Twomode cluster analysis: Monte Carlo tests of the accuracy of methods

1
Two-mode cluster analysis Monte Carlo tests of
the accuracy of methods

• Sabine Krolak-Schwerdt
• Saarland University

2
Two-mode cluster analysis Monte Carlo tests of
the accuracy of methods

• Sabine Krolak-Schwerdt
• Saarland University

• Overview
• Indication for two-mode clustering
• Classification of two-mode clustering methods
• Monte Carlo study
• Data model used to construct the data sets
• Experiment 1 Non-overlapping clusters
• Experiment 2 Overlapping clusters
• Conclusions for selection of methods
  
  
  

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Classification of two-mode clustering methods

• Generalizations of the ADCLUS model
• GENNCLUS (DeSarbo, 1982)
• PENCLUS (Both Gaul, 1987)
• Baier et al. (1996)
• Representations by ultrametric tree structures
• Missing value method (Espejo Gaul, 1986)
• Centroid effect method (Eckes Orlik, 1993)
• ESOCLUS (Schwaiger, 1997)
• ...
• Reordering methods
• Bond energy algorithm (McCormick, Schweitzer
  White, 1972)
• Modal block method (Hartigan, 1976)
• Two-way joining (Hartigan, 1975)
• Gridpat (Krolak-Schwerdt, Orlik Ganter, 1994)
• ...

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Generalizations of the ADCLUS model

• Data
• is a nonsymmetric (similarity) matrix
• of order n x m
• Model
• where
• binary l x k matrix designating membership
  of the n objects in k clusters
• k x k matrix of weights
• binary m x k matrix designating membership
  of the m attributes in k clusters
• 
  
  (cf. DeSarbo, 1982)

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Representations by ultrametric trees
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Representations by ultrametric trees
Grand matrix
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Reordering approaches Two-way joining


(Hartigan, 1975)
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Monte Carlo study Selected methods

• Generalizations of the ADCLUS model
• GENNCLUS (DeSarbo, 1982)
• PENCLUS (Both Gaul, 1987)
• Baier et al. (1996)
• Representations by ultrametric tree structures
• Missing value method (Espejo Gaul, 1986)
• Centroid effect method (Eckes Orlik, 1993)
• ESOCLUS (Schwaiger, 1997)
• ...
• Reordering methods
• Bond energy algorithm (McCormick, Schweitzer
  White, 1972)
• Modal block method (Hartigan, 1976)
• Two-way joining (Hartigan, 1975)
• Gridpat (Krolak-Schwerdt, Orlik Ganter, 1994)
• ...

9
Monte Carlo study Selected methods

• Generalizations of the ADCLUS model
• GENNCLUS (DeSarbo, 1982)
• PENCLUS (Both Gaul, 1987)
• Baier et al. (1996)
• Representations by ultrametric tree structures
• Missing value method (Espejo Gaul, 1986)
• Centroid effect method (Eckes Orlik, 1993)
• ESOCLUS (Schwaiger, 1996)
• ...
• Reordering methods
• Bond energy algorithm (McCormick, Schweitzer
  White, 1972)
• Modal block method (Hartigan, 1976)
• Two-way joining (Hartigan, 1975)
• Gridpat (Krolak-Schwerdt, Orlik Ganter, 1994)
• ...

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Data model
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Data model
nonsymmetric matrix of order n x
m n objects
- m attributes binary n x K
matrix designating membership of the n
objects in K clusters K x K matrix of
weights binary m x K matrix
designating membership of the m attributes
in K clusters
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Data model
Model of nonoverlapping clusters

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Non-overlapping clusters
...
...
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Data model
M overlapping clusters
M
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Data model
Weight matrix of experiment 2 Toeplitz Matrix
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Non-overlapping clusters
...
...
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Model parameters of Experiment 1
(3 clusters, non-overlapping)
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Model parameters of Experiment 2
Factors of the experimental design
Overlap large vs. small Cluster number
3, 5 or 8 Parameter of Toeplitz matrix
large vs. small Size of variance large
vs. small
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Experiment 1 ANOVA of Adjusted Rand indices
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Experiment 1 ANOVA of Adjusted Rand indices
Number of clusters F(2,180) 112.21,
3 5 8 p ? 0.001 0.81 0.69 0.56
Structure of clusters F(3,180)
19.86, p ?? 0.001
1 2 3 4
0.75 0.71 0.68 0.61
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Experiment 1 ANOVA of Adjusted Rand indices
Number of clusters F(8,180)
68.44, Method 3 5 8 p ?
0.001 ESOCLUS 1.00 0.90 0.52 Centroid effect
method 0.96 0.78 0.57 Baier et
al. 0.54 0.53 0.50 GRIDPAT 0.90 0.76 0.30 Two-
way joining 0.63 0.48 0.94
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Experiment 1 ANOVA of Adjusted Rand indices
Number of clusters F(8,180)
68.44, Method 3 5 8 p ?
0.001 ESOCLUS 1.00 0.90 0.52 Centroid effect
method 0.96 0.78 0.57 Baier et
al. 0.54 0.53 0.50 GRIDPAT 0.90 0.76 0.30 Two-
way joining 0.63 0.48 0.94
Structure of clusters F(12,180)
3.12, Method 1 2 3 4 p ??
0.001 ESOCLUS 0.88 0.84 0.80 0.71 Centroid
effect method 0.87 0.84 0.78 0.59 Baier et
al. 0.61 0.50 0.50 0.47 GRIDPAT 0.67 0.69 0.60
0.65 Two-way joining 0.70 0.70 0.71 0.63
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Experiment 2 ANOVA of Omega indices
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Experiment 2 ANOVA of Omega indices
Cluster Overlap F(1,240) 29.72,
p ? 0.001
Large
Small
0.84
0.87
s of the normal distribution F(1,240)
28.66, p?? 0.001
Large
Small
0.84
0.87
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Experiment 2 ANOVA of Omega indices
Large overlap Method 3 5
8 ESOCLUS 0.80 0.81 0.81 Centroid effect
method 0.81 0.81 0.82 Baier et
al. 0.92 0.85 0.78 GRIDPAT 0.92 0.87 0.82 Two-
way joining 0.80 0.89 0.76
F(8,240) 6.61, p ? 0.001
Small overlap Method 3 5
8 ESOCLUS 0.88 0.90 0.91 Centroid effect
method 0.87 0.91 0.92 Baier et
al. 0.85 0.84 0.86 GRIDPAT 0.82 0.87 0.87 Two-
way joining 0.68 0.78 0.79
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Conclusions

• Recovery performance of two-mode clustering
  methods depends on the type and complexity of the
  data structure.
• Methods performed best if the input data
  correspond to the data structure presumed by the
  method
• - Non-overlapping clusters ESOCLUS, Centroid
  effect method
• - Overlapping clusters Baier et al.,
  Two-way joining, GRIDPAT
• Some apriori knowledge or hypothesis on the type
  and structure of data is necessary for the
  selection of an optimal method.