Description Usage Arguments Details Value Author(s) References See Also Examples

Produces the Xie and Beni index. The optimal number of cluster *k* is achieved when the index value is minimized.

1 | ```
XB (Xca, U, H, m)
``` |

`Xca` |
Matrix or data.frame |

`U` |
Membership degree matrix |

`H` |
Prototype matrix |

`m` |
Parameter of fuzziness (default: 2) |

`Xca`

should contain the same dataset used in the clustering algorithm, i.e., if the clustering algorithm is run using standardized data, then `XB`

should be computed using the same standardized data.

`m`

should be the same parameter of fuzziness used in the clustering algorithm.

`xb` |
Value of the Xie and Beni index |

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

Xie X.L., Beni G. (1991). A validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841-847.

`PC`

, `PE`

, `MPC`

, `SIL`

, `SIL.F`

, `Fclust`

, `Mc`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## McDonald's data
data(Mc)
names(Mc)
## data normalization by dividing the nutrition facts by the Serving Size (column 1)
for (j in 2:(ncol(Mc)-1))
Mc[,j]=Mc[,j]/Mc[,1]
## removing the column Serving Size
Mc=Mc[,-1]
## fuzzy k-means
## (excluded the factor column Type (last column))
clust=FKM(Mc[,1:(ncol(Mc)-1)],k=6,m=1.5,stand=1)
## Xie and Beni index
xb=XB(clust$Xca,clust$U,clust$H,clust$m)
``` |

```
[1] "Serving Size" "Calories" "Total Fat (g)"
[4] "Saturated Fat (g)" "Trans Fat (g)" "Cholesterol (mg)"
[7] "Sodium (mg)" "Carbohydrates (g)" "Dietary Fiber (g)"
[10] "Sugars (g)" "Protein (g)" "Vitamin A (%DV)"
[13] "Vitamin C (%DV)" "Calcium (%DV)" "Iron (%DV)"
[16] "Type"
```

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