pclust {clue} | R Documentation |
Compute prototype-based partitions of a cluster ensemble by minimizing sum u_{bj}^m d(x_b, p_j)^2, the sum of the membership-weighted squared Euclidean dissimilarities between the elements x_b of the ensemble and the prototypes p_j.
cl_pclust(x, k, m = 1, control = list())
x |
an ensemble of partitions or hierarchies, or or something
coercible to that (see cl_ensemble ). |
k |
an integer giving the number of classes to be used in the partition. |
m |
a number not less than 1 controlling the softness of the partition (as the “fuzzification parameter” of the fuzzy c-means algorithm). The default value of 1 corresponds to hard partitions obtained from a generalized k-means problem; values greater than one give partitions of increasing softness obtained from a generalized fuzzy c-means problem. |
control |
a list of control parameters. See Details. |
For m = 1, a generalization of the Lloyd-Forgy variant of the k-means algorithm is used, which iterates between reclassifying objects to their closest prototypes, and computing new prototypes as the least squares consensus clusterings for the classes. This may result in degenerate solutions, and will be replaced by a Hartigan-Wong style algorithm eventually.
For m > 1, a generalization of the fuzzy c-means recipe (e.g., Bezdek (1981)) is used, which alternates between computing optimal memberships for fixed prototypes, and computing new prototypes as the least squares consensus clusterings for the classes.
This procedure is repeated until convergence occurs, or the maximal number of iterations is reached.
Consensus clusterings are computed using cl_consensus
.
Available control parameters are as follows.
maxiter
reltol
sqrt(.Machine$double.eps)
.method
cl_consensus
.control
cl_consensus
.The fixed point approach employed is a heuristic which cannot be guaranteed to find the global minimum (as this is already true for the computation of consensus clusterings). Standard practice would recommend to use the best solution found in “sufficiently many” replications of the base algorithm.
An object of class "cl_pclust"
representing the obtained
“secondary” partition, which is a list with the following
components.
prototypes |
a cluster ensemble with the k prototypes. |
membership |
an object of class "cl_membership"
with the membership values u_{bj}. |
cluster |
the class ids of the “nearest” hard partition. |
silhouette |
Silhouette information for the partition, see
silhouette . |
validity |
precomputed validity measures for the partition. |
m |
the softness control argument. |
J. C. Bezdek (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum.
## Use a precomputed ensemble of 50 k-means partitions of the ## Cassini data. data("CKME") CKME <- CKME[1 : 30] # for saving precious time ... diss <- cl_dissimilarity(CKME) hc <- hclust(diss) plot(hc) ## This suggests using a partition with three classes, which can be ## obtained using cutree(hc, 3). Could use cl_consensus() to compute ## prototypes as the least squares consensus clusterings of the classes, ## or alternatively: x1 <- cl_pclust(CKME, 3, m = 1) x2 <- cl_pclust(CKME, 3, m = 2) ## Agreement of solutions. cl_dissimilarity(x1, x2) table(cl_class_ids(x1), cl_class_ids(x2))