, Quirin Stier [aut,
rev] | Title: | Swarm Intelligence for Self-Organized Clustering |
|---|---|
| Description: | 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>. |
| Authors: | Michael Thrun [aut, cre, cph]
, Quirin Stier [aut,
rev] |
| Maintainer: | Michael Thrun <[email protected]> |
| License: | GPL-3 |
| Version: | 2.0.0 |
| Built: | 2024-07-21 05:52:28 UTC |
| Source: | CRAN |
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>.
For a brief introduction to DatabionicSwarm please see the vignette Short Intro to the Databionic Swarm (DBS). The license is CC BY-NC-SA 4.0.
Index of help topics:
DBSclustering Databonic swarm clustering (DBS)
DatabionicSwarm-package
Swarm Intelligence for Self-Organized
Clustering
DefaultColorSequence Default color sequence for plots
Delaunay4Points Adjacency matrix of the delaunay graph for
BestMatches of Points
Delta3DWeightsC intern function, do not use yourself
DijkstraSSSP Internal function: Dijkstra SSSP
GeneratePswarmVisualization
Generates the Umatrix for Pswarm algorithm
Hepta Hepta is part of the Fundamental Clustering
Problem Suit (FCPS) [Thrun/Ultsch, 2020].
Lsun3D Lsun3D is part of the Fundamental Clustering
Problem Suit (FCPS) [Thrun/Ultsch, 2020].
ProjectedPoints2Grid Transforms ProjectedPoints to a grid
Pswarm A Swarm of Databots based on polar coordinates
(Polar Swarm).
PswarmEpochsParallel Intern function, do not use yourself
PswarmEpochsSequential
Intern function, do not use yourself
PswarmRadiusParallel Intern function, do not use yourself
PswarmRadiusSequential
intern function, do not use yourself
RelativeDifference Relative Difference
RobustNorm_BackTrafo Transforms the Robust Normalization back
RobustNormalization RobustNormalization
ShortestGraphPathsC Shortest GraphPaths = geodesic distances
UniquePoints Unique Points
findPossiblePositionsCsingle
Intern function, do not use yourself
getCartesianCoordinates
Intern function: Transformation of Databot
indizes to coordinates
getUmatrix4Projection depricated! see GeneralizedUmatrix()
Generalisierte U-Matrix fuer
Projektionsverfahren
plotSwarm Intern function for plotting during the Pswarm
annealing process
rDistanceToroidCsingle
Intern function for 'Pswarm'
sESOM4BMUs Intern function: Simplified Emergent
Self-Organizing Map
setGridSize Sets the grid size for the Pswarm algorithm
setPolarGrid Intern function: Sets the polar grid
setRmin Intern function: Estimates the minimal radius
for the Databot scent
setdiffMatrix setdiffMatrix shortens Matrix2Curt by those
rows that are in both matrices.
trainstepC internal function for s-esom
trainstepC2 internal function for s-esom
Further information is available in the following vignettes:
DatabionicSwarm |
Short Intro to the Databionic Swarm (DBS) (source, pdf) |
For interactive Island Generation of a generalized Umatrix
see interactiveGeneralizedUmatrixIsland function in the package ProjectionBasedClustering.
If you want to verifiy your clustering result externally, you can use Heatmap or SilhouettePlot of the CRAN package DataVisualizations.
Michal Thrun
Maintainer: Michael Thrun <[email protected]>
[Thrun/Ultsch, 2021] Thrun, M. C., and Ultsch, A.: Swarm Intelligence for Self-Organized Clustering, Artificial Intelligence, Vol. 290, pp. 103237, doi:10.1016/j.artint.2020.103237, 2021.
[Thrun/Ultsch, 2021] Thrun, M. C., & Ultsch, A.: Swarm Intelligence for Self-Organized Clustering (Extended Abstract), in Bessiere, C. (Ed.), 29th International Joint Conference on Artificial Intelligence (IJCAI), Vol. IJCAI-20, pp. 5125–5129, doi:10.24963/ijcai.2020/720, Yokohama, Japan, Jan., 2021.
[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Uncovering High-Dimensional Structures of Projections from Dimensionality Reduction Methods, MethodsX, Vol. 7, pp. 101093, DOI doi:10.1016/j.mex.2020.101093, 2020.
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
[Ultsch/Thrun, 2017] Ultsch, A., & Thrun, M. C.: Credible Visualizations for Planar Projections, in Cottrell, M. (Ed.), 12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization (WSOM), IEEE Xplore, France, 2017.
[Thrun et al., 2016] Thrun, M. C., Lerch, F., Loetsch, J., & Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), Vol. 24, Plzen, http://wscg.zcu.cz/wscg2016/short/A43-full.pdf, 2016.
Successfully used in
[Thrun et al., 2018] Thrun, M. C., Breuer, L., & Ultsch, A. : Knowledge discovery from low-frequency stream nitrate concentrations: hydrology and biology contributions, Proc. European Conference on Data Analysis (ECDA), pp. 46-47, Paderborn, Germany, 2018.
[Weyer-Menkhoff et al., 2018] Weyer-Menkhoff, I., Thrun, M. C., & Loetsch, J.: Machine-learned analysis of quantitative sensory testing responses to noxious cold stimulation in healthy subjects, European Journal of Pain, Vol. 22(5), pp. 862-874, DOI doi:10.1002/ejp.1173, 2018.
[Kringel et al., 2018] Kringel, D., Geisslinger, G., Resch, E., Oertel, B. G., Thrun, M. C., Heinemann, S., & Loetsch, J. : Machine-learned analysis of the association of next-generation sequencing based human TRPV1 and TRPA1 genotypes with the sensitivity to heat stimuli and topically applied capsaicin, Pain, Vol. 159 (7 ), pp. 1366-1381, DOI doi:10.1097/j.pain.0000000000001222, 2018
[Thrun, 2019] Thrun, M. C.: : Cluster Analysis of Per Capita Gross Domestic Products, Entrepreneurial Business and Economics Review (EBER), Vol. 7(1), pp. 217-231, DOI: doi:10.15678/EBER.2019.070113, 2019.
[Lopez-Garcia et al., 2020] Lopez-Garcia, P., Argote, D. L., & Thrun, M. C.: Projection-based Classification of Chemical Groups and Provenance Analysis of Archaeological Materials, IEEE Access, Vol. 8, pp. 152439-152451, DOI doi:10.1109/ACCESS.2020.3016244, 2020.
data('Lsun3D') ##2d projection, without instant visualization of steps #Alternative I: #DistanceMatrix hast to be defined by the user. InputDistances=as.matrix(dist(Lsun3D$Data)) projection=Pswarm(InputDistances) #2d projection, with instant visualization ## Not run: #Alternative II: DataMatrix, Distance is Euclidean per default projection=Pswarm(Lsun3D$Data,Cls=Lsun3D$Cls,PlotIt=T) ## End(Not run) # ##Computation of Generalized Umatrix # If Non Euclidean Distances are used, Please Use \code{MDS} # from the ProjectionBasedClustering package with the correct OutputDimension # to generate a new DataMatrix from the distances (see SheppardDiagram # or KruskalStress) genUmatrixList=GeneratePswarmVisualization(Data = Lsun3D$Data, projection$ProjectedPoints,projection$LC) ## Visualizuation of GenerelizedUmatrix, # Estimation of the Number of Clusters=Number of valleys library(GeneralizedUmatrix)#install if not installed GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches) ## Automatic Clustering # number of Cluster from dendrogram (PlotIt=TRUE) or visualization Cls=DBSclustering(k=3, Lsun3D$Data, genUmatrixList$Bestmatches, genUmatrixList$LC,PlotIt=FALSE) # Verification, often its better to mark Outliers manually GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches,Cls) ## Not run: # To generate the 3D landscape in the shape of an island # from the toroidal topograpic map visualization # you may cut your island interactivly around high mountain ranges Imx = ProjectionBasedClustering::interactiveGeneralizedUmatrixIsland(genUmatrixList$Umatrix, genUmatrixList$Bestmatches,Cls) GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls=Cls,Imx = Imx) ## End(Not run) ## Not run: library(ProjectionBasedClustering)#install if not installed Cls2=ProjectionBasedClustering::interactiveClustering(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls) ## End(Not run)data('Lsun3D') ##2d projection, without instant visualization of steps #Alternative I: #DistanceMatrix hast to be defined by the user. InputDistances=as.matrix(dist(Lsun3D$Data)) projection=Pswarm(InputDistances) #2d projection, with instant visualization ## Not run: #Alternative II: DataMatrix, Distance is Euclidean per default projection=Pswarm(Lsun3D$Data,Cls=Lsun3D$Cls,PlotIt=T) ## End(Not run) # ##Computation of Generalized Umatrix # If Non Euclidean Distances are used, Please Use \code{MDS} # from the ProjectionBasedClustering package with the correct OutputDimension # to generate a new DataMatrix from the distances (see SheppardDiagram # or KruskalStress) genUmatrixList=GeneratePswarmVisualization(Data = Lsun3D$Data, projection$ProjectedPoints,projection$LC) ## Visualizuation of GenerelizedUmatrix, # Estimation of the Number of Clusters=Number of valleys library(GeneralizedUmatrix)#install if not installed GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches) ## Automatic Clustering # number of Cluster from dendrogram (PlotIt=TRUE) or visualization Cls=DBSclustering(k=3, Lsun3D$Data, genUmatrixList$Bestmatches, genUmatrixList$LC,PlotIt=FALSE) # Verification, often its better to mark Outliers manually GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches,Cls) ## Not run: # To generate the 3D landscape in the shape of an island # from the toroidal topograpic map visualization # you may cut your island interactivly around high mountain ranges Imx = ProjectionBasedClustering::interactiveGeneralizedUmatrixIsland(genUmatrixList$Umatrix, genUmatrixList$Bestmatches,Cls) GeneralizedUmatrix::plotTopographicMap(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls=Cls,Imx = Imx) ## End(Not run) ## Not run: library(ProjectionBasedClustering)#install if not installed Cls2=ProjectionBasedClustering::interactiveClustering(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls) ## End(Not run)
DBS is a flexible and robust clustering framework that consists
of three independent modules. The first module is the parameter-free
projection method Pswarm Pswarm, which exploits the concepts of
self-organization and emergence, game theory, swarm intelligence and symmetry
considerations [Thrun/Ultsch, 2021]. The second module is a parameter-free
high-dimensional data visualization technique, which generates projected points
on a topographic map with hypsometric colors
GeneratePswarmVisualization, called the generalized U-matrix.
The third module is a clustering method with no sensitive parameters
DBSclustering (see [Thrun, 2018, p. 104 ff]). The clustering can
be verified by the visualization and vice versa. The term DBS refers to the
method as a whole.
The DBSclustering function applies the automated Clustering
approach of the Databonic swarm using abstract U distances, which are the
geodesic distances based on high-dimensional distances combined with low
dimensional graph paths by using ShortestGraphPathsC.
DBSclustering(k, DataOrDistance, BestMatches, LC, StructureType = TRUE, PlotIt = FALSE, ylab,main, method = "euclidean",...)DBSclustering(k, DataOrDistance, BestMatches, LC, StructureType = TRUE, PlotIt = FALSE, ylab,main, method = "euclidean",...)
k |
number of clusters, how many to you see in the topographic map (3D landscape)? |
DataOrDistance |
Either [1:n,1:d] Matrix of Data (n cases, d dimensions) that will be used. One DataPoint per row or symmetric Distance matrix [1:n,1:n] |
BestMatches |
[1:n,1:2] Matrix with positions of Bestmatches or ProjectedPoints, one matrix line per data point |
LC |
grid size c(Lines,Columns), please see details |
StructureType |
Optional, bool; = TRUE: compact structure of clusters assumed, =FALSE: connected structure of clusters assumed. For the two options for Clusters, see [Thrun, 2018] or Handl et al. 2006 |
PlotIt |
Optional, bool, Plots Dendrogramm |
ylab |
Optional, character vector, ylabel of dendrogramm |
main |
Optional, character vctor, title of dendrogramm |
method |
Optional, one of 39 distance methods of |
... |
Further arguments passed on to the |
The input of the LC parameter depends on the choice of Bestmatches
input argument. Usually as the name of the argument states, the Bestmatches of
the GeneratePswarmVisualization function are used which is define
in the notation of self-organizing map. In this case please see example one.
However, as written above, clustering and visualization can be applied
independently of each other. In this case the places of Lines L and Columns C
are switched because Lines is a value slightly above the maximum of the x-coordinates and Columns is a value slightly above the maximum of the y-coordinates of ProjectedPoint.
Hence, one should give DBSclustering the argument
LC as shown in example 2.
Often it is better to mark the outliers manually after the prozess of
clustering and sometimes a clustering can be improved through human interaction
[Thrun/Ultsch,2017] <DOI:10.13140/RG.2.2.13124.53124>; use in this case the
visualization plotTopographicMap of the
package GeneralizedUmatrix. If you would like to mark the outliers interactivly
in the visualization use the ProjectionBasedClustering package with the
function interactiveClustering(), or for full interactive clustering
IPBC(). The package is available on CRAN. An example is shown in case
of interactiveClustering() function in the third example.
[1:n] numerical vector of numbers defining the classification as the main output
of this cluster analysis for the n cases of data corresponding to the n
bestmatches. It has k unique numbers representing the arbitrary labels of the
clustering. You can use plotTopographicMap(Umatrix,Bestmatches,Cls) for
verification.
If you want to verifiy your clustering result externally, you can use
Heatmap or SilhouettePlot of the package DataVisualizations
available on CRAN.
Michael Thrun
[Thrun/Ultsch, 2021] Thrun, M. C., and Ultsch, A.: Swarm Intelligence for Self-Organized Clustering, Artificial Intelligence, Vol. 290, pp. 103237, doi:10.1016/j.artint.2020.103237, 2021.
data("Lsun3D") Data=Lsun3D$Data InputDistances=as.matrix(dist(Data)) projection=Pswarm(InputDistances) ## Example One genUmatrixList=GeneratePswarmVisualization(Data, projection$ProjectedPoints,projection$LC) Cls=DBSclustering(k=3, Data, genUmatrixList$Bestmatches, genUmatrixList$LC,PlotIt=TRUE) ## Example Two #automatic Clustering without GeneralizedUmatrix visualization Cls=DBSclustering(k=3, Data, projection$ProjectedPoints,projection$LC, PlotIt=TRUE) ## Not run: ## Example Three ## Sometimes an automatic Clustering can be improved ## through an interactive approach, ## e.g. if Outliers exist (see [Thrun/Ultsch, 2017]) library(ProjectionBasedClustering) Cls2=ProjectionBasedClustering::interactiveClustering(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls) ## End(Not run)data("Lsun3D") Data=Lsun3D$Data InputDistances=as.matrix(dist(Data)) projection=Pswarm(InputDistances) ## Example One genUmatrixList=GeneratePswarmVisualization(Data, projection$ProjectedPoints,projection$LC) Cls=DBSclustering(k=3, Data, genUmatrixList$Bestmatches, genUmatrixList$LC,PlotIt=TRUE) ## Example Two #automatic Clustering without GeneralizedUmatrix visualization Cls=DBSclustering(k=3, Data, projection$ProjectedPoints,projection$LC, PlotIt=TRUE) ## Not run: ## Example Three ## Sometimes an automatic Clustering can be improved ## through an interactive approach, ## e.g. if Outliers exist (see [Thrun/Ultsch, 2017]) library(ProjectionBasedClustering) Cls2=ProjectionBasedClustering::interactiveClustering(genUmatrixList$Umatrix, genUmatrixList$Bestmatches, Cls) ## End(Not run)
Defines the default color sequence for plots made within the Projections package.
data("DefaultColorSequence")data("DefaultColorSequence")
A vector with 562 different strings describing colors for plots.
Calculates the adjacency matrix of the delaunay graph for BestMatches (BMs) in tiled form if BestMatches are located on a toroid grid
Delaunay4Points(Points, IsToroid = TRUE,LC,PlotIt=FALSE,Gabriel=FALSE)Delaunay4Points(Points, IsToroid = TRUE,LC,PlotIt=FALSE,Gabriel=FALSE)
Points |
[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! |
IsToroid |
Optional, logical, indicating if BM's are on a toroid grid. Default is True |
LC |
Optional, A vector of length 2, containing the number of lines and columns of the Grid |
PlotIt |
Optional, bool, Plots the graph |
Gabriel |
Optional, bool, default: FALSE, If TRUE: calculates the gabriel graph instead of the delaunay graph |
Delaunay[1:n,1:n] adjacency matrix of the Delaunay-Graph
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Delta3DWeightsC
Delta3DWeightsC(vx, Datasample)Delta3DWeightsC(vx, Datasample)
vx |
Array [1:n,1:m,1:d] of neuron weights on a nxm grid with d dimensional weights. |
Datasample |
One observation of a d-dimensional datapoint. |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
vx |
Array [1:n,1:m,1:l] |
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Dijkstra's SSSP (Single source shortest path) algorithm:
gets the shortest path (geodesic distance) from source vertice(point) to all other vertices(points) defined by the edges of the adjasency matrix
DijkstraSSSP(Adj, Costs, source)DijkstraSSSP(Adj, Costs, source)
Adj |
[1:n,1:n] 0/1 adjascency matrix, e.g. from delaunay graph or gabriel graph |
Costs |
[1:n,1:n] matrix, distances between n points (normally euclidean) |
source |
int, vertice(point) from which to calculate the geodesic distance to all other points |
Preallocating space for DataStructures accordingly to the maximum possible number of vertices which is fixed set at
the number 10001.
This is an internal function of ShortestGraphPathsC, no errors or mis-usage is caught here.
ShortestPaths[1:n] vector, shortest paths (geodesic) to all other vertices including the source vertice itself
runs in O(E*Log(V))
Michael Thrun
uses a changed code which is inspired by Shreyans Sheth 28.05.2015, see https://ideone.com/qkmt31
Finds all possible jumping position regarding a grid anda Radius for DataBots
findPossiblePositionsCsingle(RadiusPositionsschablone, jumplength, alpha, Lines)findPossiblePositionsCsingle(RadiusPositionsschablone, jumplength, alpha, Lines)
RadiusPositionsschablone |
NumericMatrix, see |
jumplength |
double radius of databots regarding neighborhood, they can jump to |
alpha |
double, zu streichen |
Lines |
double, jumpinglength has to smaller than Lines/2 and Lines/2 has to yield to a integer number. |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
OpenPositions |
NumericMatrix, indizes of open positions |
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
DBS is a flexible and robust clustering framework that consists
of three independent modules. The first module is the parameter-free
projection method Pswarm Pswarm, which exploits the concepts of self-organization
and emergence, game theory, swarm intelligence and symmetry considerations.
The second module is a parameter-free high-dimensional data visualization technique,
which generates projected points on a topographic map with hypsometric colors GeneratePswarmVisualization,
called the generalized U-matrix. The third module is a clustering method with no
sensitive parameters DBSclustering. The clustering can be verified by the visualization and vice versa.
The term DBS refers to the method as a whole.
The GeneratePswarmVisualization function generates the special case (please see [Thrun, 2018]) of the generalized Umatrix with the help of an unsupervised neural network (simplified emergent self-organizing map published in [Thrun/Ultsch, 2020]). From the generalized Umatrix a topographic map with hypsometric tints can be visualized. To see this visualization use plotTopographicMap of the package GeneralizedUmatrix.
GeneratePswarmVisualization(Data, ProjectedPoints, LC, PlotIt=FALSE, ComputeInR=FALSE, Parallel=TRUE, Tiled = FALSE, DataPerEpoch = 1)GeneratePswarmVisualization(Data, ProjectedPoints, LC, PlotIt=FALSE, ComputeInR=FALSE, Parallel=TRUE, Tiled = FALSE, DataPerEpoch = 1)
Data |
[1:n,1:d] array of data: n cases in rows, d variables in columns |
ProjectedPoints |
matrix, ProjectedPoints[1:n,1:2] n by 2 matrix containing coordinates of the Projection: A matrix of the fitted configuration. see output of |
LC |
size of the grid c(Lines,Columns), number of Lines and Columns automatic calculated by Sometimes is better to choose a different grid size, e.g. to to reduce computional effort contrary to SOM, here the grid size defined only the resolution of the visualizations The real grid size is predfined by Pswarm, but you may choose a factor x*res$LC if you so desire. Therefore, The resulting grid size is given back in the Output. |
PlotIt |
Optional, default(FALSE), If TRUE than uses |
ComputeInR |
Optional, =TRUE: Rcode, =FALSE C++ implementation |
Parallel |
Optional, =TRUE: Parallel C++ implementation, =FALSE Sequential C++ implementation |
Tiled |
Optional, =TRUE: arrangement of four grids for better understanding of edge behaviour, =FALSE: single grid. |
DataPerEpoch |
Optional: Number between 0 and 1 stating the ratio of data per epoch for training of the generalized u-matrix approach. |
Tiled: The topographic map is visualized 4 times because the projection is toroidal. The reason is that there are no border in the visualizations and clusters (if they exist) are not disrupted by borders of the plot.
If you used Pswarm with distance matrix instead of a data matrix (in the sense that you do not have any data matrix available), you may transform your distances into data by using MDS of the ProjectionBasedClustering package in order to use the GeneratePswarmVisualization function. The correct dimension can be found through the Sheppard diagram or kruskals stress.
list of
Bestmatches |
matrix [1:n,1:2], BestMatches of the Umatrix, contrary to ESOM they are always fixed, because predefined by GridPoints. |
Umatrix |
matrix [1:Lines,1:Columns], |
WeightsOfNeurons |
array [1:Lines,1:Columns,1:d], d is the dimension of the weights, the same as in the ESOM algorithm |
GridPoints |
matrix [1:n,1:2],quantized projected points: projected points now lie on a predefined grid. |
LC |
c(Lines,Columns), normally equal to grid size of Pswarm, sometimes it a better or a lower resolution for the visualization is better. Therefore here the grid size of the neurons is given back. |
PlotlyHandle |
If PlotIt=FALSE: NULL, otherwise plotly object for ploting topview of topographic map |
If you used pswarm with distance matrix instead of a data matrix you can mds transform your distances into data (see the MDS function of the ProjectionBasedClustering package.). The correct dimension can be found through the Sheppard diagram or kruskals stress.
The extraction of an island out of the generalized Umatrix can be performed using the interactiveGeneralizedUmatrixIsland function in the package ProjectionBasedClustering.
The main code of both functions GeneralizedUmatrix and
GeneratePswarmVisualization is the same C++ function
sESOM4BMUs which is described in [Thrun/Ultsch, 2020].
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Uncovering High-Dimensional Structures of Projections from Dimensionality Reduction Methods, MethodsX, Vol. 7, pp. 101093, doi:10.1016/j.mex.2020.101093, 2020.
Pswarm and
plotTopographicMap and GeneralizedUmatrix of the package GeneralizedUmatrix
data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) projList=Pswarm(InputDistances) genUmatrixList=GeneratePswarmVisualization(Data,projList$ProjectedPoints,projList$LC) library(GeneralizedUmatrix) plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches,Cls)data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) projList=Pswarm(InputDistances) genUmatrixList=GeneratePswarmVisualization(Data,projList$ProjectedPoints,projList$LC) library(GeneralizedUmatrix) plotTopographicMap(genUmatrixList$Umatrix,genUmatrixList$Bestmatches,Cls)
Transforms Databot indizes to exact cartesian coordinates on an toroid two dimensional grid.
getCartesianCoordinates(DataBotsPosRe, DataBotsPosIm, GridRadius, GridAngle, QuadOrHexa = TRUE)getCartesianCoordinates(DataBotsPosRe, DataBotsPosIm, GridRadius, GridAngle, QuadOrHexa = TRUE)
DataBotsPosRe |
[1:N] real part of complex vector Two Indizes per Databot describing its positions in an two dimensional grid |
DataBotsPosIm |
[1:N] imaginary part of complex vector Two Indizes per Databot describing its positions in an two dimensional grid |
GridRadius |
[Columns, Lines] Radii Matrix of all possible Positions of
DataBots in Grid, see also documentation of |
GridAngle |
[Columns, Lines] Angle Matrix of all possible Positions of
DataBots in Grid, see also documentation of |
QuadOrHexa |
Optional, FALSE=If DataPos on hexadiagonal grid, round to 2 decimals after value, Default=TRUE |
Transformation is described in [Thrun, 2018, p. 93].
BestMatchingUnits |
[1:N,2] coordinates on an two dimensional grid for
each databot excluding unique key, such that by using
|
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
depricated! see GeneralizedUmatrix()
getUmatrix4Projection(Data,ProjectedPoints, PlotIt=TRUE,Cls=NULL,toroid=T,Tiled=F,ComputeInR=F)getUmatrix4Projection(Data,ProjectedPoints, PlotIt=TRUE,Cls=NULL,toroid=T,Tiled=F,ComputeInR=F)
Data |
[1:n,1:d] array of data: n cases in rows, d variables in columns |
ProjectedPoints |
[1:n,2]n by 2 matrix containing coordinates of the Projection: A matrix of the fitted configuration. |
PlotIt |
Optional,bool, defaut=FALSE, if =TRUE: U-Marix of every current Position of Databots will be shown |
Cls |
Optional, For plotting, see |
toroid |
Optional, Default=FALSE, ==FALSE planar computation ==TRUE: toroid borderless computation, set so only if projection method is also toroidal |
Tiled |
Optional,For plotting see |
ComputeInR |
Optional, =T: Rcode, =F Cpp Code |
List with
Umatrix |
[1:Lines,1:Columns] (see |
EsomNeurons |
[Lines,Columns,weights] 3-dimensional numeric array (wide format), not wts (long format) |
Bestmatches |
[1:n,OutputDimension] GridConverted Projected Points information converted by convertProjectionProjectedPoints() to predefined Grid by Lines and Columns |
gplotres |
Ausgabe von ggplot |
unbesetztePositionen |
Umatrix[unbesetztePositionen] =NA |
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.
data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) res=cmdscale(d=InputDistances, k = 2, eig = TRUE, add = FALSE, x.ret = FALSE) ProjectedPoints=as.matrix(res$points) # Stress = KruskalStress(InputDistances, as.matrix(dist(ProjectedPoints))) #resUmatrix=GeneralizedUmatrix(Data,ProjectedPoints) #plotTopographicMap(resUmatrix$Umatrix,resUmatrix$Bestmatches,Cls)data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) res=cmdscale(d=InputDistances, k = 2, eig = TRUE, add = FALSE, x.ret = FALSE) ProjectedPoints=as.matrix(res$points) # Stress = KruskalStress(InputDistances, as.matrix(dist(ProjectedPoints))) #resUmatrix=GeneralizedUmatrix(Data,ProjectedPoints) #plotTopographicMap(resUmatrix$Umatrix,resUmatrix$Bestmatches,Cls)
clearly defined clusters, different variances
data("Hepta")data("Hepta")
Size 212, Dimensions 3, stored in Hepta$Data
Classes 7, stored in Hepta$Cls
[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Clustering Benchmark Datasets Exploiting the Fundamental Clustering Problems, Data in Brief,Vol. 30(C), pp. 105501, DOI 10.1016/j.dib.2020.105501 , 2020.
data(Hepta) str(Hepta)data(Hepta) str(Hepta)
clearly defined clusters, different variances
data("Lsun3D")data("Lsun3D")
Size 404, Dimensions 3
Dataset defined discontinuites, where the clusters have different variances. Three main Clusters, and four Outliers (in Cluster 4). See for a more detailed description in [Thrun, 2018].
[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Clustering Benchmark Datasets Exploiting the Fundamental Clustering Problems, Data in Brief,Vol. 30(C), pp. 105501, DOI 10.1016/j.dib.2020.105501 , 2020.
data(Lsun3D) str(Lsun3D) Cls=Lsun3D$Cls Data=Lsun3D$Datadata(Lsun3D) str(Lsun3D) Cls=Lsun3D$Cls Data=Lsun3D$Data
Intern function, generates a scatter plot of the progess of the Pswarm algorithm after every nash equlibirum.
Every point symbolizes a Databot. If a prior classification is given (Cls) then the Databots have the colors defined by the class labels.
plotSwarm(Points,Cls,xlab,ylab,main)plotSwarm(Points,Cls,xlab,ylab,main)
Points |
ProjectedPoints or DataBot positions in cartesian coordinates |
Cls |
optional, Classification as a numeric vector, if given |
xlab |
='X', optional, string |
ylab |
='Y', optional, string |
main |
="DataBots", optional, string |
Michael Thrun
Pswarm with PlotIt=TRUE
quantized xy cartesianncoordinates of ProjectedPoints
ProjectedPoints2Grid(ProjectedPoints, Lines, Columns, PlotIt=FALSE, Cls)ProjectedPoints2Grid(ProjectedPoints, Lines, Columns, PlotIt=FALSE, Cls)
ProjectedPoints |
[1:n,1:2] matrix of cartesian xy coordinates |
Lines |
double, length of small side of the rectangular grid |
Columns |
double, length of big side of the rectangular grid |
PlotIt |
optional, bool, shows the result if TRUE |
Cls |
Numeric vector containing the classification vector. |
intern function, described in [Thrun, 2018, p.47]
BestMatches[1:n,1:3] columns in order: Key,Lines,Columns
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
This projetion method is a part of the databionic swarm which uses the nash equlibrium [Thrun/Ultsch, 2021]. Using polar coordinates for agents (here Databots) in two dimensions has many advantages, for further details see [Thrun, 2018] and [Thrun/Ultsch, 2021].
Pswarm(DataOrDistance, Cls = NULL, QuadOrHexa = "Hexa", NumJumps = 4, LC = NULL, Parallel = FALSE, NCores = "max", Verbose = 1, PlotIt = FALSE, Debug = FALSE, DistanceMeasure = "euclidean", Eps = 0.001)Pswarm(DataOrDistance, Cls = NULL, QuadOrHexa = "Hexa", NumJumps = 4, LC = NULL, Parallel = FALSE, NCores = "max", Verbose = 1, PlotIt = FALSE, Debug = FALSE, DistanceMeasure = "euclidean", Eps = 0.001)
DataOrDistance |
Numeric matrix nxd. Two cases here: d=n => assuming distance matrix d!=n => assuming data matrix with n cases and d features implying the need to compute the distance matrix internally. |
Cls |
Numeric vector [1:n] with class labels for each observation in DataOrDistance. |
QuadOrHexa |
Optional, Boolean indicating the geometry of tiles the 2D projection plane is built with. |
NumJumps |
Integer indicating the number of jumps to be considered for each single databot selected for jumping. |
LC |
Optional, grid size c(Columns, Lines), sometimes it is better to call
|
Parallel |
Optional, Boolean: TRUE = parallel execution, FALSE = single thread execution. |
NCores |
Character or integer: choice of number of cores of CPU (in case). Can be 'max' or a number. The max will always be 'all available cores - 1', to avoid core overload. |
PlotIt |
Optional, bool, default=FALSE, If =TRUE, Plots the projection during the computation prozess after every nash equlibirum. |
Debug |
Optional, Debug, default=FALSE, =TRUE results in various console messages, depricated for CRAN, because cout is not allowed. |
DistanceMeasure |
Optional, one of 39 distance methods of |
Verbose |
optional, integer stating the degree of textual feedback. 0 = no output, 1 = basic notifications, 2 = progress bar, 3 = details. |
Eps |
optional, double: Stop criterion for convergence of each epoche. |
DBS is a flexible and robust clustering framework that consists of three
independent modules. The first module is the parameter-free projection method
Pswarm Pswarm, which exploits the concepts of self-organization
and emergence, game theory, swarm intelligence and symmetry considerations. The
second module is a parameter-free high-dimensional data visualization technique,
which generates projected points on a topographic map with hypsometric colors
GeneratePswarmVisualization, called the generalized U-matrix. The
third module is a clustering method with no sensitive parameters
DBSclustering. The clustering can be verified by the visualization
and vice versa. The term DBS refers to the method as a whole.
List with
ProjectedPoints |
[1:n,1:2] xy cartesian coordinates of projection |
LC |
number of Lines and Columns in c(Lines, Columns) |
Control |
List, only for intern debugging |
LC is now automatically estimated; LC is the size of the grid c(Lines, Columns),
number of Lines and Columns, default c(NULL,NULL) and automatic calculation by
setGridSize.
Michael Thrun, Quirin Stier
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
[Thrun/Ultsch, 2021] Thrun, M. C., and Ultsch, A.: Swarm Intelligence for Self-Organized Clustering, Artificial Intelligence, Vol. 290, pp. 103237, doi:10.1016/j.artint.2020.103237, 2021.
[Stier/Thrun, 2024] Stier, Q. and Thrun, M. C.: An efficient multicore CPU implementation of the DatabionicSwarm, 18th conference of the International Federation of Classification Societies (IFCS), San José, Costa Rica, July 14-19, 2024.
data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) #If not called separately setGridSize() is called in Pswarm LC=setGridSize(InputDistances) res=Pswarm(InputDistances,LC=LC,Cls=Cls,PlotIt=TRUE)data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) #If not called separately setGridSize() is called in Pswarm LC=setGridSize(InputDistances) res=Pswarm(InputDistances,LC=LC,Cls=Cls,PlotIt=TRUE)
Finds the weak Nash equilibirium of the data bots for one epoch depending on a
radius, which requires the setting of constants, grid, and so on in, see
Pswarm.
PswarmEpochsParallel(AllDataBotsPosRe, AllDataBotsPosIm, MyDistanceMatrix, AllFreePosR0, GridRadii, GridAngle, JumpsPerRadius, NumJumps, NumAllDB, Lines, Columns, Origin, Happiness, QuadOrHexa, RadiusVector, Rmin, Rmax, Cls, Debug, pp, PlotIt = FALSE, Verbose = 1, Eps = 0.0001)PswarmEpochsParallel(AllDataBotsPosRe, AllDataBotsPosIm, MyDistanceMatrix, AllFreePosR0, GridRadii, GridAngle, JumpsPerRadius, NumJumps, NumAllDB, Lines, Columns, Origin, Happiness, QuadOrHexa, RadiusVector, Rmin, Rmax, Cls, Debug, pp, PlotIt = FALSE, Verbose = 1, Eps = 0.0001)
AllDataBotsPosRe |
Numeric vector [1:n] of the current positions for the databots on first of two dimensions. |
AllDataBotsPosIm |
Numeric vector [1:n] of the current positions for the databots on second of two dimensions. |
MyDistanceMatrix |
Numeric vector with vectorized distance matrix of the datapoints in the original (high-dimensional) data space |
AllFreePosR0 |
NumericMatrix, see |
GridRadii |
Numeric matrix with radius information of polar transformation for each grid position |
GridAngle |
Numeric matrix with angle information of polar transformation for each grid position |
JumpsPerRadius |
Numeric Vector of possible positions of the 1st coordinate. |
NumJumps |
Integer number of jumps. |
NumAllDB |
Integer total number of databots |
Lines |
Integer stating the number of Lines the polar grid consists of. |
Columns |
Integer stating the number of columns the polar grid consists of. |
Origin |
Numeric origin of the positions of grid in two dimensions |
Happiness |
Numeric value indicating the global happiness over all databots |
QuadOrHexa |
optional, bool: If TRUE prints status every 100 iterations |
RadiusVector |
Numeric vector stating all moving radius in a descending order (cooling down scheme). |
Rmin |
Integer stating minimum radius. |
Rmax |
Integer stating maximum radius. |
Cls |
Integer vector stating the classification vector for each datapoints/databots. |
Debug |
optional, bool: If TRUE prints information for debugging. |
pp |
Numeric vector stating ratio of number of jumping simultaneously DataBots of one eppoch (per nash-equilibirum), this vector is linearly monotonically decreasing. |
PlotIt |
optional, bool: If TRUE creates plot of projection after each epoch. |
Verbose |
optional, integer stating degree of textual feedback. 0 = no output, 1 = basic notifications, 2 = progress bar, 3 = details. |
Eps |
optional, double: Stop criterion for convergence of each epoche. |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
list of
AllDataBotsPosRe |
Numeric vector [1:n] of the current positions for the databots on first of two dimensions. |
AllDataBotsPosIm |
Numeric vector [1:n] of the current positions for the databots on second of two dimensions. |
CourseOfHappiness |
NumericVector, states the global happiness value per epoch. |
RadiusPerEpoch |
NumericVector, stating the radius used per epoch in order of computation. |
Quirin Stier
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
[Thrun/Ultsch, 2021] Thrun, M. C., and Ultsch, A.: Swarm Intelligence for Self-Organized Clustering, Artificial Intelligence, Vol. 290, pp. 103237, doi:10.1016/j.artint.2020.103237, 2021.
[Stier/Thrun, 2024] Stier, Q. and Thrun, M. C.: An efficient multicore CPU implementation of the DatabionicSwarm, 18th conference of the International Federation of Classification Societies (IFCS), San José, Costa Rica, July 14-19, 2024.
Finds the weak Nash equilibirium of the data bots for one epoch depending on a
radius, which requires the setting of constants, grid, and so on in, see
Pswarm.
PswarmEpochsSequential(AllDataBotsPos, MyDistanceMatrix, IndPossibleDBPosR, AllFreePosR0, NumAllDB, Lines, Columns, Origin, Happiness, GridRadii, GridAngle, QuadOrHexa, RadiusVector, Rmin, Rmax, Cls, Debug, pp, PlotIt = FALSE, Verbose = 1)PswarmEpochsSequential(AllDataBotsPos, MyDistanceMatrix, IndPossibleDBPosR, AllFreePosR0, NumAllDB, Lines, Columns, Origin, Happiness, GridRadii, GridAngle, QuadOrHexa, RadiusVector, Rmin, Rmax, Cls, Debug, pp, PlotIt = FALSE, Verbose = 1)
AllDataBotsPos |
Complex vector [1:n] of the current positions for the databots on a 2d and real plane in complex numbers. |
MyDistanceMatrix |
Numeric vector with vectorized distance matrix of the datapoints in the original (high-dimensional) data space |
IndPossibleDBPosR |
Numeric vector containing the possible positions around a databot dependent on the radius. |
AllFreePosR0 |
NumericMatrix, see |
NumAllDB |
Integer total number of databots |
Lines |
Integer stating the number of Lines the polar grid consists of. |
Columns |
Integer stating the number of columns the polar grid consists of. |
Origin |
Numeric origin of the positions of grid in two dimensions |
Happiness |
Numeric value indicating the global happiness over all databots |
GridRadii |
Numeric matrix with radius information of polar transformation for each grid position |
GridAngle |
Numeric matrix with angle information of polar transformation for each grid position |
QuadOrHexa |
optional, bool: If TRUE prints status every 100 iterations |
RadiusVector |
Numeric vector stating all moving radius in a descending order (cooling down scheme). |
Rmin |
Integer stating minimum radius. |
Rmax |
Integer stating maximum radius. |
Cls |
Integer vector stating the classification vector for each datapoints/databots. |
Debug |
optional, bool: If TRUE prints information for debugging. |
pp |
Numeric vector stating ratio of number of jumping simultaneously DataBots of one eppoch (per nash-equilibirum), this vector is linearly monotonically decreasing. |
PlotIt |
optional, bool: If TRUE creates plot of projection after each epoch. |
Verbose |
optional, integer stating degree of textual feedback. 0 = no output, 1 = basic notifications, 2 = progress bar, 3 = details. |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
list of
AllDataBotsPosRe |
Numeric vector [1:n] of the current positions for the databots on first of two dimensions. |
AllDataBotsPosIm |
Numeric vector [1:n] of the current positions for the databots on second of two dimensions. |
CourseOfHappiness |
NumericVector, states the global happiness value per epoch. |
RadiusPerEpoch |
NumericVector, stating the radius used per epoch in order of computation. |
Quirin Stier
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Finds the weak Nash equilibirium of the data bots for one epoch depending on a
radius, which requires the setting of constants, grid, and so on in, see
Pswarm.
PswarmRadiusParallel(DataBotsPos, DataDists, AllallowedDBPosR0, IndPossibleDBPosRe, IndPossibleDBPosIm, Lines, Columns, Radius, NumAllDB, NumChoDB, NumFreeShape1, NumJumps, Origin1, Origin2, Happiness, MinIterations, HappinessInclination, Eps, debug)PswarmRadiusParallel(DataBotsPos, DataDists, AllallowedDBPosR0, IndPossibleDBPosRe, IndPossibleDBPosIm, Lines, Columns, Radius, NumAllDB, NumChoDB, NumFreeShape1, NumJumps, Origin1, Origin2, Happiness, MinIterations, HappinessInclination, Eps, debug)
DataBotsPos |
Numeric vector [1:NumJumps*n*2] containing the current positions and all positions for considered/possible jumps which can be computed (depending on number of jumps parameter NumJumps) for the databots on two dimensions. |
DataDists |
Numeric vector with vectorized distance matrix of the datapoints in the original (high-dimensional) data space |
AllallowedDBPosR0 |
NumericMatrix, see |
IndPossibleDBPosRe |
Numeric Vector of possible positions of the 1st coordinate. |
IndPossibleDBPosIm |
Numeric Vector of possible positions of the 2nd coordinate. |
Lines |
Integer stating the number of Lines the polar grid consists of. |
Columns |
Integer stating the number of columns the polar grid consists of. |
Radius |
Numeric (Integer) stating the moving radius of the databots |
NumAllDB |
Integer total number of databots |
NumChoDB |
Integer number of databots chosen for moving/jumps. |
NumFreeShape1 |
Integer stating the first dimension of the numeric matrix book keeping the possible position grid |
NumJumps |
Integer number of jumps |
Origin1 |
Numeric origin coordinate 1 |
Origin2 |
Numeric origin coordinate 2 |
Happiness |
Numeric value indicating the global happiness over all databots |
MinIterations |
asdf |
HappinessInclination |
asdf |
Eps |
optional, double: Stop criterion for convergence of each epoche. |
debug |
optional, bool: If TRUE prints status every 100 iterations |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
list of
AllDataBotsPos |
ComplexVector, indizes of DataBot Positions after a weak Nash equlibrium is found |
stressverlauf |
NumericVector, intern result, for debugging only |
fokussiertlaufind |
NumericVector, intern result, for debugging only |
Quirin Stier
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
[Thrun/Ultsch, 2021] Thrun, M. C., and Ultsch, A.: Swarm Intelligence for Self-Organized Clustering, Artificial Intelligence, Vol. 290, pp. 103237, doi:10.1016/j.artint.2020.103237, 2021.
[Stier/Thrun, 2024] Stier, Q. and Thrun, M. C.: An efficient multicore CPU implementation of the DatabionicSwarm, 18th conference of the International Federation of Classification Societies (IFCS), San José, Costa Rica, July 14-19, 2024.
Finds the weak Nash equilibirium for DataBots in one epoch(Radius), requires the setting of constants, grid, and so on in Pswarm
PswarmRadiusSequential( AllDataBotsPosOld, Radius, DataDists, IndPossibleDBPosR, RadiusPositionsschablone, pp, Nullpunkt, Lines, Columns, nBots, limit, steigungsverlaufind, Happiness, debug)PswarmRadiusSequential( AllDataBotsPosOld, Radius, DataDists, IndPossibleDBPosR, RadiusPositionsschablone, pp, Nullpunkt, Lines, Columns, nBots, limit, steigungsverlaufind, Happiness, debug)
AllDataBotsPosOld |
ComplexVector [1:n,1], DataBots position in the last Nash-Equlibriuum |
Radius |
double, Radius of payoff function, neighborhood, where other DatsBots can be smelled |
DataDists |
NumericMatrix, Inputdistances[1:n,1:n] |
IndPossibleDBPosR |
ComplexVector, see output of |
RadiusPositionsschablone |
NumericMatrix, see |
pp |
NumericVector, number of jumping simultaneously DataBots of one eppoch (per nash-equilibirum), this vector is linearly monotonically decreasing |
Nullpunkt |
NumericVector, equals |
Lines |
double, small edge length of rectangulare grid |
Columns |
double, big edge length of rectangulare grid |
nBots |
double, intern constant, equals |
limit |
int, intern constant, equals |
steigungsverlaufind |
int, intern constant |
Happiness |
double, intern constant, sum of payoff of all databots in random condition before the algorithm starts |
debug |
optional, bool: If TRUE prints status every 100 iterations |
Algorithm is described in [Thrun, 2018, p. 95, Listing 8.1].
list of
AllDataBotsPos |
ComplexVector, indizes of DataBot Positions after a weak Nash equlibrium is found |
stressverlauf |
NumericVector, intern result, for debugging only |
fokussiertlaufind |
NumericVector, intern result, for debugging only |
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Pswarm
toroid distance calculation
rDistanceToroidCsingle( AllDataBotsPosX, AllDataBotsPosY, AllallowedDBPosR0, Lines, Columns, Nullpunkt)rDistanceToroidCsingle( AllDataBotsPosX, AllDataBotsPosY, AllallowedDBPosR0, Lines, Columns, Nullpunkt)
AllDataBotsPosX |
NumericVector [1:n,1], positions of on grid |
AllDataBotsPosY |
NumericVector [1:n,1], positions of on grid |
AllallowedDBPosR0 |
NumericMatrix |
Lines |
double |
Columns |
double |
Nullpunkt |
NumericVector |
Part of the algorithm described in [Thrun, 2018, p. 95, Listing 8.1].
numeric matrix of toroid Distances[1:n,1:n]
do not use yourself
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Calculates the difference between positive x and y values
RelativeDifference(X, Y, epsilon = 10^-10,na.rm=FALSE)RelativeDifference(X, Y, epsilon = 10^-10,na.rm=FALSE)
X |
either a value or numerical vector of [1:n] |
Y |
either a value or numerical vector of [1:n] |
epsilon |
Optional, If both x and y are approximatly zero the output is also zero |
na.rm |
Optional, function does not work with non finite values. If these cases should be automatically removed, set parameter TRUE |
Contrary to other approaches in this cases the range of values lies between
[-2,2]. The approach is only valid for positive values ofX and Y.
The realtive difference R is defined with
Negative value indicate that X is higher than Y and positive
values that X is lower than Y.
R
It can be combined with the GabrielClassificationError if a clear baseline is defined.
Michael Thrun
Ultsch, A.: Is Log Ratio a Good Value for Measuring Return in Stock Investments? GfKl 2008, pp, 505-511, 2008.
x=c(1:5) y=runif(5,min=1,max=10) RelativeDifference(x,y)x=c(1:5) y=runif(5,min=1,max=10) RelativeDifference(x,y)
Transforms the Robust Normalization back if Capped=FALSE
RobustNorm_BackTrafo(TransformedData, MinX,Denom,Center=0)RobustNorm_BackTrafo(TransformedData, MinX,Denom,Center=0)
TransformedData |
[1:n,1:d] matrix |
MinX |
scalar |
Denom |
scalar |
Center |
scalar |
For details see RobustNormalization
[1:n,1:d] Data matrix
Michael Thrun
data(Hepta) Data = Hepta$Data TransList = RobustNormalization(Data, Centered = TRUE, WithBackTransformation = TRUE) HeptaData = RobustNorm_BackTrafo(TransList$TransformedData, TransList$MinX, TransList$Denom, TransList$Center) sum(HeptaData - Data) #<e-15data(Hepta) Data = Hepta$Data TransList = RobustNormalization(Data, Centered = TRUE, WithBackTransformation = TRUE) HeptaData = RobustNorm_BackTrafo(TransList$TransformedData, TransList$MinX, TransList$Denom, TransList$Center) sum(HeptaData - Data) #<e-15
RobustNormalization as described in [Milligan/Cooper, 1988].
RobustNormalization(Data,Centered=FALSE,Capped=FALSE, na.rm=TRUE,WithBackTransformation=FALSE, pmin=0.01,pmax=0.99)RobustNormalization(Data,Centered=FALSE,Capped=FALSE, na.rm=TRUE,WithBackTransformation=FALSE, pmin=0.01,pmax=0.99)
Data |
[1:n,1:d] data matrix of n cases and d features |
Centered |
centered data around zero by median if TRUE |
Capped |
TRUE: outliers are capped above 1 or below -1 and set to 1 or -1. |
na.rm |
If TRUE, infinite vlaues are disregarded |
WithBackTransformation |
If in the case for forecasting with neural networks a backtransformation is required, this parameter can be set to 'TRUE'. |
pmin |
defines outliers on the lower end of scale |
pmax |
defines outliers on the higher end of scale |
Normalizes features either between -1 to 1 (Centered=TRUE) or 0-1 (Centered=TRUE) without changing the distribution of a feature itself. For a more precise description please read [Thrun, 2018, p.17].
"[The] scaling of the inputs determines the effective scaling of the weights in the last layer of a MLP with BP neural netowrk, it can have a large effect on the quality of the final solution. At the outset it is besto to standardize all inputs to have mean zero and standard deviation 1 [(or at least the range under 1)]. This ensures all inputs are treated equally in the regularization prozess, and allows to choose a meaningful range for the random starting weights."[Friedman et al., 2012]
if WithBackTransformation=FALSE: TransformedData[1:n,1:d] i.e., normalized data matrix of n cases and d features
if WithBackTransformation=TRUE: List with
TransformedData |
[1:n,1:d] normalized data matrix of n cases and d features |
MinX |
[1:d] numerical vector used for manual back-transformation of each feature |
MaxX |
[1:d] numerical vector used for manual back-transformation of each feature |
Denom |
[1:d] numerical vector used for manual back-transformation of each feature |
Center |
[1:d] numerical vector used for manual back-transformation of each feature |
Michael Thrun
[Milligan/Cooper, 1988] Milligan, G. W., & Cooper, M. C.: A study of standardization of variables in cluster analysis, Journal of Classification, Vol. 5(2), pp. 181-204. 1988.
[Friedman et al., 2012] Friedman, J., Hastie, T., & Tibshirani, R.: The Elements of Statistical Learning, (Second ed. Vol. 1), Springer series in statistics New York, NY, USA:, ISBN, 2012.
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Scaled = RobustNormalization(rnorm(1000, 2, 100), Capped = TRUE) hist(Scaled) m = cbind(c(1, 2, 3), c(2, 6, 4)) List = RobustNormalization(m, FALSE, FALSE, FALSE, TRUE) TransformedData = List$TransformedData mback = RobustNorm_BackTrafo(TransformedData, List$MinX, List$Denom, List$Center) sum(m - mback)Scaled = RobustNormalization(rnorm(1000, 2, 100), Capped = TRUE) hist(Scaled) m = cbind(c(1, 2, 3), c(2, 6, 4)) List = RobustNormalization(m, FALSE, FALSE, FALSE, TRUE) TransformedData = List$TransformedData mback = RobustNorm_BackTrafo(TransformedData, List$MinX, List$Denom, List$Center) sum(m - mback)
Intern function for the simplified ESOM (sESOM) algorithm for fixed BestMatchingUnits.
sESOM4BMUs(BMUs,Data, esom, toroid, CurrentRadius, ComputeInR=FALSE, Parallel=TRUE)sESOM4BMUs(BMUs,Data, esom, toroid, CurrentRadius, ComputeInR=FALSE, Parallel=TRUE)
BMUs |
[1:Lines,1:Columns], BestMAtchingUnits generated by ProjectedPoints2Grid() |
Data |
[1:n,1:d] array of data: n cases in rows, d variables in columns |
esom |
[1:Lines,1:Columns,1:weights] array of NeuronWeights, see ListAsEsomNeurons() |
toroid |
TRUE/FALSE - topology of points |
CurrentRadius |
number betweeen 1 to x |
ComputeInR |
=T: Rcode, =F Cpp Code. |
Parallel |
Optional, =TRUE: Parallel C++ implementation, =FALSE C++ implementation |
Algorithm is described in [Thrun, 2018, p. 48, Listing 5.1].
esom |
numeric array [1:Lines,1:Columns,1:d], d is the dimension of the weights, the same as in the ESOM algorithm. modified esomneuros regarding a predefined neighborhood defined by a radius |
Usually not for seperated usage!
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
setdiffMatrix shortens Matrix2Curt by those rows that are in both matrices.
Matrix2Curt |
[n,k] matrix, which will be shortened by x rows |
Matrix2compare |
[m,k] matrix whose rows will be compared to those of Matrix2Curt x rows in Matrix2compare equal rows of Matrix2Curt (order of rows is irrelevant). Has the same number of columns as Matrix2Curt. |
V$CurtedMatrix[n-x,k] Shortened Matrix2Curt
CL,MT 12/2014
Automatically sets the size of the grid, formula see [Thrun, 2018, p. 93-94].
setGridSize(InputDistances,minp=0.01,maxp=0.99,alpha=4, Verbose = 0)setGridSize(InputDistances,minp=0.01,maxp=0.99,alpha=4, Verbose = 0)
InputDistances |
[1:n,1:n] symmetric matrix of input distances |
minp |
default value: 0.01,see |
maxp |
default value: 0.99, see |
alpha |
Do not change! Intern parameter, Only if Java Version of Pswarm instead of C++ version is used. |
Verbose |
optional, integer stating degree of textual feedback. 0 = no output, 1 = basic notifications, 2 = progress bar, 3 = details. |
grid is set such that minimum and maximum distances can be shown on the grid
LC=c(Lines, Columns) size of the grid for Pswarm
Michael Thrun, Florian Lerch
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
automatic choice of LC for Pswarm
data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) #If not called separately setGridSize() is called in Pswarm LC=setGridSize(InputDistances)data("Lsun3D") Data=Lsun3D$Data Cls=Lsun3D$Cls InputDistances=as.matrix(dist(Data)) #If not called separately setGridSize() is called in Pswarm LC=setGridSize(InputDistances)
Sets a polar grid for a swarm in an rectangular shape
setPolarGrid(Lines,Columns,QuadOrHexa,PlotIt,global)setPolarGrid(Lines,Columns,QuadOrHexa,PlotIt,global)
Lines |
Integer, hast to be able to be divided by 2 |
Columns |
Integer, with Columns>=Lines |
QuadOrHexa |
bool, default(TRUE) If False Hexagonal grid, default quad grid |
PlotIt |
bool, default(FALSE) |
global |
bool, default(TRUE), intern parameter, how shall the radii be calculated? |
Part of the Algorithm described in [Thrun, 2018, p. 95, Listing 8.1].
list of
GridRadii |
matrix [1:Lines,1:Columns], Radii Matrix of all possible Positions of DataBots in Grid |
GridAngle |
matrix [1:Lines,1:Columns], Angle Matrix of all possible Positions of DataBots in Grid |
AllallowedDBPosR0 |
matrix [1:Lines+1,1:Columns+1], Matrix of radii in polar coordinates respecting origin (0,0) of all allowed DataBots Positions in one jump |
AllallowedDBPosPhi0 |
matrix [1:Lines+1,1:Columns+1], # V$AllallowedDBPosPhi0[Lines+1,Lines+1] Matrix of angle in polar coordinates respecting origin (0,0) of all allowed DataBots Positions in one jump |
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
estimates the minimal radius on apolar grid in the automated annealing process of Pswarm, details of how can be read in [Thrun, 2018, p. 97]
Lines |
x-value determining the size of the map, i.e. how many open places for DataBots will be available on the 2-dimensional grid BEWARE: has to be able to be divided by 2 |
Columns |
y-value determining the size of the map, i.e. how many open places for DataBots will be available on the 2-dimensional grid Columns>Lines |
AllallowedDBPosR0 |
[1:Lines+1,1:Lines+1]Matrix of radii in polar coordinates respecting origin (0,0) of all allowed DataBots Positions in one jump |
p |
percent of gitterpositions, which should be considered |
Rmin Minimum Radius
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Dijkstra's SSSP (Single source shortest path) algorithm, from all points to all points
ShortestGraphPathsC(Adj, Cost)ShortestGraphPathsC(Adj, Cost)
Adj |
[1:n,1:n] 0/1 adjascency matrix, e.g. from delaunay graph or gabriel graph |
Cost |
[1:n,1:n] matrix, distances between n points (normally euclidean) |
Vertices are the points, edges have the costs defined by weights (normally a distance). The algorithm runs in runs in O(n*E*Log(V)), see also [Jungnickel, 2013, p. 87]. Further details can be foubd in [Jungnickel, 2013, p. 83-87] and [Thrun, 2018, p. 12].
ShortestPaths[1:n,1:n] vector, shortest paths (geodesic) to all other vertices including the source vertice itself from al vertices to all vertices, stored as a matrix
require C++11 standard (set flag in Compiler, if not set automatically)
Michael Thrun
[Dijkstra,1959] Dijkstra, E. W.: A note on two problems in connexion with graphs, Numerische mathematik, Vol. 1(1), pp. 269-271. 1959.
[Jungnickel, 2013] Jungnickel, D.: Graphs, networks and algorithms, (4th ed ed. Vol. 5), Berlin, Heidelberg, Germany, Springer, ISBN: 978-3-642-32278-5, 2013.
[Thrun/Ultsch, 2017] Thrun, M.C., Ultsch, A.: Projection based Clustering, Conf. Int. Federation of Classification Societies (IFCS),DOI:10.13140/RG.2.2.13124.53124, Tokyo, 2017.
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Does the training for fixed bestmatches in one epoch of the sESOM.
trainstepC(vx,vy, DataSampled,BMUsampled,Lines,Columns, Radius, toroid, NoCases)trainstepC(vx,vy, DataSampled,BMUsampled,Lines,Columns, Radius, toroid, NoCases)
vx |
array [1:Lines,1:Columns,1:Weights], WeightVectors that will be trained, internally transformed von NumericVector to cube |
vy |
array [1:Lines,1:Columns,1:2], meshgrid for output distance computation |
DataSampled |
NumericMatrix, n cases shuffled Dataset[1:n,1:d] by |
BMUsampled |
NumericMatrix, n cases shuffled BestMatches[1:n,1:2] by |
Lines |
double, Height of the grid |
Columns |
double, Width of the grid |
Radius |
double, The current Radius that should be used to define neighbours to the bm |
toroid |
bool, Should the grid be considered with cyclically connected borders? |
NoCases |
int, number of samples in the given non-sampled dataset |
Algorithm is described in [Thrun, 2018, p. 48, Listing 5.1].
WeightVectors, array[1:Lines,1:Columns,1:weights] with the adjusted Weights
Usually not for seperated usage!
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
Does the training for fixed bestmatches in one epoch of the sESOM.
trainstepC2(esomwts,aux, DataSampled,BMUsampled,Lines,Columns, Weights, Radius, toroid, NoCases)trainstepC2(esomwts,aux, DataSampled,BMUsampled,Lines,Columns, Weights, Radius, toroid, NoCases)
esomwts |
array [1:Lines,1:Columns,1:Weights], WeightVectors that will be trained, internally transformed von NumericVector to cube |
aux |
array [1:Lines,1:Columns,1:2], meshgrid for output distance computation |
DataSampled |
NumericMatrix, n cases shuffled Dataset[1:n,1:d] by |
BMUsampled |
NumericMatrix, n cases shuffled BestMatches[1:n,1:2] by |
Lines |
double, Height of the grid |
Columns |
double, Width of the grid |
Weights |
double, number of weights |
Radius |
double, The current Radius that should be used to define neighbours to the bm |
toroid |
bool, Should the grid be considered with cyclically connected borders? |
NoCases |
int, number of samples in the given non-sampled dataset |
Algorithm is described in [Thrun, 2018, p. 48, Listing 5.1].
WeightVectors, array[1:Lines,1:Columns,1:weights] with the adjusted Weights
Usually not for seperated usage!
Michael Thrun
[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.
return only the unique points in Datapoints
UniquePoints(Datapoints, Eps=1e-10)UniquePoints(Datapoints, Eps=1e-10)
Datapoints |
[1:n,1:d] matrix of Datapoints points of dimension d, the points are in the rows |
Eps |
Optional,scalar above zero that defines minimum non-identical euclidean distance between two points |
Euclidean distance is computed and used within. Setting Eps to a very small number results in the identification of unique data points. Setting epsilon to a higher number results in the definition of mesh points within an d-dimensional R-ball graph.
List with
Unique |
[1:k,1:d] Datapoints points without duplicate points |
IsDuplicate |
[1:n,1:n] matrix,for i!=j IsDuplicate[i,j]== 1 if Datapoints[i,] == Datapoints[j,] IsDuplicate[i,i]==0 |
UniqueInd |
[1:k] index vector such that Unique == Datapoints[UniqueInd,], it has k non-consecutive numbers or labels, each label defines a row number within Datapoints[1:n,1:d] of a unique data point |
Uniq2DatapointsInd |
[1:n] index vector. It has k unique index numbers representing the arbitrary labels. Each labels is mapped uniquely to a point in |
Michael Thrun
Datapoints2D=rbind(c(1,2),c(1,2),c(1,3),c(3,1)) V=UniquePoints(Datapoints2D)Datapoints2D=rbind(c(1,2),c(1,2),c(1,3),c(3,1)) V=UniquePoints(Datapoints2D)