14. Januar 2020

Swarms used

  • Particle Swarm Optimization with Quantization Error and kmeans Initialization [Merwe/Engelbrecht,2003]
    • kmeans itself also
  • Ant Based Clustering [Handl, 2005]
  • Databionic Swarm [Thrun/Ultsch, 2020]
library(DatabionicSwarm)
library(BehaviorBasedSystems)

PSO clustering

  • kmeans not always clusters the hepta dataset correctly
  • PSO initialized with keans outperforms usually kmeans [Merwe/Engelbrecht,2003]
    • if the number iterations is high enough (unknown parameter ot be set)
  • PSO advantage: Can be easly parralelized
data(Hepta)
Data = Hepta$Data
ClusterNo = 7
res = kmeans(
  x = Data,
  centers = ClusterNo,
  trace = FALSE,
  iter.max = 100
)
Clskmeans = res$cluster
DataVisualizations::Plot3D(Data, Clskmeans)

out = BehaviorBasedSystems::PSOclustering(
  Data,
  ClusterNo,
  ParticleNo = 20,
  Iterations = 300,
  Hybrid_kmeans = T,
  Inertia = 0.72,
  Cognitive = 1.49,
  Social = 1.49,
  Silent = F
)
## [1] "Make clusters..."
## [1] "Using Centroids of K-Means for Initializtion of one particle\n"
## [1] "1. Iteration: Global Fitness is 0.823889724421761"
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## [1] "300. Iteration: Global Fitness is 0.820971869609631"
## [1] "stop clusters..."

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PSO clustering Results

  • PSO depends on optimization function
    • Quantization error prefers hyperspherical cluster structures
    • Intertia, Cognitive and Sovial Parameters have to be set
  • Contingency table yields:
table(out$Cls,Hepta$Cls)
##    
##      1  2  3  4  5  6  7
##   1  0 30  0  0  0  0  0
##   2  0  0  0  0  0  0 30
##   3  0  0  0  0  0 30  0
##   4  0  0 19  0  0  0  0
##   5 32  0  0 30  0  0  0
##   6  0  0 11  0  0  0  0
##   7  0  0  0  0 30  0  0

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PSO with Quantization Error

  • without kmeans init takes usually longer but with same result (not shown)
  • However, optimization function for PSO is usually unknown because cluster structures are unknown
    • For example, optimzing quantization error does not fit the Atom data set
  • Number of clusters has to be derived otherwise
  • Quantization error is on Euclidean distances defined
data(Atom)
Data = Atom$Data
out = BehaviorBasedSystems::PSOclustering(
  Data,
  2,
  ParticleNo = 20,
  Iterations = 300,
  Hybrid_kmeans = T,
  BreakIfNoChange = F,
  Silent = T
)
## [1] "Make clusters..."
## KMNS(*, k=2): iter=  1, indx=3
##  QTRAN(): istep=800, icoun=51
##  QTRAN(): istep=1600, icoun=419
##  QTRAN(): istep=2400, icoun=545
table(out$Cls, Atom$Cls)
##    
##       1   2
##   1 214 196
##   2 186 204
DataVisualizations::Plot3D(Data, out$Cls)

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What happens if not cluster structures exist?

  • If no clusters are given, optimization is still performed and data set grouped
data(GolfBall)
Data = GolfBall$Data
out = BehaviorBasedSystems::PSOclustering(
  Data,
  4,
  ParticleNo = 20,
  Iterations = 300,
  Hybrid_kmeans = F,
  BreakIfNoChange = F,
  Silent = F
)
## [1] "Make clusters..."
## [1] "1. Iteration: Global Fitness is 2.39812846531847"
## [1] "2. Iteration: Global Fitness is 0.741175891907314"
## [1] "3. Iteration: Global Fitness is 0.741175891907314"
## [1] "4. Iteration: Global Fitness is 0.741175891907314"
## [1] "5. Iteration: Global Fitness is 0.726325016535343"
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## [1] "7. Iteration: Global Fitness is 0.698521161452634"
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## [1] "296. Iteration: Global Fitness is 0.621672410873117"
## [1] "297. Iteration: Global Fitness is 0.621667201893647"
## [1] "298. Iteration: Global Fitness is 0.621667201893647"
## [1] "299. Iteration: Global Fitness is 0.62153831054051"
## [1] "300. Iteration: Global Fitness is 0.621487331376075"
## [1] "stop clusters..."

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Objective Function can still be optimized!

  • If no clusters are given, data set is optimally (in the sense of mathematics) grouped
  • But is the result a valid clustering of the data?
  • Are the most similiar datapoints whithin a group and dissimilar datapoints between groups?
table(out$Cls,GolfBall$Cls)
##    
##        1
##   1 1996
##   2    1
##   3  978
##   4 1027
DataVisualizations::Plot3D(Data,out$Cls)

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Antbased Clustering

  • alot of paramters to be set
  • currently not available as open source
  • uses currently only one of three distances (euclidean, cosinus,?)
  • my version still does not work correctly
  • does not indicate if no structure exists
data(Lsun3D)
Data=Lsun3D$Data
#out=BehaviorBasedSystems::AntBasedClustering(Data,ClusterNo = 4)
#table(out$Cls,Golfball$Cls)
#DataVisualizations::Plot3D(Data,out$Cls)

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Databionic Swarm: First Module

  • Flexible distance choice
  • Independent of the number of dimensions
  • Consists of three modules
  • Instead of global optimization function, self-organization and emergence are exploited
data(Hepta)
InputDistances = as.matrix(dist(Hepta$Data))
#First Module
projection = Pswarm(InputDistances,Debug = T,Silent = F)
## [1] "Operator: Setting options"
## [1] "Operator: Starting algorithm"
## [1] "Operator: 0% calculated."
## [1] "Operator: 86.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 1.7 %"
## [1] "Operator: 6% calculated."
## [1] "Operator: 101.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.035 %"
## [1] "Operator: 12% calculated."
## [1] "Operator: 25.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.0027 %"
## [1] "Operator: 18% calculated."
## [1] "Operator: 165.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.036 %"
## [1] "Operator: 24% calculated."
## [1] "Operator: 53.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.012 %"
## [1] "Operator: 29% calculated."
## [1] "Operator: 4.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with -0.00042 %"
## [1] "Operator: 35% calculated."
## [1] "Operator: 182.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.059 %"
## [1] "Operator: 41% calculated."
## [1] "Operator: 45.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.0094 %"
## [1] "Operator: 47% calculated."
## [1] "Operator: 81.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.0082 %"
## [1] "Operator: 53% calculated."
## [1] "Operator: 150.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.04 %"
## [1] "Operator: 59% calculated."
## [1] "Operator: 339.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.12 %"
## [1] "Operator: 65% calculated."
## [1] "Operator: 379.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.17 %"
## [1] "Operator: 71% calculated."
## [1] "Operator: 98.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.042 %"
## [1] "Operator: 76% calculated."
## [1] "Operator: 24.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.0022 %"
## [1] "Operator: 82% calculated."
## [1] "Operator: 56.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.0057 %"
## [1] "Operator: 88% calculated."
## [1] "Operator: 281.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.1 %"
## [1] "Operator: 94% calculated."
## [1] "Operator: 15.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with -0.00029 %"
## [1] "Operator: 99% calculated."
## [1] "Operator: 44.iteration"
## [1] "Operator: weak Nash equilibrium found. Paypoff maximized with 0.00086 %"
## [1] "Operator: 100 % calculated."
ProjectionBasedClustering::PlotProjectedPoints(projection$ProjectedPoints,Hepta$Cls)

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Databionic Swarm: Second Module

  • simplified ESOM (sESOM) algorithm is internally used
visualization = GeneratePswarmVisualization(
  Data = Hepta$Data, 
  projection$ProjectedPoints, 
  projection$LC,PlotIt = T)
## [1] "Initializing sESOM algorithm"
## [1] "Operator: getUmatrix4BMUs() at 8%"
## [1] "Operator: getUmatrix4BMUs() at 17%"
## [1] "Operator: getUmatrix4BMUs() at 25%"
## [1] "Operator: getUmatrix4BMUs() at 33%"
## [1] "Operator: getUmatrix4BMUs() at 42%"
## [1] "Operator: getUmatrix4BMUs() at 50%"
## [1] "Operator: getUmatrix4BMUs() at 58%"
## [1] "Operator: getUmatrix4BMUs() at 67%"
## [1] "Operator: getUmatrix4BMUs() at 75%"
## [1] "Operator: getUmatrix4BMUs() at 83%"
## [1] "Operator: getUmatrix4BMUs() at 92%"
## [1] "Operator: getUmatrix4BMUs() at 92%"
## [1] "Calculating Umatrix"

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Databionic Swarm: Third Module

  • One paramter to be set (Boolean StructureType)
    • effect of parameter directly visible in topographic map
Cls = DBSclustering(
  k = 7,
  Hepta$Data,
  visualization$Bestmatches,
  visualization$LC,
  StructureType = TRUE,
  PlotIt = TRUE
)

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Clustering results can be verified by visualization

  • Quaity of Clustering can be investigated using topographic map
    • if not structures are given, this will be evident
library(GeneralizedUmatrix)
GeneralizedUmatrix::plotTopographicMap(
  visualization$Umatrix,
  visualization$Bestmatches,
  Cls,
  NoLevels = 10)

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