kpbm | R Documentation |
Computes the Modified Kernel Form of Pakhira-Bandyopadhyay-Maulik (KPBM) index for validating the result of a fuzzy clustering analysis.
kpbm(x, u, v, m, t=NULL, eta, tidx="f")
x |
an object of class ‘ppclust’ containing the clustering results from a fuzzy clustering algorithm in the package ppclust. Alternatively, a numeric data frame or matrix containing the data set. |
u |
a numeric data frame or matrix containing the fuzzy membership values. It should be specified if |
v |
a numeric data frame or matrix containing the cluster prototypes. It should be specified if |
t |
a numeric data frame or matrix containing the cluster prototypes. It should be specified if |
m |
a number specifying the fuzzy exponent. It should be specified if |
eta |
a number specifying the typicality exponent. It should be specified if |
tidx |
a character specifying the type of index. The default is ‘f’ for fuzzy index. The other options are ‘e’ for extended and ‘g’ for generalized index. |
The modified Kernel form of Pakhira-Bandyopadhyay-Maulik (KPBM) index avoids to use the numerator term E_0 of the original PBM (Pakhira et al, 2005) index. In this way, the computation time required by PBM is reduced without affecting its characteristic. For the modified form so-called KPBM, the prefix K means kernel or core. The equation for calculating the KPBM index is:
I_{KPBM}=\frac{1}{k} \;\frac{1}{E_k} \; D_k
, where: E_k = ∑\limits_{j=1}^k E_j, E_j = ∑\limits_{j=1}^k u_{ij} \; d_{ij}^2, D_k = \max\limits_{j,l=1}^k ||\vec{v}_j - \vec{v}_l||^2
The optimal clustering is obtained with the maximum value of I_{KPBM}.
kpbm |
KPBM index value, if |
kpbm.e |
extended KPBM index, if |
kpbm.g |
generalized KPBM index value, if |
Zeynel Cebeci
PatternWiz - A software package for pattern recognition. http://shodhganga.inflibnet.ac.in/bitstream/10603/93443/16/16_chapter%208.pdf
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# Load the dataset iris and use the first four feature columns data(iris) x <- iris[,1:4] # For 3 clusters, run FCM algorithm in the package ppclust res.fcm <- ppclust::fcm(x, centers=3) # Compute the KPBM index using ppclust object idx <- kpbm(res.fcm) print(idx) # Compute the KPBM index using X,U,V matrices idx <- kpbm(res.fcm$x, res.fcm$u, res.fcm$v, m=2) print(idx)
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