EMGauss

Expectation-Maximization algorithm to calculate optimal Gaussian Mixture Model for given data in one Dimension.

EM algorithm

Expectation-Maximization

Expectation

Maximization

Expectation-Maximization algorithm

Multimodal distributions can be modelled as a mixture of components. The model is derived using the Pareto Density Estimation (PDE) for an estimation of the pdf. PDE has been designed in particular to identify groups/classes in a dataset. Precise limits for the classes can be calculated using the theorem of Bayes. Verification of the model is possible by QQ plot, Chi-squared test and Kolmogorov-Smirnov test. The package is based on the publication of Ultsch, A., Thrun, M.C., Hansen-Goos, O., Lotsch, J. (2015) <DOI:10.3390/ijms161025897>.

Michael Thrun

AdaptGauss

Gaussian Mixture Models (GMM)

Onno Hansen-Goos

Rabea Griese

Catharina Lippmann

Florian Lerch

Quirin Stier

Jorn Lotsch

Luca Brinkmann

Alfred Ultsch

EMGauss function

<dl> <dt>Data</dt>
<dd>vector of data points</dd> <dt>K</dt>
<dd>estimated amount of Gaussian Kernels</dd> <dt>Means</dt>
<dd>vector(1:L), Means of Gaussians, L == Number of Gaussians</dd> <dt>SDs</dt>
<dd>estimated Gaussian Kernels = standard deviations</dd> <dt>Weights</dt>
<dd>optional, relative number of points in Gaussians (prior probabilities): 
 sum(Weights) ==1, default weight is 1/L</dd> <dt>MaxNumberofIterations</dt>
<dd>Optional, Number of Iterations; default=10</dd>	<dt>fast</dt>
<dd>Default: FALSE: Using mclust's EM see function <code>densityMclust</code> of that package, TRUE: Naive but faster EM implementation, which may be numerical unstable, because log(gauss) is not used</dd></dl>

Arguments

Onno Hansen-Goos, Michael Thrun, Florian Lerch

Author

EM Algorithm for GMM — EMGauss

<dl>

 <dt>Data</dt>
<dd>vector of data points</dd>

 <dt>K</dt>
<dd>estimated amount of Gaussian Kernels</dd>

 <dt>Means</dt>
<dd>vector(1:L), Means of Gaussians, L == Number of Gaussians</dd>

 <dt>SDs</dt>
<dd>estimated Gaussian Kernels = standard deviations</dd>

 <dt>Weights</dt>
<dd>optional, relative number of points in Gaussians (prior probabilities): 
 sum(Weights) ==1, default weight is 1/L</dd>

 <dt>MaxNumberofIterations</dt>
<dd>Optional, Number of Iterations; default=10</dd>

	<dt>fast</dt>
<dd>Default: FALSE: Using mclust's EM see function <code>densityMclust</code> of that package, TRUE: Naive but faster EM implementation, which may be numerical unstable, because log(gauss) is not used</dd>

</dl>

EM Algorithm for GMM

EMGauss: EM Algorithm for GMM

Description

Usage

Value

Arguments

Author

Details

References

See Also