Compute fuzzy evaluation statistics

Computes several evaluation statistics on the fuzzy clustering results on objects of class vegclust.

Usage

vegclustIndex(y)

Arguments

y: An object of class vegclust or a membership matrix.

Details

These statistics were conceived to be computed on fuzzy partitions, such as the ones coming from Fuzzy C-means (Bezdek 1981). Maximum values of PCN or minimum values of PEN can be used as criteria to choose the number of clusters.

Value

Returns an vector of four values: partition coefficient (PC), normalized partition coefficient (PCN), partition entropy (PE) and normalized partition entropy (PEN).

References

Bezdek, J. C. (1981) Pattern recognition with fuzzy objective functions. Plenum Press, New York.

Author

Miquel De Cáceres, CREAF.

Examples


## Loads data  
data(wetland)
  
## This equals the chord transformation 
## (see also  \code{\link{decostand}} in package vegan)
wetland.chord = as.data.frame(sweep(as.matrix(wetland), 1, 
                              sqrt(rowSums(as.matrix(wetland)^2)), "/"))
                              
## Create noise clustering with 2, 3 and 4 clusters. Perform 10 starts from random seeds 
## and keep the best solutions
wetland.fcm2 = vegclust(wetland.chord, mobileCenters=2, m = 1.2, method="FCM", nstart=10)
wetland.fcm3 = vegclust(wetland.chord, mobileCenters=3, m = 1.2, method="FCM", nstart=10)
wetland.fcm4 = vegclust(wetland.chord, mobileCenters=4, m = 1.2, method="FCM", nstart=10)

## Compute statistics. Both PCN and PEN indicate that three groups are more advisable 
## than 2 or 4.
print(vegclustIndex(wetland.fcm2))
#>        PC       PCN        PE       PEN 
#> 0.9201143 0.8402286 0.1462538 0.1537540 
print(vegclustIndex(wetland.fcm3))
#>        PC       PCN        PE       PEN 
#> 0.9366770 0.9050155 0.1267064 0.1367095 
print(vegclustIndex(wetland.fcm4))
#>        PC       PCN        PE       PEN 
#> 0.9251150 0.9001534 0.1506888 0.1669794