Random.PAM.validity: PAM clustering and validity indices computation using random projections of data

Description

This function applies the Prediction Around Medoids (PAM) clustering algorithm to the data and then computes stability indices for the obtained cluster using multiple random subspace projections. It computes the validity indices for each cluster found in the original space, the overall validity index for the clustering and (optionally) the set of the AC indices. Different randomized maps (e.g. PMO, Achlioptas, Normal, Random Subspace projections) may be applied. It assumes that the label of the examples are integer starting from 1 to ncol(M). The pam function of the package cluster is used as implementation of the base PAM algorithm.

Usage

Random.PAM.validity(M, dim, pmethod = "PMO", c = 3, n = 50, scale = TRUE, 
                    seed = -1, AC = TRUE, distance = "euclidean")

Value

a list with esixight components: "validity", "overall.validity", "similarity.matrix", "dim", "cluster", "orig.cluster":

validity: a vector with the validity of each of the c clusters
overall.validity: validity index of the overall clustering
similarity.matrix: pairwise similarity matrix between examples
dimension: random projection dimension
cluster: is the list of the n clustering obtained by multiple PAM clustering on the projected subspace
orig.cluster: list of the clusters in the original space
AC: matrix with the Assignment Confidence index for each example. Each row corresponds to an example, each column to a cluster (optional)

Arguments

M: matrix of data: rows are variables and columns are examples
dim: subspace dimension
pmethod: projection method. It must be one of the following: "RS" (random subspace projection) "PMO" (Plus Minus One random projection) "Norm" (normal random projection) "Achlioptas" (Achlioptas random projection)
c: number of clusters
n: number of random projections
scale: if TRUE (default) the random projections are scaled
seed: numerical seed for the random generator
AC: if TRUE (default) the AC indices are computed.
distance: it must be one of the two: "euclidean" (default) or "pearson" (that is 1 - Pearson correlation)

Author

Giorgio Valentini valentini@di.unimi.it

Examples

Run this code

# Assessment of the reliability of clusters discovered 
# by fuzzy k-means using RS projections. 
M <- generate.sample0(n=10, m=2, sigma=1, dim=800)
l<-Random.PAM.validity(M, dim=30, pmethod = "RS", c = 3,  n = 20)
# The same as above, but using PMO projections. 
l<-Random.PAM.validity(M, dim=30, pmethod = "PMO", c = 3, n = 20)
# The same as above, but evaluating clusterings with 5 clusters 
l<-Random.PAM.validity(M, dim=30, pmethod = "PMO", c = 5, n = 20)
# The same as above, but evaluating clusterings with 10 clusters 
l<-Random.PAM.validity(M, dim=30, pmethod = "PMO", c = 10, n = 20)
# Assessment of the reliability of the clusters 
# using projections with limited distortion (max. 
# expansion lower than 1.3 according to the Johnson Lindenstrauss lemma)
d <- JL.predict.dim(n=30, epsilon=0.3)
l<-Random.PAM.validity(M, dim=d, pmethod = "PMO", c = 3, n = 20)