gen_K

Generate a sample of a Gaussian Mixture Model whose centers are generate randomly on a sphere of radius <code>radius</code>.

gaussian mixture model

Online, Semi-online, and Offline K-medians algorithms are
given. For both methods, the algorithms can be initialized
randomly or with the help of a robust hierarchical
clustering. The number of clusters can be selected with the
help of a penalized criterion. We provide functions to provide
robust clustering. Function gen_K() enables to generate a sample
of data following a contaminated Gaussian mixture.
Functions Kmedians() and Kmeans() consists in a K-median and a
K-means algorithms while Kplot() enables to produce graph for both
methods.
Cardot, H., Cenac, P. and Zitt, P-A. (2013). "Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm". Bernoulli, 19, 18-43. <doi:10.3150/11-BEJ390>.
Cardot, H. and Godichon-Baggioni, A. (2017). "Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis". Test, 26(3), 461-480 <doi:10.1007/s11749-016-0519-x>.
Godichon-Baggioni, A. and Surendran, S. "A penalized criterion for selecting the number of clusters for K-medians" <arXiv:2209.03597>
Vardi, Y. and Zhang, C.-H. (2000). "The multivariate L1-median and associated data depth". Proc. Natl. Acad. Sci. USA, 97(4):1423-1426. <doi:10.1073/pnas.97.4.1423>.

Antoine Godichon-Baggioni

Kmedians

K-Medians

Sobihan Surendran

gen_K function

<dl><dt>n</dt>
<dd>A positive integer giving the number of data per cluster. Default is <code>500</code>.</dd><dt>d</dt>
<dd>A positive integer giving the dimension. Default is <code>5</code>.</dd><dt>K</dt>
<dd>A positive integer giving the number of clusters. Default is <code>3</code>.</dd><dt>pcont</dt>
<dd>A scalar between <code>0</code> and <code>1</code> giving the proportion of contaminated data.</dd><dt>df</dt>
<dd>A positive integer giving the degrees of freedom of the law of the contaminated data if <code>cont='Student'</code>. Default is <code>1</code>.</dd><dt>cont</dt>
<dd>The law of the contaminated data. Can be <code>'Student'</code> (default) and <code>'Unif'</code>.</dd><dt>min</dt>
<dd>A scalar giving the lower bound of the uniform law if <code>cont='Unif'</code>. Default is <code>-5</code>.</dd><dt>max</dt>
<dd>A scalar giving the upper bound of the uniform law if <code>cont='Unif'</code>. Default is <code>5</code>.</dd><dt>radius</dt>
<dd>The radius of the sphere on each the centers of the class are generated. Default is <code>5</code>.</dd></dl>

Arguments

gen_K — gen_K

<dl>

<dt>n</dt>
<dd>A positive integer giving the number of data per cluster. Default is <code>500</code>.</dd>

<dt>d</dt>
<dd>A positive integer giving the dimension. Default is <code>5</code>.</dd>

<dt>K</dt>
<dd>A positive integer giving the number of clusters. Default is <code>3</code>.</dd>

<dt>pcont</dt>
<dd>A scalar between <code>0</code> and <code>1</code> giving the proportion of contaminated data.</dd>

<dt>df</dt>
<dd>A positive integer giving the degrees of freedom of the law of the contaminated data if <code>cont='Student'</code>. Default is <code>1</code>.</dd>

<dt>cont</dt>
<dd>The law of the contaminated data. Can be <code>'Student'</code> (default) and <code>'Unif'</code>.</dd>

<dt>min</dt>
<dd>A scalar giving the lower bound of the uniform law if <code>cont='Unif'</code>. Default is <code>-5</code>.</dd>

<dt>max</dt>
<dd>A scalar giving the upper bound of the uniform law if <code>cont='Unif'</code>. Default is <code>5</code>.</dd>

<dt>radius</dt>
<dd>The radius of the sphere on each the centers of the class are generated. Default is <code>5</code>.</dd>

</dl>

gen_K: gen_K

Description

Usage

Value

Arguments

See Also

Examples