Package 'CrossClustering' reference manual

Title:	A Partial Clustering Algorithm
Description:	Provide the 'CrossClustering' algorithm (Tellaroli et al. (2016) <doi:10.1371/journal.pone.0152333>), which is a partial clustering algorithm that combines the Ward's minimum variance and Complete Linkage algorithms, providing automatic estimation of a suitable number of clusters and identification of outlier elements.
Authors:	Paola Tellaroli [cre, aut], Marco Bazzi [aut], Michele Donato [aut], Livio Finos [aut], Philippe Courcoux [aut], Corrado Lanera [aut]
Maintainer:	Paola Tellaroli <[email protected]>
License:	GPL-3
Version:	4.1.2
Built:	2024-11-04 05:19:57 UTC
Source:	https://github.com/corradolanera/crossclustering

Computes the adjusted Rand index and the confidence interval, comparing two classifications from a contingency table.

Description

Computes the adjusted Rand index and the confidence interval, comparing two classifications from a contingency table.

print method for ari class

Usage

ari(mat, alpha = 0.05, digits = 2)

## S3 method for class 'ari'
print(x, ...)
ari(mat, alpha = 0.05, digits = 2)

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

Arguments

`mat`	A matrix of integers representing the contingency table of reference
`alpha`	A single number strictly included between 0 and 1 representing the significance level of interest. (default is 0.05)
`digits`	An integer for the returned significant digits to return (default is 2)
`x`	an object used to select a method.
`...`	further arguments passed to or from other methods.

Details

The adjusted Rand Index (ARI) should be interpreted as follows:

ARI >= 0.90 excellent recovery; 0.80 =< ARI < 0.90 good recovery; 0.65 =< ARI < 0.80 moderate recovery; ARI < 0.65 poor recovery.

As the confidence interval is based on the approximation to the Normal distribution, it is recommended to trust in the confidence interval only in cases of total number of object clustered greater than 100.

Value

An object of class ari with the following elements:

`AdjustedRandIndex`	The adjusted Rand Index
`CI`	The confidence interval

Methods (by generic)

print(ari):

Author(s)

Paola Tellaroli, <paola dot tellaroli at unipd dot it>;

References

L. Hubert and P. Arabie (1985) Comparing partitions, Journal of Classification, 2, 193-218.

E.M. Qannari, P. Courcoux and Faye P. (2014) Significance test of the adjusted Rand index. Application to the free sorting task, Food Quality and Preference, (32)93-97

M.H. Samuh, F. Leisch, and L. Finos (2014), Tests for Random Agreement in Cluster Analysis, Statistica Applicata-Italian Journal of Applied Statistics, vol. 26, no. 3, pp. 219-234.

D. Steinley (2004) Properties of the Hubert-Arabie Adjusted Rand Index, Psychological Methods, 9(3), 386-396

D. Steinley, M.J. Brusco, L. Hubert (2016) The Variance of the Adjusted Rand Index, Psychological Methods, 21(2), 261-272

Examples


#### This example compares the adjusted Rand Index as computed on the
### partitions given by Ward's algorithm with the ground truth on the
### famous Iris data set by the adjustedRandIndex function
### {mclust package} and by the ari function.

library(CrossClustering)
library(mclust)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |> as.numeric()

mc_ari <- adjustedRandIndex(clusters, ground_truth)
mc_ari

ari_cc <- table(ground_truth, clusters) |>
  ari(digits = 7)
ari_cc

all.equal(mc_ari, unclass(ari_cc)[["ari"]], check.attributes = FALSE)

#### This example compares the adjusted Rand Index as computed on the
### partitions given by Ward's algorithm with the ground truth on the
### famous Iris data set by the adjustedRandIndex function
### {mclust package} and by the ari function.

library(CrossClustering)
library(mclust)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |> as.numeric()

mc_ari <- adjustedRandIndex(clusters, ground_truth)
mc_ari

ari_cc <- table(ground_truth, clusters) |>
  ari(digits = 7)
ari_cc

all.equal(mc_ari, unclass(ari_cc)[["ari"]], check.attributes = FALSE)

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, ...)
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"
)

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"
)

Provides the vector of clusters' ID to which each element belong to.

Description

Provides the vector of clusters' ID to which each element belong to.

Usage

cc_get_cluster(x, n_elem)

## Default S3 method:
cc_get_cluster(x, n_elem)

## S3 method for class 'crossclustering'
cc_get_cluster(x, n_elem)
cc_get_cluster(x, n_elem)

## Default S3 method:
cc_get_cluster(x, n_elem)

## S3 method for class 'crossclustering'
cc_get_cluster(x, n_elem)

Arguments

`x`	list of clustered elements or a `crossclustering` object
`n_elem`	total number of elements clustered (ignored if x is of class `crossclustering`)

Value

An integer vector of clusters to which the elements belong (1 for the outliers, ID + 1 for the others).

Methods (by class)

cc_get_cluster(default): default method for cc_get_cluster.
cc_get_cluster(crossclustering): automatically extract inputs from a crossclustering object

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

Examples

library(CrossClustering)

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
toyres <- cc_crossclustering(
  toy_dist,
  k_w_min = 2,
  k_w_max = 5,
  k2_max  = 6,
  out     = TRUE
)

### cc_get_cluster
cc_get_cluster(toyres[], 7)


### cc_get_cluster directly from a crossclustering object
cc_get_cluster(toyres)
library(CrossClustering)

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
toyres <- cc_crossclustering(
  toy_dist,
  k_w_min = 2,
  k_w_max = 5,
  k2_max  = 6,
  out     = TRUE
)

### cc_get_cluster
cc_get_cluster(toyres[], 7)


### cc_get_cluster directly from a crossclustering object
cc_get_cluster(toyres)

A test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Description

A test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Usage

cc_test_ari(ground_truth, partition)
cc_test_ari(ground_truth, partition)

Arguments

`ground_truth`	(int) A vector of the actual membership of elements in clusters
`partition`	The partition coming from a clustering algorithm

Value

A list with six elements:

`Rand`	the Rand Index
`ExpectedRand`	expected value of Rand Index
`AdjustedRand`	Adjusted Rand Index
`var_ari`	variance of Rand Index
`nari`	nari
`p-value`	the p-value of the test

Author(s)

Paola Tellaroli, <paola dot tellaroli at unipd dot it>; Philippe Courcoux, <philippe dot courcoux at oniris-nantes dot fr>

References

E_M. Qannari, p. Courcoux and Faye p. (2014) Significance test of the adjusted Rand index. Application to the free sorting task, Food Quality and Preference, (32)93-97

L. Hubert and p. Arabie (1985) Comparing partitions, Journal of Classification, 2, 193-218.

Examples

library(CrossClustering)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |>
  as.numeric()

cc_test_ari(ground_truth, clusters)

library(CrossClustering)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |>
  as.numeric()

cc_test_ari(ground_truth, clusters)

A permutation test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Description

A permutation test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Usage

cc_test_ari_permutation(ground_truth, partition)
cc_test_ari_permutation(ground_truth, partition)

Arguments

`ground_truth`	(int) A vector of the actual membership of elements in clusters
`partition`	The partition coming from a clustering algorithm

Value

A data_frame with two columns:

`ari`	the adjusted Rand Index
`p_value`	the p-value of the test

Author(s)

Paola Tellaroli, <paola dot tellaroli at unipd dot it>; Livio Finos, <livio dot finos at unipd dot it>

References

Samuh M. H., Leisch F., and Finos L. (2014), Tests for Random Agreement in Cluster Analysis, Statistica Applicata-Italian Journal of Applied Statistics, vol. 26, no. 3, pp. 219-234.

L. Hubert and P. Arabie (1985) Comparing partitions, Journal of Classification, 2, 193-218.

Examples

library(CrossClustering)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |>
  as.numeric()

cc_test_ari_permutation(ground_truth, clusters)

library(CrossClustering)

clusters <- iris[-5] |>
  dist() |>
  hclust(method = 'ward.D') |>
  cutree(k = 3)

ground_truth <- iris[[5]] |>
  as.numeric()

cc_test_ari_permutation(ground_truth, clusters)

A toy dataset for illustrating the chain effect.

Description

A toy dataset for illustrating the chain effect.

Usage

chain_effect
chain_effect

Format

A data frame with 28 rows and 2 variables:

X: num

x coordinates 0 is negative.

Y: num

y coordinates.

Get clusters which reach max consensus

Description

Computes the consensus between Ward's minimum variance and Complete-linkage (or Single-linkage) algorithms (i.e., the number of elements classified together by both algorithms).

Usage

consensus_cluster(k, cluster_ward, cluster_other)
consensus_cluster(k, cluster_ward, cluster_other)

Arguments

`k`	(int) a vector containing the number of clusters for Ward and for Complete-linkage (or Single-linkage) algorithms, respectively
`cluster_ward`	an object of class hclust for the Ward algorithm
`cluster_other`	an object of class hclust for the Complete-linkage (or Single-linkage) algorithm

Value

an object of class consensus_cluster with the following elements:

elements

list of the elements belonging to each cluster

;

a_star

contingency table of the clustering

;

max_consensus

maximum clustering consensus

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

Examples

library(CrossClustering)

data(toy)

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

### Hierarchical clustering
cluster_ward <- toy_dist |>
  hclust(method = "ward.D")
cluster_other <- toy_dist |>
  hclust(method = "complete")


### consensus_cluster
consensus_cluster(
  c(3, 4),
  cluster_ward,
  cluster_other
)

library(CrossClustering)

data(toy)

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

### Hierarchical clustering
cluster_ward <- toy_dist |>
  hclust(method = "ward.D")
cluster_other <- toy_dist |>
  hclust(method = "complete")


### consensus_cluster
consensus_cluster(
  c(3, 4),
  cluster_ward,
  cluster_other
)

Check for zero

Description

Check if a given, single, number is 0 or not

Usage

is_zero(num)
is_zero(num)

Arguments

num

a numerical vector of length one

Value

a boolean, TRUE if num is 0

Examples

is_zero(1)
is_zero(0)
is_zero(1)
is_zero(0)

RNA-Seq dataset example

Description

nb_data contains a subset of a bigger normalized negative binomial simulated dataset.

Usage

nb_data
nb_data

Format

A data frame with 100 observations on 36 numeric variables.

Details

This dataset is part of a larger simulated and normalized dataset with 2 experimental groups, 6 time-points and 3 replicates. Simulation has been done by using a negative binomial distribution. The first 20 genes are simulated with changes among time.

Source

Data included in the bioconductor package maSigPro. https://doi.org/doi:10.18129/B9.bioc.maSigPro

Prune tail made of zeros

Description

Given a diagonal matrix which is supposed to have no non-zero entry in the diagonal after the first one (if any) the function returns the diagonal (sub-)matrix without the columns and the row corresponding to the zero-entries in the diagonal (if any).

Usage

prune_zero_tail(diag_mat)
prune_zero_tail(diag_mat)

Arguments

diag_mat

a diagonal matrix which must satisfy the following property: in the diagonal, every element after a zero is a zero.

Value

a diagonal matrix without zeros in the diagonal, composed by the first rows and columns of the original matrix with non zeros in the diagonal (which are also the only ones)

Examples

diag_mat <- diag(c(1, 2, 3, 0, 0, 0, 0))
prune_zero_tail(diag_mat)
diag_mat <- diag(c(1, 2, 3, 0, 0, 0, 0))
prune_zero_tail(diag_mat)

Reverse the process of create a contingency table

Description

Reverse the process of create a contingency table

Usage

reverse_table(x)
reverse_table(x)

Arguments

`x`	a contingency table

Value

a list of 2 vector corresponding to the unrolled table

Examples

clust_1 <- iris[, 1:4] |>
  dist() |>
  hclust() |>
  cutree(k = 3)
clust_2 <- iris[, 1:4] |>
  dist() |>
  hclust() |>
  cutree(k = 4)
cont_table <- table(clust_1, clust_2)

reverse_table(cont_table)
clust_1 <- iris[, 1:4] |>
  dist() |>
  hclust() |>
  cutree(k = 3)
clust_2 <- iris[, 1:4] |>
  dist() |>
  hclust() |>
  cutree(k = 4)
cont_table <- table(clust_1, clust_2)

reverse_table(cont_table)

A toy example matrix

Description

A toy example matrix

Usage

toy
toy

Format

A matrix of 10 row and 7 columns

A famous shape data set containing two clusters with two moons shapes and outliers

Description

A famous shape data set containing two clusters with two moons shapes and outliers

Usage

twomoons
twomoons

Format

A data frame with 52 rows and 3 variables:

x: num

x coordinates

y: num

y coordinates.

clusters: integer

cluster membership (outliers classified as 3rd cluster).

A famous shape data set containing two clusters with two worms shapes and outliers

Description

A famous shape data set containing two clusters with two worms shapes and outliers

Usage

worms
worms

Format

A data frame with 87 rows and 3 variables:

x: num

x coordinates

y: num

y coordinates.

cluster: integer

cluster membership (outliers classified as 3rd cluster).

Package 'CrossClustering'

Help Index

Computes the adjusted Rand index and the confidence interval, comparing two classifications from a contingency table.

Description

Usage

Arguments

Details

Value

Methods (by generic)

Author(s)

References

Examples

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

Description

Usage

Arguments

Details

Value

Functions

Author(s)

References

Examples

Provides the vector of clusters' ID to which each element belong to.

Description

Usage

Arguments

Value

Methods (by class)

Author(s)

References

Examples

A test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Description

Usage

Arguments

Value

Author(s)

References

Examples

A permutation test for testing the null hypothesis of random agreement (i.e., adjusted Rand Index equal to 0) between two partitions.

Description

Usage

Arguments

Value

Author(s)

References

Examples

A toy dataset for illustrating the chain effect.

Description

Usage

Format

Get clusters which reach max consensus

Description

Usage

Arguments

Value

Author(s)

References

Examples

Check for zero

Description

Usage

Arguments

Value

Examples

RNA-Seq dataset example

Description

Usage

Format

Details

Source

Prune tail made of zeros

Description

Usage

Arguments

Value

Examples

Reverse the process of create a contingency table

Description

Usage