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Introduction to fcmTFN
Introduction
The fcmTFN function extends the fuzzy c-means
algorithm to handle ordinal data through a triangular fuzzy number (TFN)
representation.
Example Dataset
data(sim_likert7)
head(sim_likert7)
#> Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12
#> 1 2 2 3 2 2 3 2 1 2 2 2 2
#> 2 2 2 2 3 2 1 2 2 2 2 2 2
#> 3 2 1 2 2 2 3 2 2 2 2 2 2
#> 4 2 2 2 2 2 2 1 3 2 2 2 2
#> 5 2 2 2 2 2 3 2 3 1 2 2 2
#> 6 2 2 2 2 2 2 2 2 2 3 2 1
Running the Clustering Algorithm
result <- fcmTFN(
data = sim_likert7,
option = "B",
k_values = 2:6
)
#> Running k = 2
#> Running k = 3
#> Running k = 4
#> Running k = 5
#> Running k = 6
summary(result)
#>
#> Fuzzy C-Means Clustering for TFN
#> ---------------------------------
#>
#> Optimal number of clusters (k): 3
#>
#> Weights:
#> wc = 0.61997
#> ws = 0.38003
#>
#> Iterations: 11
#>
#> Scale configuration:
#> Type : symmetric
#> Option : B
#>
#> Xie-Beni values:
#> k = 2 : 0.067732
#> k = 3 : 0.044298
#> k = 4 : 4.477249e+14
#> k = 5 : 4.077275e+15
#> k = 6 : 3.137093e+15
Cluster Assignment
clusters <- cluster_assignment(result)
table(clusters)
#> clusters
#> 1 2 3
#> 100 100 100
Cluster Quality
Prototype Interpretation
prototype_results(result, format = "table")
#> $Cluster_1
#> l c r
#> Var1 3.007 4.007 5.007
#> Var2 3.061 4.061 5.060
#> Var3 2.970 3.970 4.969
#> Var4 3.008 4.008 5.007
#> Var5 3.062 4.061 5.061
#> Var6 3.006 4.006 5.006
#> Var7 2.972 3.972 4.971
#> Var8 3.028 4.027 5.027
#> Var9 2.993 3.993 4.992
#> Var10 3.006 4.006 5.005
#> Var11 3.005 4.005 5.005
#> Var12 2.971 3.970 4.970
#>
#> $Cluster_2
#> l c r
#> Var1 1.081 2.022 3.022
#> Var2 1.133 2.038 3.038
#> Var3 1.140 2.023 3.023
#> Var4 1.081 1.952 2.952
#> Var5 1.102 1.976 2.976
#> Var6 1.113 1.997 2.997
#> Var7 1.110 2.041 3.041
#> Var8 1.102 1.933 2.933
#> Var9 1.093 2.034 3.034
#> Var10 1.071 1.995 2.995
#> Var11 1.113 2.046 3.045
#> Var12 1.152 2.044 3.044
#>
#> $Cluster_3
#> l c r
#> Var1 4.969 5.969 6.851
#> Var2 5.060 6.060 6.930
#> Var3 5.060 6.060 6.912
#> Var4 5.030 6.030 6.909
#> Var5 4.957 5.957 6.918
#> Var6 4.945 5.945 6.859
#> Var7 5.018 6.018 6.881
#> Var8 5.029 6.029 6.930
#> Var9 4.989 5.989 6.881
#> Var10 4.989 5.989 6.891
#> Var11 4.994 5.994 6.898
#> Var12 4.985 5.985 6.888
plot_prototypes(result, view = "global")
Xie-Beni Index Visualization
Conclusion
This vignette demonstrated the basic workflow for fuzzy clustering of
ordinal data using the fcmTFN function from the fcmfd
package.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.