Performs the fuzzy k-medoids clustering algorithm with noise cluster.
Differently from fuzzy k-means where the cluster prototypes (centroids) are artificial objects computed as weighted means, in the fuzzy k-medoids the cluster prototypes (medoids) are a subset of the observed objects.
The noise cluster is an additional cluster (with respect to the k standard clusters) such that objects recognized to be outliers are assigned to it with high membership degrees.
FKM.med.noise (X, k, m, delta, RS, stand, startU, index, alpha, conv, maxit, seed)Object of class fclust, which is a list with the following components:
Membership degree matrix
Prototype matrix
Array containing the covariance matrices of all the clusters (NULL for FKM.med.noise)
Matrix containing the indexes of the clusters where the objects are assigned (column 1) and the associated membership degrees (column 2)
Vector containing the indexes of the medoid objects
Vector containing the loss function values for the RS starts
Vector containing the values of clustering index
Vector containing the numbers of iterations for the RS starts
Number of clusters
Parameter of fuzziness
Degree of fuzzy entropy (NULL for FKM.med.noise)
Parameter of the polynomial fuzzifier (NULL for FKM.med.noise)
Volume parameter (NULL for FKM.med.noise)
Noise distance
Weighting parameter for the fuzzy covariance matrices (NULL for FKM.med.noise)
Maximum condition number for the fuzzy covariance matrices (NULL for FKM.med.noise)
Standardization (Yes if stand=1, No if stand=0)
Data used in the clustering algorithm (standardized data if stand=1)
Raw data
Dissimilarity matrix (NULL for FKM.med.noise)
Matched call
Matrix or data.frame
An integer value or vector specifying the number of clusters for which the index is to be calculated (default: 2:6)
Parameter of fuzziness (default: 1.5)
Noise distance (default: average Euclidean distance between objects and prototypes from FKM.med using the same values of k and m)
Number of (random) starts (default: 1)
Standardization: if stand=1, the clustering algorithm is run using standardized data (default: no standardization)
Rational start for the membership degree matrix U (default: no rational start)
Cluster validity index to select the number of clusters: PC (partition coefficient), PE (partition entropy), MPC (modified partition coefficient), SIL (silhouette), SIL.F (fuzzy silhouette), XB (Xie and Beni) (default: "SIL.F")
Weighting coefficient for the fuzzy silhouette index SIL.F (default: 1)
Convergence criterion (default: 1e-9)
Maximum number of iterations (default: 1e+6)
Seed value for random number generation (default: NULL)
Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini
If startU is given, the argument k is ignored (the number of clusters is ncol(startU)).
If startU is given, the first element of value, cput and iter refer to the rational start.
As for FKM.med, in FKM.med.noise the parameter of fuzziness is usually lower than the one used in FKM.
Dave' R.N., 1991. Characterization and detection of noise in clustering. Pattern Recognition Letters, 12, 657-664.
Krishnapuram R., Joshi A., Nasraoui O., Yi L., 2001. Low-complexity fuzzy relational clustering algorithms for web mining. IEEE Transactions on Fuzzy Systems, 9, 595-607.
FKM.med, Fclust, Fclust.index, print.fclust, summary.fclust, plot.fclust, butterfly
## butterfly data
data(butterfly)
## fuzzy k-medoids with noise cluster, fixing the number of clusters
clust=FKM.med.noise(butterfly,k=2,RS=5,delta=3)
## fuzzy k-medoids with noise cluster, selecting the number of clusters
clust=FKM.med.noise(butterfly,RS=5,delta=3)
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