cc_crossclustering {CrossClustering}

A partial clustering algorithm with automatic estimation of the number of clusters and identification of outliers

Description

This function performs the CrossClustering algorithm. This method combines the Ward's minimum variance and Complete-linkage (default, useful for finding spherical clusters) or Single-linkage (useful for finding elongated clusters) algorithms, providing automatic estimation of a suitable number of clusters and identification of outlier elements.

Usage

cc_crossclustering(
  dist,
  k_w_min = 2,
  k_w_max = attr(dist, "Size") - 2,
  k2_max = k_w_max + 1,
  out = TRUE,
  method = c("complete", "single")
)

## S3 method for class 'crossclustering'
print(x, ...)

Arguments

dist

A dissimilarity structure as produced by the function dist

k_w_min

(int) Minimum number of clusters for the Ward's minimum variance method. By default is set equal 2

k_w_max

(int) Maximum number of clusters for the Ward's minimum variance method (see details)

k2_max

(int) Maximum number of clusters for the Complete/Single-linkage method. It can not be equal or greater than the number of elements to cluster (see details)

out

(lgl) If TRUE (default) outliers must be searched (see details)

method

(chr) "complete" (default) or "single". CrossClustering combines Ward's algorithm with Complete-linkage if method is set to "complete", otherwise (if method is set to 'single') Single-linkage will be used.

x

an object used to select a method.

...

further arguments passed to or from other methods.

Details

See cited document for more details.

Value

A list of objects describing characteristics of the partitioning as follows:

Optimal_cluster

number of clusters

cluster_list_elements

a list of clusters; each element of this lists contains the indices of the elements belonging to the cluster

Silhouette

the average silhouette width over all the clusters

n_total

total number of input elements

n_clustered

number of input elements that have actually been clustered

Functions

• print(crossclustering):

Author(s)

Paola Tellaroli, <paola dot tellaroli at unipd dot it>;; Marco Bazzi, <bazzi at stat dot unipd dot it>; Michele Donato, <mdonato at stanford dot edu>

References

Tellaroli P, Bazzi M., Donato M., Brazzale A. R., Draghici S. (2016). Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters. PLoS ONE 11(3): e0152333. doi:10.1371/journal.pone.0152333

#' Tellaroli P, Bazzi M., Donato M., Brazzale A. R., Draghici S. (2017). E1829: Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters. CMStatistics 2017, London 16-18 December, Book of Abstracts (ISBN 978-9963-2227-4-2)

Examples

library(CrossClustering)

#### Example of Cross-Clustering as in reference paper
#### method = "complete"

data(toy)

### toy is transposed as we want to cluster samples (columns of the
### original matrix)
toy_dist <- t(toy) |>
  dist(method = "euclidean")

### Run CrossClustering
cc_crossclustering(
  toy_dist,
  k_w_min = 2,
  k_w_max = 5,
  k2_max = 6,
  out = TRUE
)

#### Simulated data as in reference paper
#### method = "complete"
set.seed(10)
sg <- c(500, 250, 700, 300, 100)

# 5 clusters

t <- matrix(0, nrow = 5, ncol = 5)
t[1, ] <- rep(6, 5)
t[2, ] <- c( 0,  5, 12, 13, 15)
t[3, ] <- c(15, 11,  9,  5,  0)
t[4, ] <- c( 6, 12, 15, 10,  5)
t[5, ] <- c(12, 17,  3,  7, 10)

t_mat <- NULL
for (i in seq_len(nrow(t))) {
  t_mat <- rbind(
    t_mat,
    matrix(rep(t[i, ], sg[i]), nrow = sg[i], byrow = TRUE)
  )
}

data_15 <- matrix(NA, nrow = 2000, ncol = 5)
data_15[1:1850, ] <- matrix(
  abs(rnorm(sum(sg) * 5, sd = 1.5)),
  nrow = sum(sg),
  ncol = 5
) + t_mat

set.seed(100) # simulate outliers
data_15[1851:2000, ] <- matrix(
  runif(n = 150 * 5, min = 0, max = max(data_15, na.rm = TRUE)),
  nrow = 150,
  ncol = 5
)

### Run CrossClustering
cc_crossclustering(
  dist(data_15),
  k_w_min = 2,
  k_w_max = 19,
  k2_max = 20,
  out = TRUE
)


#### Correlation-based distance is often used in gene expression time-series
### data analysis. Here there is an example, using the "complete" method.

data(nb_data)
nb_dist <- as.dist(1 - abs(cor(t(nb_data))))
cc_crossclustering(dist = nb_dist, k_w_max = 20, k2_max = 19)




#### method = "single"
### Example on a famous shape data set
### Two moons data

data(twomoons)

moons_dist <- twomoons[, 1:2] |>
  dist(method = "euclidean")

cc_moons <- cc_crossclustering(
  moons_dist,
  k_w_max = 9,
  k2_max = 10,
  method = 'single'
)

moons_col <- cc_get_cluster(cc_moons)
plot(
  twomoons[, 1:2],
  col = moons_col,
  pch      = 19,
  xlab     = "",
  ylab     = "",
  main     = "CrossClustering-Single"
)

### Worms data
data(worms)

worms_dist <- worms[, 1:2] |>
  dist(method = "euclidean")

cc_worms <- cc_crossclustering(
  worms_dist,
  k_w_max = 9,
  k2_max  = 10,
  method  = "single"
)

worms_col <-  cc_get_cluster(cc_worms)

plot(
  worms[, 1:2],
  col = worms_col,
  pch = 19,
  xlab = "",
  ylab = "",
  main = "CrossClustering-Single"
)


### CrossClustering-Single is not affected to chain-effect problem

data(chain_effect)

chain_dist <- chain_effect |>
  dist(method = "euclidean")
cc_chain <- cc_crossclustering(
  chain_dist,
  k_w_max = 9,
  k2_max = 10,
  method = "single"
)

chain_col <- cc_get_cluster(cc_chain)

plot(
  chain_effect,
  col = chain_col,
  pch = 19,
  xlab = "",
  ylab = "",
  main = "CrossClustering-Single"
)