extractMass computes different ouputs (hard, fuzzy, rough partions, etc.)
from a credal partition and creates an object of class "credpart".
extractMass(
mass,
F,
g = NULL,
S = NULL,
method,
crit = NULL,
Kmat = NULL,
trace = NULL,
D = NULL,
W = NULL,
J = NULL,
param = NULL
)An object of class "credpart" with the following components:
The method used to construct the credal partition (a character string).
Matrix of focal sets. The first row always corresponds to the empty set.
Masses assigned to the empty set, vector of length n.
Mass functions, matrix of size (n,f).
Normalized mass functions, matrix of size (n,f-1).
The prototypes (if defined).
The matrices \(S_j\) defining the metrics for each cluster and each group of cluster (if defined).
Unnormalized plausibilities of the singletons, matrix of size (n,c).
Normalized plausibilities of the singletons, matrix of size (n,c).
Probabilities derived from pl by the plausibility transformation, matrix of size (n,c).
Unnormalized beliefs of the singletons, matrix of size (n,c).
Normalized beliefs of the singletons, matrix of size (n,c).
Maximum plausibility clusters, vector of length n.
Maximum belief clusters, vector of length n.
Unnormalized pignistic probabilities of the singletons, matrix of size (n,c).
Normalized pignistic probabilities of the singletons, matrix of size (n,c).
Sets of clusters with maximum mass, matrix of size (n,c).
n-vector of 0's and 1's, indicating which objects are outliers. An outlier is an object such that the largest mass is assigned to the empty set.
Lower approximations of clusters, a list of length c. Each element lower.approx[[i]] is a vector of object indices.
Upper approximations of clusters, a list of length c. Each element upper.approx[[i]] is a vector of object indices.
Sets of clusters selected by the interval dominance rule, matrix of size (n,c).
Lower approximations of clusters using the interval dominance rule, a list of length c. Each element lower.approx.nd[[i]] is a vector of objects.
Upper approximations of clusters using the interval dominance rule, a list of length c. Each element upper.approx.nd[[i]] is a vector of objects.
Average nonspecificity.
The value of the optimized criterion (depends on the method used).
The matrix of degrees of conflict. Same size as D (for method kevclus).
The normalized dissimilarity matrix (for method kevclus).
The trace of criterion values (for methods kevclus and
EkNNclus).
The weight matrix (for method EkNNclus).
The matrix of indices (for method kevclus).
A method-dependent list of parameters.
A credal partition (a matrix of n rows and f columns, where n is the number of objects and f is the number of focal sets).
Matrix (f,c) of focal sets. If the empty set is a focal set, it must correspond to the first row of F.
A c x d matrix of prototypes.
A list of length f containing the matrices \(S_j\) defining the metrics for each cluster and each group of cluster.
The method used to construct the credal partition (a character string).
The value of the optimized criterion (depends on the method used).
The matrix of degrees of conflict. Same size as D (for method kevclus).
The trace of criterion values (for methods kevclus and
EkNNclus).
The normalized dissimilarity matrix (for method kevclus).
The weight matrix (for method EkNNclus).
The matrix of indices (for method kevclus).
A method-dependent list of parameters.
This function collects varied information on a credal partition and stores it in
an object of class "credpart". The lower and upper
approximations of clusters define rough partitions. They can be computed in two ways:
either from the set of clusters with maximum mass, or from the set of non dominated clusters.
A cluster \(\omega_k\) is non dominated if \(pl(\omega_k)\ge bel(\omega_l)\) for
all l different from k. Once a set of cluster \(Y_i\) has been computed for each object,
object i belongs to the lower approximation of cluster k if \(Y_i={\omega_k}\). It
belongs to the upper approximation of cluster k if \(\omega_k \in Y_i\). See
Masson and Denoeux (2008) for more details, and Denoeux and Kanjanatarakul (2016) for
the interval dominance rule. The function creates an object of class "credpart".
There are three methods for this class: plot.credpart,
summary.credpart and predict.credpart.
T. Denoeux and O. Kanjanatarakul. Beyond Fuzzy, Possibilistic and Rough: An Investigation of Belief Functions in Clustering. 8th International conference on soft methods in probability and statistics, Rome, 12-14 September, 2016.
M.-H. Masson and T. Denoeux. ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition, Vol. 41, Issue 4, pages 1384-1397, 2008.
plot.credpart, summary.credpart
if (FALSE) {
## Four-class data
data(fourclass)
x<-fourclass[,1:2]
y<-fourclass[,3]
D<-as.matrix(dist(x))^2
clus<-recm(D,c=4,delta=10,ntrials=1)
summary(clus)
plot(clus,X=x,mfrow=c(1,1),ytrue=y,Outliers=TRUE)
}
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