Fuzzy Clustering
11.03.2020
Problem der Zuweisung
Unscharfe Klassen
Zadeh1965
Fuzzy Sets
Scharfe Klassen
Unscharfe Klassen
Abonyi 2007
Gustafson-Kessel Algorithmus n. Abonyi u. a. 2007
library(cluster)
keramik_funny <- cluster::fanny(x=Keramik[,2:3],
k=3, metric = "euclidean",
cluster.only = FALSE)
keramik_funny$membership## [,1] [,2] [,3]
## [1,] 0.94372810 0.01658067 0.03969124
## [2,] 0.94862966 0.01521798 0.03615236
## [3,] 0.93864333 0.01784508 0.04351160
## [4,] 0.94784892 0.01529401 0.03685708
## [5,] 0.88320702 0.03161274 0.08518025
## [6,] 0.87490169 0.03456651 0.09053179
## [7,] 0.04543928 0.87130718 0.08325354
## [8,] 0.03815490 0.90076781 0.06107730
## [9,] 0.13283595 0.16500331 0.70216074
## [10,] 0.05134867 0.03931871 0.90933263
## [11,] 0.05722993 0.03800922 0.90476085
## [12,] 0.21616485 0.09163579 0.69219936
##
## Fuzzy clustering object of class 'fclust'
##
## Number of objects:
## 12
##
## Number of clusters:
## 3
##
## Cluster sizes:
## Clus 1 Clus 2 Clus 3
## 6 4 2
##
##
## Clustering index values:
## SIL.F k=3
## 0.9253483
##
##
## Closest hard clustering partition:
## Obj 1 Obj 2 Obj 3 Obj 4 Obj 5 Obj 6 Obj 7 Obj 8 Obj 9 Obj 10 Obj 11
## 1 1 1 1 1 1 3 3 2 2 2
## Obj 12
## 2
##
## Cluster memberships:
## Clus 1
## [1] "Obj 1" "Obj 2" "Obj 3" "Obj 4" "Obj 5" "Obj 6"
## Clus 2
## [1] "Obj 9" "Obj 10" "Obj 11" "Obj 12"
## Clus 3
## [1] "Obj 7" "Obj 8"
##
## Number of objects with unclear assignment (maximal membership degree <0.5):
## 0
##
## Membership degree matrix (rounded):
## Clus 1 Clus 2 Clus 3
## Obj 1 0.99 0.01 0.00
## Obj 2 1.00 0.00 0.00
## Obj 3 1.00 0.00 0.00
## Obj 4 0.99 0.01 0.00
## Obj 5 0.99 0.01 0.00
## Obj 6 0.98 0.02 0.00
## Obj 7 0.01 0.03 0.96
## Obj 8 0.01 0.02 0.98
## Obj 9 0.06 0.86 0.08
## Obj 10 0.00 1.00 0.00
## Obj 11 0.01 0.99 0.00
## Obj 12 0.17 0.80 0.03
##
## Cluster summary:
## Cl.size Min.memb.deg. Max.memb.deg. Av.memb.deg. N.uncl.assignm.
## Clus 1 6 0.98 1.00 0.99 0
## Clus 2 4 0.80 1.00 0.91 0
## Clus 3 2 0.96 0.98 0.97 0
##
## Euclidean distance matrix for the prototypes (rounded):
## Clus 1 Clus 2
## Clus 2 19.40
## Clus 3 45.32 28.20
##
## Available components:
## [1] "U" "H" "F" "clus" "medoid" "value"
## [7] "criterion" "iter" "k" "m" "ent" "b"
## [13] "vp" "delta" "stand" "Xca" "X" "D"
## [19] "call"
##
## 
##
## Fuzzy clustering object of class 'fclust'
##
## Number of objects:
## 12
##
## Number of clusters:
## 3
##
## Cluster sizes:
## Clus 1 Clus 2 Clus 3
## 4 2 6
##
##
## Clustering index values:
## SIL.F k=3
## 0.6092347
##
##
## Closest hard clustering partition:
## Obj 1 Obj 2 Obj 3 Obj 4 Obj 5 Obj 6 Obj 7 Obj 8 Obj 9 Obj 10 Obj 11
## 3 3 3 3 3 3 1 1 1 1 2
## Obj 12
## 2
##
## Cluster memberships:
## Clus 1
## [1] "Obj 7" "Obj 8" "Obj 9" "Obj 10"
## Clus 2
## [1] "Obj 11" "Obj 12"
## Clus 3
## [1] "Obj 1" "Obj 2" "Obj 3" "Obj 4" "Obj 5" "Obj 6"
##
## Number of objects with unclear assignment (maximal membership degree <0.5):
## 0
##
## Membership degree matrix (rounded):
## Clus 1 Clus 2 Clus 3
## Obj 1 0.00 0 1.00
## Obj 2 0.00 0 1.00
## Obj 3 0.00 0 1.00
## Obj 4 0.00 0 1.00
## Obj 5 0.00 0 1.00
## Obj 6 0.00 0 1.00
## Obj 7 1.00 0 0.00
## Obj 8 1.00 0 0.00
## Obj 9 0.99 0 0.01
## Obj 10 0.99 0 0.01
## Obj 11 0.00 1 0.00
## Obj 12 0.00 1 0.00
##
## Cluster summary:
## Cl.size Min.memb.deg. Max.memb.deg. Av.memb.deg. N.uncl.assignm.
## Clus 1 4 0.99 1 0.99 0
## Clus 2 2 1.00 1 1.00 0
## Clus 3 6 1.00 1 1.00 0
##
## Euclidean distance matrix for the prototypes (rounded):
## Clus 1 Clus 2
## Clus 2 20.15
## Clus 3 33.69 16.76
##
## Available components:
## [1] "U" "H" "F" "clus" "medoid" "value"
## [7] "criterion" "iter" "k" "m" "ent" "b"
## [13] "vp" "delta" "stand" "Xca" "X" "D"
## [19] "call"
##
## 