ExtendToroidalUmatrix

Extends Umatrix by toroidal continuation of the given Umatrix defined by
<code>ExtendBorders</code> in all four directions.

Umatrix

Projections are common dimensionality reduction methods, which represent high-dimensional data in a two-dimensional space. However, when restricting the output space to two dimensions, which results in a two dimensional scatter plot (projection) of the data, low dimensional similarities do not represent high dimensional distances coercively [Thrun, 2018] <DOI: 10.1007/978-3-658-20540-9>. This could lead to a misleading interpretation of the underlying structures [Thrun, 2018]. By means of the 3D topographic map the generalized Umatrix is able to depict errors of these two-dimensional scatter plots. The package is derived from the book of Thrun, M.C.: "Projection Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9> and the main algorithm called simplified self-organizing map for dimensionality reduction methods is published in <DOI: 10.1016/j.mex.2020.101093>.

Michael Thrun

GeneralizedUmatrix

Credible Visualization for Two-Dimensional Projections of Data

Felix Pape

Tim Schreier

Luis Winckelman

Quirin Stier

Alfred Ultsch

ExtendToroidalUmatrix function

<dl><dt>Umatrix</dt>
<dd>[1:Lines,1:Columns] Matrix of Umatrix Heights</dd><dt>Bestmatches</dt>
<dd>[1:n, 1:2] Matrix with positions of Bestmatches for n
datapoints, first columns is the position in <code>Lines</code> and second column in
<code>Columns</code></dd><dt>ExtendBorders</dt>
<dd>number of lines and columns the umatrix should be extended with</dd></dl>

Arguments

Author

Extend Toroidal Umatrix — ExtendToroidalUmatrix

<dl>

<dt>Umatrix</dt>
<dd>[1:Lines,1:Columns] Matrix of Umatrix Heights</dd>

<dt>Bestmatches</dt>
<dd>[1:n, 1:2] Matrix with positions of Bestmatches for n
datapoints, first columns is the position in <code>Lines</code> and second column in
<code>Columns</code></dd>

<dt>ExtendBorders</dt>
<dd>number of lines and columns the umatrix should be extended with</dd>

</dl>

ExtendToroidalUmatrix: Extend Toroidal Umatrix

Description

Usage

Value

Arguments

Author

Details

References

Examples