Delaunay4Points

Calculates the adjacency matrix of the delaunay graph for BestMatches (BMs) in tiled form if BestMatches are located on a toroid grid

points

graph

voronoi

Delaunay

Delaunay Graph

Algorithms implementing populations of agents that interact with one another and sense their environment may exhibit emergent behavior such as self-organization and swarm intelligence. Here, a swarm system called Databionic swarm (DBS) is introduced which was published in Thrun, M.C., Ultsch A.: "Swarm Intelligence for Self-Organized Clustering" (2020), Artificial Intelligence, <DOI:10.1016/j.artint.2020.103237>. DBS is able to adapt itself to structures of high-dimensional data such as natural clusters characterized by distance and/or density based structures in the data space. The first module is the parameter-free projection method called Pswarm (Pswarm()), which exploits the concepts of self-organization and emergence, game theory, swarm intelligence and symmetry considerations. The second module is the parameter-free high-dimensional data visualization technique, which generates projected points on the topographic map with hypsometric tints defined by the generalized U-matrix (GeneratePswarmVisualization()). The third module is the clustering method itself with non-critical parameters (DBSclustering()). Clustering can be verified by the visualization and vice versa. The term DBS refers to the method as a whole. It enables even a non-professional in the field of data mining to apply its algorithms for visualization and/or clustering to data sets with completely different structures drawn from diverse research fields. The comparison to common projection methods can be found in the book of Thrun, M.C.: "Projection Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9>.

Michael Thrun

DatabionicSwarm

Swarm Intelligence for Self-Organized Clustering

Quirin Stier

Delaunay4Points function

<dl><dt>Points</dt>
<dd>[1:n,1:3] matrix containing the BMKey, X and Y coordinates of the n, BestMatches NEED NOT to be UNIQUE, however, there is an edge in the Deaunay between duplicate points!</dd><dt>IsToroid</dt>
<dd>Optional, logical, indicating if BM's are on a toroid grid. Default is True</dd><dt>LC</dt>
<dd>Optional, A vector of length 2, containing the number of lines and columns of the Grid</dd><dt>PlotIt</dt>
<dd>Optional, bool, Plots the graph</dd><dt>Gabriel</dt>
<dd>Optional, bool, default: FALSE, If TRUE: calculates the gabriel graph instead of the delaunay graph</dd></dl>

Arguments

Author

Adjacency matrix of the delaunay graph for BestMatches of Points — Delaunay4Points

<dl>

<dt>Points</dt>
<dd>[1:n,1:3] matrix containing the BMKey, X and Y coordinates of the n, BestMatches NEED NOT to be UNIQUE, however, there is an edge in the Deaunay between duplicate points!</dd>

<dt>IsToroid</dt>
<dd>Optional, logical, indicating if BM's are on a toroid grid. Default is True</dd>

<dt>LC</dt>
<dd>Optional, A vector of length 2, containing the number of lines and columns of the Grid</dd>

<dt>PlotIt</dt>
<dd>Optional, bool, Plots the graph</dd>

<dt>Gabriel</dt>
<dd>Optional, bool, default: FALSE, If TRUE: calculates the gabriel graph instead of the delaunay graph</dd>

</dl>

Delaunay4Points: Adjacency matrix of the delaunay graph for BestMatches of Points

Description

Usage

Value

Arguments

Author

References