\name{Cluster}
\alias{Cluster}
\title{
The K-means cluster analysis.
}
\description{
This function computes cluster centers and their time series of occurrences, 
with the K-means clustering method using Euclidean distance, of an array of 
input data with any number of dimensions, one of them (the 'posdates'th) 
corresponding to time. By default the first dimension is expected to correspond
to time.
Specifically, it partitions the array along time axis in K groups or clusters 
in which each space vector/array belongs to (i.e., is a member of) the cluster 
with the nearest center or centroid. This function relies on the NbClust 
package (Charrad et al., 2014 JSS). For more information about the K-means see 
Chapter 15 Cluster Analysis in Wilks, 2011, Statistical Methods in the 
Atmospheric Sciences, 3rd ed., Elsevire, pp 676. 
}
\usage{
Cluster(var, weights, nclusters = NULL, index = 'sdindex', posdates = 1)
}
\arguments{
  \item{var}{
An array with any number of dimensions, one of them (the 'posdates'th) 
corresponding to time with either area-averages over a series of domains or 
the grid points for any sptial grid structure (x), (y), (z), (x,y), (x,y,z), 
(y,z), ...
  }
  \item{weights}{ 
A vector/array of multiplicative weights based on the areas covering each 
domain/region or grid-cell of var; the dimensions of weights vector must be 
equal to the dimensions of 'var' without the 'posdates'th dimension.
  }
  \item{nclusters}{
This is positive integer K that must be bigger than 1. K is the number of clusters 
to be computed, or K initial cluster centers to be used in the method. Default is NULL 
and then user has to specify which index from NbClust and the associated criteria for 
selecting the optimal number of clusters will be used for K-means clustering of var.
  }
  \item{index}{
A validity index from NbClust package that can be used to determine optimal K 
if K is not specified as positive integer bigger than 1 or initial/seed cluster 
centers in nclusters. 'sdindex' is deafult (Halkidi et al. 2001, JIIS). Other 
indices also available in NBClust are "kl", "ch", "hartigan", "ccc", "scott", "marriot", 
"trcovw", "tracew", "friedman", "rubin", "cindex", "db", "silhouette", "duda", "pseudot2", 
"beale", "ratkowsky", "ball", "ptbiserial", "gap", "frey", "mcclain", "gamma", "gplus", 
"tau", "dunn", "hubert", "sdindex", and "sdbw". One can also use all of them with
the option 'alllong' or almost all indices except gap, gamma, gplus and tau with 'all', 
when the optimal number of clusters K is detremined by the majority rule (the maximum of 
histogram of the results of all indices with finite solutions). Use of some indices on 
a big and/or unstructured dataset can be computationally intense and/or could lead to 
numerical singularity. 
  }
  \item{posdates}{
The index of the dimension that corresponds to time in the provided array in the parameter 
'var', the first by default.
  }
}
\value{
  \item{cluster}{ 
A vector (time series) of integers indicating the occurrence of a cluster, i.e., when
certain data member in time is allocated to a specific cluster (e.g., 2 1 3 1 1 1 ..).
  }
  \item{centers}{
A matrix of cluster centres or centroids (e.g. [1:K, 1:spatial degrees of freedom]).
  }
  \item{totss}{
The total sum of squares. 
  }
  \item{withinss}{
A vector of within-cluster sum of squares, one component per cluster. 
  }
  \item{tot.withinss}{
Total within-cluster sum of squares, i.e., sum(withinss). 
  }
  \item{betweenss}{
The between-cluster sum of squares, i.e. totss-tot.withinss. 
  }
  \item{size}{
The number of points in each cluster. 
  }
}
\examples{
# Generating synthetic data
a1 <- array(dim = c(200, 4))
mean1 <- 0
sd1 <- 0.3 

c0 <- seq(1, 200)
c1 <- sort(sample(x = 1:200, size = sample(x = 50:150, size = 1), replace = FALSE))
x1 <- c(1, 1, 1, 1)
for (i1 in c1) {
  a1[i1, ] <- x1 + rnorm(4, mean = mean1, sd = sd1)
}

c1p5 <- c0[!(c0 \%in\% c1)]
c2 <- c1p5[seq(1, length(c1p5), 2)] 
x2 <- c(2, 2, 4, 4)
for (i2 in c2) {
  a1[i2, ] <- x2 + rnorm(4, mean = mean1, sd = sd1)
}

c3 <- c1p5[seq(2, length(c1p5), 2)]
x3 <- c(3, 3, 1, 1)
for (i3 in c3) {
  a1[i3, ] <- x3 + rnorm(4, mean = mean1, sd = sd1)
}

# Computing the clusters
res1 <- Cluster(var = a1, weights = array(1, dim = dim(a1)[2]), nclusters = 3)
print(res1$cluster)
print(res1$centers)

res2 <- Cluster(var = a1, weights = array(1, dim = dim(a1)[2]))
print(res2$cluster)
print(res2$centers)
}
\author{
History:
1.0  #  2014-10  (N.S. Fuckar, neven.fuckar@bsc.es)  #  Original code
}
\keyword{datagen}
