEstimator

Estimate the parameters of a RayleighDistribution using the MAD.

###### Rayleigh MLE Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.RayleighMLEEstimator

Estimate the scale parameter of a (non-shifted) RayleighDistribution using a
maximum likelihood estimate.

###### Skew G Normal LMM Estimator

[Hos00] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.SkewGNormalLMMEstimator

Estimate the parameters of a skew Normal Distribution (Hoskin’s Generalized
Normal Distribution), using the methods of L-Moments (LMM).

###### Uniform Enhanced Min Max Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.UniformEnhancedMinMaxEstimator

Slightly improved estimation, that takes sample size into account and enhances
the interval appropriately.

###### Uniform LMM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.UniformLMMEstimator

Estimate the parameters of a normal distribution using the method of L-Moments
(LMM).

###### Uniform MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.UniformMADEstimator

Estimate Uniform distribution parameters using Median and MAD.

###### Uniform Min Max Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.UniformMinMaxEstimator

Estimate the uniform distribution by computing min and max.

###### Weibull LMM Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.WeibullLMMEstimator

Estimate parameters of the Weibull distribution using the method of L-Moments
(LMM).

###### Weibull Log MAD Estimator

[Oli08] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.WeibullLogMADEstimator

Parameter estimation via median and median absolute deviation from median
(MAD).

######  AJ.2.2 Distribution Estimator Meta

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.meta package:

Meta estimators: estimators that do not actually estimate themselves, but
instead use other estimators, e.g. on a trimmed data set, or as an ensemble.

###### Best Fit Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.meta.BestFitEstimator

A meta estimator that will try a number of (inexpensive) estimations, then
choose whichever works best.

###### Trimmed Estimator

(since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.meta.TrimmedEstimator

Trimmed wrapper around other estimators. Sorts the data, trims it, then
analyzes it using another estimator.

###### Winsorizing Estimator

[HMTW47] (since 0.6.0)

de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.meta.WinsorizingEstimator

Winsorizing or Georgization estimator. Similar to trimming, this is supposed
to be more robust to outliers. However, instead of removing the extreme
values, they are instead replaced with the cutoff value. This keeps the
quantity of the data the same, and will have a lower impact on variance and
similar measures.

#####  AJ.3 Intrinsicdimensionality

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality package:

Methods for estimating the intrinsic dimensionality.

###### ALID Estimator

[CHK16] (since 0.7.5)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.ALIDEstimator

ALID estimator of the intrinsic dimensionality (maximum likelihood estimator
for ID using auxiliary distances).

###### Aggregated Hill Estimator

[HKKP01] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.AggregatedHillEstimator

Estimator using the weighted average of multiple hill estimators.

###### Ensemble Estimator

(since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.EnsembleEstimator

Ensemble estimator taking the median of three of our best estimators.

However, the method-of-moments estimator seems to work best at least on
artificial distances - you don’t benefit from always choosing the second best,
so this ensemble approach does not appear to help.

This is an experimental estimator. Please cite ELKI when using.

###### GED Estimator

[HKN12] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.GEDEstimator

Generalized Expansion Dimension for estimating the intrinsic dimensionality.

###### Hill Estimator

[Hil75] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.HillEstimator

Hill estimator of the intrinsic dimensionality (maximum likelihood estimator
for ID).

###### L Moments Estimator

[Hos00, ACF+15] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.LMomentsEstimator

Probability weighted moments based estimator using L-Moments.

This is dervied from the PWM estimators of Amsaleg et al. using the L-Moments
estimation for the exponential distribution.

###### MOM Estimator

[ACF+15] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.MOMEstimator

Methods of moments estimator, using the first moment (i.e. average).

This could be generalized to higher order moments, but the variance increases
with the order, and we need this to work well with small sample sizes.

###### PWM2 Estimator

[ACF+15, MMW79] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.PWM2Estimator

Probability weighted moments based estimator, using the second moment.

It can be shown theoretically that this estimator is expected to have a higher
variance than the one using the first moment only, it is included for
completeness only.

###### PWM Estimator

[ACF+15, MMW79] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.PWMEstimator

Probability weighted moments based estimator.

###### RV Estimator

[ACF+15] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.RVEstimator

Regularly Varying Functions estimator of the intrinsic dimensionality

###### Zipf Estimator

[BDG05, SS96, KR96] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.ZipfEstimator

Zipf estimator (qq-estimator) of the intrinsic dimensionality.

Unfortunately, this estimator appears to have a bias. We have empirically
modified the plot position such that bias is reduced, but could not find the
proper way of removing this bias for small samples.

#####  AJ.4 Kernelfunctions

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

Kernel functions from statistics.

###### Biweight Kernel Density Function

[MN88] (since 0.6.0)

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

Biweight (Quartic) kernel density estimator.

###### Cosine Kernel Density Function

(since 0.6.0)

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

Cosine kernel density estimator.

###### Epanechnikov Kernel Density Function

[MN88] (since 0.6.0)

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

Epanechnikov kernel density estimator.

###### Gaussian Kernel Density Function

[MN88] (since 0.6.0)

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

Gaussian kernel density estimator.

###### Kernel Density Function

[MN88] (since 0.6.0)

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

Inner function of a kernel density estimator.

Note: as of now, this API does not support asymmetric kernels, which would be
difficult in the multivariate case.

###### Triangular Kernel Density Function

(since 0.6.0)

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

Triangular kernel density estimator.

###### Tricube Kernel Density Function

(since 0.6.0)

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

Tricube kernel density estimator.

###### Triweight Kernel Density Function

[MN88] (since 0.6.0)

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

Triweight kernel density estimator.

###### Uniform Kernel Density Function

[MN88] (since 0.6.0)

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

Uniform / Rectangular kernel density estimator.

#####  AJ.5 Tests

de.lmu.ifi.dbs.elki.math.statistics.tests package:

Statistical tests.

###### Anderson Darling Test

[AD52, Ste74] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.tests.AndersonDarlingTest

Perform Anderson-Darling test for a Gaussian distribution.

This is a test against normality / goodness of fit. I.e. you can use it to
reject the hypothesis that the data is normal distributed. Such tests are
sensitive to data set size: on small samples, even large deviations could be
by-chance and thus not allow rejection. On the other hand, on large data sets
even a slight deviation can be unlikely to happen if the data were indeed
normal distributed. Thus, this test is more likely to fail to reject small
data sets even when they intuitively do not appear to be normal distributed,
while it will reject large data sets that originate from a distribution only
slightly different from the normal distribution.

Before using, make sure you have understood statistical tests, and the
difference between failure-to-reject and acceptance!

The data size should be at least 8 before the results start getting somewhat
reliable. For large data sets, the chance of rejecting the normal distribution
hypothesis increases a lot: no real data looks exactly like a normal
distribution.

###### Kolmogorov Smirnov Test

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.tests.KolmogorovSmirnovTest

Kolmogorov-Smirnov test.

Class that tests two given real-valued data samples on whether they might have
originated from the same underlying distribution using the Kolmogorov-Smirnov
test statistic that compares the two empirical cumulative distribution
functions. The KS statistic is defined as the maximum absolute difference of
the empirical CDFs.

###### Standardized Two Sample Anderson Darling Test

[Pet76, SS87, Dar57] (since 0.7.0)

de.lmu.ifi.dbs.elki.math.statistics.tests.StandardizedTwoSampleAndersonDarlingTest

Perform a two-sample Anderson-Darling rank test, and standardize the statistic
according to Scholz and Stephens. Ties are handled as discussed in Equation 7
of Scholz and Stephens.

To access the non-standardized A2 scores, use the function
unstandardized(double[][]).

Compared to the Cramer-van Mises test, the Anderson-Darling test puts more
weight on the tail of the distribution. This variant only uses the ranks.

###### Welch T Test

(since 0.5.0)

de.lmu.ifi.dbs.elki.math.statistics.tests.WelchTTest

Calculates a test statistic according to Welch’s t test for two samples
Supplies methods for calculating the degrees of freedom according to the
Welch-Satterthwaite Equation. Also directly calculates a two-sided p-value for
the underlying t-distribution

###  Chapter Utilities

de.lmu.ifi.dbs.elki.utilities package:

Utility and helper classes - commonly used data structures, output formatting,
exceptions, …

Specialized utility classes (which often collect static utility methods only)
can be found in other places of ELKI as well, as seen below.

Important utility function collections:

  * •

Basic and low-level:

    * ◦

Util: Miscellaneous utility functions.

    * ◦

LoggingUtil: simple logging access.

    * ◦

MathUtil: Mathematics utility functions.

    * ◦

VectorUtil: Vector and Matrix functions.

    * ◦

SpatialUtil: Spatial MBR computations (intersection, union etc.).

    * ◦

ByteArrayUtil: byte array processing (low-level IO via byte arrays).

    * ◦

FileUtil: File and file name utility functions.

    * ◦

ClassGenericsUtil: Generic classes (instantiation, arrays of arrays, sets that
require safe but unchecked casts).

  * •

Database-related:

    * ◦

TypeUtil: Data type utility functions and common type definitions.

    * ◦

QueryUtil: Database Query API simplifications.

    * ◦

DBIDUtil: Database ID DBID handling.

    * ◦

DataStoreUtil: Data storage layer (like Maps).

    * ◦

DatabaseUtil: database utility functions (centroid etc.).

    * ◦

ResultUtil: result processing functions (e.g. extracting sub-results).

  * •

Output-related:

    * ◦

FormatUtil: output formatting.

    * ◦

SVGUtil: SVG generation (XML DOM based).

    * ◦

BatikUtil: Apache Batik SVG utilities (coordinate transforms screen to
canvas).

  * •

Specialized:

    * ◦

OptionUtil: Managing parameter settings

    * ◦

ELKIServiceRegistry: class and classpath inspection.

    * ◦

RStarTreeUtil: reporting page file accesses.

###  Appendix AK Datastructures

de.lmu.ifi.dbs.elki.utilities.datastructures package:

Basic memory structures such as heaps and object hierarchies.

#####  AK.1 Arrays

de.lmu.ifi.dbs.elki.utilities.datastructures.arrays package:

Utilities for arrays: advanced sorting for primitvie arrays.

###### Integer Array Quick Sort

[Yar09] (since 0.5.5)

de.lmu.ifi.dbs.elki.utilities.datastructures.arrays.IntegerArrayQuickSort

Class to sort an int array, using a modified quicksort.

#####  AK.2 Unionfind

de.lmu.ifi.dbs.elki.utilities.datastructures.unionfind package:

Union-find data structures.

###### Weighted Quick Union Integer

[Sed98] (since 0.7.1)

de.lmu.ifi.dbs.elki.utilities.datastructures.unionfind.WeightedQuickUnionInteger

Union-find algorithm for primitive integers, with optimizations.

This is the weighted quick union approach, weighted by count and using path-
halving for optimization.

###### Weighted Quick Union Range DBI Ds

[Sed98] (since 0.7.0)

de.lmu.ifi.dbs.elki.utilities.datastructures.unionfind.WeightedQuickUnionRangeDBIDs

Union-find algorithm for DBIDRange only, with optimizations.

To instantiate, use
UnionFindUtil.make(de.lmu.ifi.dbs.elki.database.ids.StaticDBIDs). This version
is optimized for DBIDRanges.

This is the weighted quick union approach, weighted by count and using path-
halving for optimization.

###### Weighted Quick Union Static DBI Ds

[Sed98] (since 0.7.0)

de.lmu.ifi.dbs.elki.utilities.datastructures.unionfind.WeightedQuickUnionStaticDBIDs

Union-find algorithm for StaticDBIDs, with optimizations.

To instantiate, use
UnionFindUtil.make(de.lmu.ifi.dbs.elki.database.ids.StaticDBIDs), which will
automatically choose the best implementation available.

This is the weighted quick union approach, weighted by count and using path-
halving for optimization.

This version needs more memory than WeightedQuickUnionRangeDBIDs but can work
with any unmodifiable DBID set (although ArrayDBIDs are recommended).

###  Appendix AL Ensemble

de.lmu.ifi.dbs.elki.utilities.ensemble package:

Utility classes for simple ensembles.

###### Ensemble Voting Inverse Multiplicative

(since 0.6.0)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingInverseMultiplicative

Inverse multiplicative voting: $1-\prod_{i}(1-s_{i})$

###### Ensemble Voting Max

(since 0.5.5)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingMax

Simple combination rule, by taking the maximum.

###### Ensemble Voting Mean

(since 0.5.5)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingMean

Simple combination rule, by taking the mean

###### Ensemble Voting Median

(since 0.5.5)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingMedian

Simple combination rule, by taking the median.

Note: median is very similar to a majority voting!

###### Ensemble Voting Min

(since 0.5.5)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingMin

Simple combination rule, by taking the minimum.

###### Ensemble Voting Multiplicative

(since 0.6.0)

de.lmu.ifi.dbs.elki.utilities.ensemble.EnsembleVotingMultiplicative

Inverse multiplicative voting: $\prod_{i}s_{i}$

###  Appendix AM Random

de.lmu.ifi.dbs.elki.utilities.random package:

Random number generation.

###### Fast Non Threadsafe Random

[Lem16] (since 0.6.0)

de.lmu.ifi.dbs.elki.utilities.random.FastNonThreadsafeRandom

Drop-in replacement for Random, but not using atomic long seeds. This
implementation is no longer thread-safe (but faster)!

It is still the same Linear Congruential Generator (LCG), with a cycle length
of 248, of which we only use 32 bits at a time. Given the same seed, it is
expected to produce the exact same random sequence as Java’s Random.

###### Xor Shift 1024 Non Threadsafe Random

[Lem16, Vig14] (since 0.7.0)

de.lmu.ifi.dbs.elki.utilities.random.XorShift1024NonThreadsafeRandom

Replacement for Java’s Random class, using a different random number
generation strategy. Java’s random generator is optimized for speed, but may
lack the randomness needed for more complex experiments.

This approach is based on the work on XorShift1024* by Sebastiano Vigna, with
the original copyright statement:

Written in 2014 by Sebastiano Vigna<EMAIL_ADDRESS>
To the extent possible under law, the author has dedicated all copyright and
related and neighboring rights to this software to the public domain
worldwide. This software is distributed without any warranty.

See http://creativecommons.org/publicdomain/zero/1.0/

###### Xor Shift 64 Non Threadsafe Random

[Lem16, Vig14] (since 0.7.0)

de.lmu.ifi.dbs.elki.utilities.random.XorShift64NonThreadsafeRandom

Replacement for Java’s Random class, using a different random number
generation strategy. Java’s random generator is optimized for speed, but may
lack the randomness needed for more complex experiments.

This approach is based on the work on XorShift64* by Sebastiano Vigna, with
the original copyright statement:

Written in 2014 by Sebastiano Vigna<EMAIL_ADDRESS>
To the extent possible under law, the author has dedicated all copyright and
related and neighboring rights to this software to the public domain
worldwide. This software is distributed without any warranty.

See http://creativecommons.org/publicdomain/zero/1.0/

###### Xoroshiro 128 Non Threadsafe Random

[Lem16, BV16] (since 0.7.5)

de.lmu.ifi.dbs.elki.utilities.random.Xoroshiro128NonThreadsafeRandom

Replacement for Java’s Random class, using a different random number
generation strategy. Java’s random generator is optimized for speed, but may
lack the randomness needed for more complex experiments.

This approach is based on the work on Xoroshiro128+ by Sebastiano Vigna, with
the original copyright statement:

Written in 2016 by David Blackman and Sebastiano Vigna<EMAIL_ADDRESS>
To the extent possible under law, the author has dedicated all copyright and
related and neighboring rights to this software to the public domain
worldwide. This software is distributed without any warranty.

See http://creativecommons.org/publicdomain/zero/1.0/

###  Appendix AN Referencepoints

de.lmu.ifi.dbs.elki.utilities.referencepoints package:

Package containing strategies to obtain reference points

Shared code for various algorithms that use reference points.

###### Axis Based Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.AxisBasedReferencePoints

Strategy to pick reference points by placing them on the axis ends.

This strategy produces n+2 reference points that lie on the edges of the
surrounding cube.

###### Full Database Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.FullDatabaseReferencePoints

Strategy to use the complete database as reference points.

###### Grid Based Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.GridBasedReferencePoints

Grid-based strategy to pick reference points.

###### Random Generated Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.RandomGeneratedReferencePoints

Reference points generated randomly within the used data space.

###### Random Sample Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.RandomSampleReferencePoints

Random-Sampling strategy for picking reference points.

###### Star Based Reference Points

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.referencepoints.StarBasedReferencePoints

Star-based strategy to pick reference points.

###  Appendix AO Scaling

de.lmu.ifi.dbs.elki.utilities.scaling package:

Scaling functions: linear, logarithmic, gamma, clipping, …

###### Clip Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.ClipScaling

Scale implementing a simple clipping. Values less than the specified minimum
will be set to the minimum, values larger than the maximum will be set to the
maximum.

###### Gamma Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.GammaScaling

Non-linear scaling function using a Gamma curve.

###### Identity Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.IdentityScaling

The trivial "identity" scaling function.

###### Linear Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.LinearScaling

Simple linear scaling function.

###### Minus Log Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.MinusLogScaling

Scaling function to invert values by computing -1 * Math.log(x)

#####  AO.1 Outlier

de.lmu.ifi.dbs.elki.utilities.scaling.outlier package:

Scaling of Outlier scores, that require a statistical analysis of the
occurring values

###### COP Outlier Scaling

[KKSZ12, KKSZ11] (since 0.6.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.COPOutlierScaling

CDF based outlier score scaling.

Enhanced version of the scaling proposed in:

Hans-Peter Kriegel, Peer Kröger, Erich Schubert, Arthur Zimek
Interpreting and Unifying Outlier Scores
Proc. 11th SIAM International Conference on Data Mining (SDM 2011)

See also:

Hans-Peter Kriegel, Peer Kröger, Erich Schubert, Arthur Zimek
Outlier Detection in Arbitrarily Oriented Subspaces
in: Proc. IEEE Int. Conf. on Data Mining (ICDM 2012)

###### HeDES Normalization Outlier Scaling

[NAG10] (since 0.4.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.HeDESNormalizationOutlierScaling

Normalization used by HeDES

###### Log Ranking Pseudo Outlier Scaling

(since 0.7.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.LogRankingPseudoOutlierScaling

This is a pseudo outlier scoring obtained by only considering the ranks of the
objects. However, the ranks are not mapped linearly to scores, but using a
normal distribution.

###### Minus Log Gamma Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.MinusLogGammaScaling

Scaling that can map arbitrary values to a probability in the range of [0:1],
by assuming a Gamma distribution on the data and evaluating the Gamma CDF.

###### Minus Log Standard Deviation Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.MinusLogStandardDeviationScaling

Scaling that can map arbitrary values to a probability in the range of [0:1].

Transformation is done using the formula
$\max\\{0,\mathrm{erf}(\lambda\frac{x-\mu}{\sigma\sqrt{2}})\\}$

Where mean can be fixed to a given value, and stddev is then computed against
this mean.

###### Mixture Model Outlier Scaling

[GT06] (since 0.4.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.MixtureModelOutlierScaling

Tries to fit a mixture model (exponential for inliers and gaussian for
outliers) to the outlier score distribution.

Note: we found this method to often fail, and fit the normal distribution to
the inliers instead of the outliers, yielding reversed results.

###### Multiplicative Inverse Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.MultiplicativeInverseScaling

Scaling function to invert values by computing 1/x, but in a variation that
maps the values to the [0:1] interval and avoiding division by 0.

The exact formula can be written as

$1/(v\cdot\max_{x\neq 0}\frac{1}{|x|})=\min_{x\neq 0}(|x|)/v$

with 1 / 0 := 1

###### Outlier Gamma Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.OutlierGammaScaling

Scaling that can map arbitrary values to a probability in the range of [0:1]
by assuming a Gamma distribution on the values.

###### Outlier Linear Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.OutlierLinearScaling

Scaling that can map arbitrary values to a value in the range of [0:1].

Transformation is done by linear mapping onto 0:1 using the minimum and
maximum values.

###### Outlier Minus Log Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.OutlierMinusLogScaling

Scaling function to invert values by computing -log(x)

Useful for example for scaling ABOD, but see MinusLogStandardDeviationScaling
and MinusLogGammaScaling for more advanced scalings for this algorithm.

###### Outlier Sqrt Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.OutlierSqrtScaling

Scaling that can map arbitrary positive values to a value in the range of
[0:1].

Transformation is done by taking the square root, then doing a linear linear
mapping onto 0:1 using the minimum values seen.

###### Ranking Pseudo Outlier Scaling

(since 0.4.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.RankingPseudoOutlierScaling

This is a pseudo outlier scoring obtained by only considering the ranks of the
objects. However, the ranks are not mapped linearly to scores, but using a
normal distribution.

###### Sigmoid Outlier Scaling

[GT06] (since 0.4.0)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.SigmoidOutlierScaling

Tries to fit a sigmoid to the outlier scores and use it to convert the values
to probability estimates in the range of 0.0 to 1.0

###### Sqrt Standard Deviation Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.SqrtStandardDeviationScaling

Scaling that can map arbitrary values to a probability in the range of [0:1].

Transformation is done using the formulas

$y=\sqrt{x-\min}$
$s=\max\\{0,\textrm{erf}(\lambda\frac{y-\mu}{\sigma\sqrt{2}})\\}$

Where min and mean $\mu$ can be fixed to a given value, and stddev $\sigma$ is
then computed against this mean.

###### Standard Deviation Scaling

[KKSZ11] (since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.StandardDeviationScaling

Scaling that can map arbitrary values to a probability in the range of [0:1].

Transformation is done using the formula
$\max\\{0,\mathrm{erf}(\lambda\frac{x-\mu}{\sigma\sqrt{2}})\\}$

Where mean can be fixed to a given value, and stddev is then computed against
this mean.

###### TopK Outlier Scaling

(since 0.3)

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.TopKOutlierScaling

Outlier scaling function that only keeps the top k outliers.

###  Chapter Visualization

de.lmu.ifi.dbs.elki.visualization package:

Visualization package of ELKI.

###  Appendix AP Parallel3d

de.lmu.ifi.dbs.elki.visualization.parallel3d package:

3DPC: 3D parallel coordinate plot visualization for ELKI.

This is an add-on module. Details were published as:

###### Open GL3D Parallel Coordinates

[AKSZ13] (since 0.6.0)

de.lmu.ifi.dbs.elki.visualization.parallel3d.OpenGL3DParallelCoordinates

Simple JOGL2 based parallel coordinates visualization.

###### Parallel 3D Renderer

[AKSZ13] (since 0.6.0)

de.lmu.ifi.dbs.elki.visualization.parallel3d.Parallel3DRenderer

Renderer for 3D parallel plots.

The tricky part here is the vertex buffer layout. We are drawing lines, so we
need two vertices for each macro edge (edge between axes in the plot). We
furthermore need the following properties: we need to draw edges sorted by
depth to allow alpha and smoothing to work, and we need to be able to have
different colors for clusters. An efficient batch therefore will consist of
one edge-color combination. The input data comes in color-object ordering, so
we need to seek through the edges when writing the buffer.

In total, we have 2 * obj.size * edges.size vertices.

Where obj.size = sum(col.sizes)

#####  AP.1 Layout

de.lmu.ifi.dbs.elki.visualization.parallel3d.layout package:

Layouting algorithms for 3D parallel coordinate plots.

###### Compact Circular MST Layout 3DPC

[AKSZ13] (since 0.6.0)

de.lmu.ifi.dbs.elki.visualization.parallel3d.layout.CompactCircularMSTLayout3DPC

Simple circular layout based on the minimum spanning tree.

###### Multidimensional Scaling MST Layout 3DPC

[AKSZ13] (since 0.6.0)

de.lmu.ifi.dbs.elki.visualization.parallel3d.layout.MultidimensionalScalingMSTLayout3DPC

Layout the axes by multi-dimensional scaling.

###### Simple Circular MST Layout 3DPC

[AKSZ13] (since 0.6.0)

de.lmu.ifi.dbs.elki.visualization.parallel3d.layout.SimpleCircularMSTLayout3DPC

Simple circular layout based on the minimum spanning tree.

###  Appendix AQ Projector

de.lmu.ifi.dbs.elki.visualization.projector package:

Projectors are responsible for finding appropriate projections for data
relations.

###### Histogram Factory

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.projector.HistogramFactory

Produce one-dimensional projections.

###### OPTICS Projector Factory

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.projector.OPTICSProjectorFactory

Produce OPTICS plot projections

###### Parallel Plot Factory

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.projector.ParallelPlotFactory

Produce parallel axes projections.

###### Parallel Plot Projector

[Ins09] (since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.projector.ParallelPlotProjector

ParallelPlotProjector is responsible for producing a parallel axes
visualization.

###### Scatter Plot Factory

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.projector.ScatterPlotFactory

Produce scatterplot projections.

###  Appendix AR Visualizers

de.lmu.ifi.dbs.elki.visualization.visualizers package:

Visualizers for various results

#####  AR.1 Actions

de.lmu.ifi.dbs.elki.visualization.visualizers.actions package:

Action-only "visualizers" that only produce menu entries.

###### Cluster Style Action

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.actions.ClusterStyleAction

Actions to use clusterings for styling.

#####  AR.2 Histogram

de.lmu.ifi.dbs.elki.visualization.visualizers.histogram package:

Visualizers based on 1D projected histograms.

###### Colored Histogram Visualizer

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.histogram.ColoredHistogramVisualizer

Generates a SVG-Element containing a histogram representing the distribution
of the database’s objects.

#####  AR.3 Optics

de.lmu.ifi.dbs.elki.visualization.visualizers.optics package:

Visualizers that do work on OPTICS plots

###### OPTICS Cluster Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.optics.OPTICSClusterVisualization

Visualize the clusters and cluster hierarchy found by OPTICS on the OPTICS
Plot.

###### OPTICS Plot Cut Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.optics.OPTICSPlotCutVisualization

Visualizes a cut in an OPTICS Plot to select an Epsilon value and generate a
new clustering result.

###### OPTICS Plot Selection Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.optics.OPTICSPlotSelectionVisualization

Handle the marker in an OPTICS plot.

###### OPTICS Plot Visualizer

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.optics.OPTICSPlotVisualizer

Visualize an OPTICS result by constructing an OPTICS plot for it.

###### OPTICS Steep Area Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.optics.OPTICSSteepAreaVisualization

Visualize the steep areas found in an OPTICS plot

#####  AR.4 Pairsegments

de.lmu.ifi.dbs.elki.visualization.visualizers.pairsegments package:

Visualizers for inspecting cluster differences using pair counting segments.

###### Circle Segments Visualizer

[AGK+12] (since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.pairsegments.CircleSegmentsVisualizer

Visualizer to draw circle segments of clusterings and enable interactive
selection of segments. For "empty" segments, all related segments are selected
instead, to visualize the differences.

#####  AR.5 Parallel

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel package:

Visualizers based on parallel coordinates.

###### Axis Reorder Visualization

(since 0.5.5)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.AxisReorderVisualization

Interactive SVG-Elements for reordering the axes.

###### Axis Visibility Visualization

(since 0.5.5)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.AxisVisibilityVisualization

Layer for controlling axis visbility in parallel coordinates.

###### Bounding Box Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.BoundingBoxVisualization

Draw spatial objects (except vectors!)

###### Line Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.LineVisualization

Generates data lines.

###### Parallel Axis Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.ParallelAxisVisualization

Generates a SVG-Element containing axes, including labeling.

######  AR.5.1 Parallel Cluster

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.cluster package:

Visualizers for clustering results based on parallel coordinates.

###### Cluster Outline Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.cluster.ClusterOutlineVisualization

Generates a SVG-Element that visualizes the area covered by a cluster.

###### Cluster Parallel Mean Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.cluster.ClusterParallelMeanVisualization

Generates a SVG-Element that visualizes cluster means.

######  AR.5.2 Parallel Index

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.index package:

Visualizers for index structure based on parallel coordinates.

###### R Tree Parallel Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.index.RTreeParallelVisualization

Visualize the of an R-Tree based index.

######  AR.5.3 Parallel Selection

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.selection package:

Visualizers for object selection based on parallel projections.

###### Selection Axis Range Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.selection.SelectionAxisRangeVisualization

Visualizer for generating an SVG-Element representing the selected range.

###### Selection Line Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.selection.SelectionLineVisualization

Visualizer for generating SVG-Elements representing the selected objects

###### Selection Tool Axis Range Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.selection.SelectionToolAxisRangeVisualization

Tool-Visualization for the tool to select axis ranges

###### Selection Tool Line Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.parallel.selection.SelectionToolLineVisualization

Tool-Visualization for the tool to select objects

#####  AR.6 Scatterplot

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot package:

Visualizers based on scatterplots.

###### Axis Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.AxisVisualization

Generates a SVG-Element containing axes, including labeling.

###### Marker Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.MarkerVisualization

Visualize e.g. a clustering using different markers for different clusters.
This visualizer is not constraint to clusters. It can in fact visualize any
kind of result we have a style source for.

###### Polygon Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.PolygonVisualization

Renders PolygonsObject in the data set.

###### Reference Points Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.ReferencePointsVisualization

The actual visualization instance, for a single projection

###### Tooltip Score Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.TooltipScoreVisualization

Generates a SVG-Element containing Tooltips. Tooltips remain invisible until
their corresponding Marker is touched by the cursor and stay visible as long
as the cursor lingers on the marker.

###### Tooltip String Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.TooltipStringVisualization

Generates a SVG-Element containing Tooltips. Tooltips remain invisible until
their corresponding Marker is touched by the cursor and stay visible as long
as the cursor lingers on the marker.

######  AR.6.1 Scatterplot Cluster

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster package:

Visualizers for clustering results based on 2D projections.

###### Cluster Hull Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.ClusterHullVisualization

Visualizer for generating an SVG-Element containing the convex hull / alpha
shape of each cluster.

###### Cluster Mean Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.ClusterMeanVisualization

Visualize the mean of a KMeans-Clustering

###### Cluster Order Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.ClusterOrderVisualization

Cluster order visualizer: connect objects via the spanning tree the cluster
order represents.

###### Cluster Star Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.ClusterStarVisualization

Visualize the mean of a KMeans-Clustering using stars.

###### EM Cluster Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.EMClusterVisualization

Visualizer for generating SVG-Elements containing ellipses for first, second
and third standard deviation. In more than 2-dimensional data, the class tries
to approximate the cluster extends.

###### Voronoi Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.cluster.VoronoiVisualization

Visualizer drawing Voronoi cells for k-means clusterings.

See also: KMeans clustering

######  AR.6.2 Scatterplot Density

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.density package:

Visualizers for data set density in a scatterplot projection.

###### Density Estimation Overlay

[Sco92] (since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.density.DensityEstimationOverlay

A simple density estimation visualization, based on a simple kernel-density in
the projection, not the actual data!

######  AR.6.3 Scatterplot Index

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.index package:

Visualizers for index structures based on 2D projections.

###### Tree MBR Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.index.TreeMBRVisualization

Visualize the bounding rectangles of an R-Tree based index.

###### Tree Sphere Visualization

(since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.index.TreeSphereVisualization

Visualize the bounding sphere of a metric index.

######  AR.6.4 Scatterplot Outlier

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.outlier package:

Visualizers for outlier scores based on 2D projections.

###### Bubble Visualization

[AKR+10] (since 0.5.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.outlier.BubbleVisualization

Generates a SVG-Element containing bubbles. A Bubble is a circle visualizing
an outlierness-score, with its center at the position of the visualized object
and its radius depending on the objects score.

###### COP: Correlation Outlier Probability

[KKSZ12] (since 0.5.5)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.outlier.COPVectorVisualization

Visualize error vectors as produced by COP.

######  AR.6.5 Scatterplot Selection

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection package:

Visualizers for object selection based on 2D projections.

###### Distance Function Visualization

(since 0.5.5)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.DistanceFunctionVisualization

Factory for visualizers to generate an SVG-Element containing dots as markers
representing the kNN of the selected Database objects.

To use this, add a kNN preprocessor index to your database!

###### Move Objects Tool Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.MoveObjectsToolVisualization

Tool to move the currently selected objects.

###### Selection Convex Hull Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.SelectionConvexHullVisualization

Visualizer for generating an SVG-Element containing the convex hull of the
selected points

###### Selection Cube Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.SelectionCubeVisualization

Visualizer for generating an SVG-Element containing a cube as marker
representing the selected range for each dimension

###### Selection Dot Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.SelectionDotVisualization

Visualizer for generating an SVG-Element containing dots as markers
representing the selected Database’s objects.

###### Selection Tool Cube Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.SelectionToolCubeVisualization

Tool-Visualization for the tool to select ranges.

###### Selection Tool Dot Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.selection.SelectionToolDotVisualization

Tool-Visualization for the tool to select objects

######  AR.6.6 Scatterplot Uncertain

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.uncertain package:

Visualizers for uncertain data.

###### Uncertain Bounding Box Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.uncertain.UncertainBoundingBoxVisualization

Visualize uncertain objects by their bounding box.

Note: this is currently a hack. Our projection only applies to vector field
relations currently, and this visualizer activates if such a relation (e.g. a
sample, or the center of mass) has a parent relation of type UncertainObject.
But it serves the purpose.

###### Uncertain Instances Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.uncertain.UncertainInstancesVisualization

Visualize a single derived sample from an uncertain database.

Note: this is currently a hack. Our projection only applies to vector field
relations currently, and this visualizer activates if such a relation (e.g. a
sample, or the center of mass) has a parent relation of type UncertainObject.
But it serves the purpose.

###### Uncertain Samples Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.uncertain.UncertainSamplesVisualization

Visualize uncertain objects by multiple samples.

Note: this is currently a hack. Our projection only applies to vector field
relations currently, and this visualizer activates if such a relation (e.g. a
sample, or the center of mass) has a parent relation of type UncertainObject.
But it serves the purpose.

#####  AR.7 Visunproj

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj package:

Visualizers that do not use a particular projection.

###### Dendrogram Visualization

(since 0.7.5)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.DendrogramVisualization

Dendrogram visualizer.

###### Evaluation Visualization

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.EvaluationVisualization

Pseudo-Visualizer, that lists the cluster evaluation results found.

###### Histogram Visualization

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.HistogramVisualization

Visualizer to draw histograms.

###### Key Visualization

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.KeyVisualization

Visualizer, displaying the key for a clustering.

###### Label Visualization

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.LabelVisualization

Trivial "visualizer" that displays a static label. The visualizer is meant to
be used for dimension labels in the overview.

###### Pixmap Visualizer

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.PixmapVisualizer

Visualize an arbitrary pixmap result.

###### Settings Visualization

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.SettingsVisualization

Pseudo-Visualizer, that lists the settings of the algorithm-

###### Similarity Matrix Visualizer

(since 0.4.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.SimilarityMatrixVisualizer

Visualize a similarity matrix with object labels

###### XY Curve Visualization

(since 0.3)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.XYCurveVisualization

Visualizer to render a simple 2D curve such as a ROC curve.

###### XY Plot Visualization

(since 0.7.0)

de.lmu.ifi.dbs.elki.visualization.visualizers.visunproj.XYPlotVisualization

Visualizer to render a simple 2D curve such as a ROC curve.

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