diceR: Diverse Cluster Ensemble in R

Description

Performs cluster analysis using an ensemble clustering framework, Chiu & Talhouk (2018) doi:10.1186/s12859-017-1996-y. Results from a diverse set of algorithms are pooled together using methods such as majority voting, K-Modes, LinkCluE, and CSPA. There are options to compare cluster assignments across algorithms using internal and external indices, visualizations such as heatmaps, and significance testing for the existence of clusters.

Author(s)

Maintainer: Derek Chiu dchiu@bccrc.ca

Authors:

• Aline Talhouk a.talhouk@ubc.ca

Other contributors:

• Johnson Liu gliu@bccrc.ca [contributor, compiler]

See Also

Useful links:

• https://github.com/AlineTalhouk/diceR/

• https://alinetalhouk.github.io/diceR/

• Report bugs at https://github.com/AlineTalhouk/diceR/issues

Cluster-based Similarity Partitioning Algorithm (CSPA)

Description

Performs hierarchical clustering on a stack of consensus matrices to obtain consensus class labels.

Usage

CSPA(E, k)

Arguments

Value

cluster assignments for the consensus class

Author(s)

Derek Chiu

References

Strehl, A., & Ghosh, J. (2002). Cluster ensembles—a knowledge reuse framework for combining multiple partitions. Journal of machine learning research, 3(Dec), 583-617.

See Also

Other consensus functions: LCA(), LCE(), k_modes(), majority_voting()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
x <- consensus_cluster(dat, nk = 4, reps = 4, algorithms = c("hc", "diana"),
progress = FALSE)
CSPA(x, k = 4)

Latent Class Analysis

Description

Combine clustering results using latent class analysis.

Usage

LCA(E, is.relabelled = TRUE, seed = 1)

Arguments

Value

a vector of cluster assignments based on LCA

Author(s)

Derek Chiu

See Also

Other consensus functions: CSPA(), LCE(), k_modes(), majority_voting()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
cc <- consensus_cluster(dat, nk = 4, reps = 6, algorithms = "pam", progress =
FALSE)
table(LCA(cc[, , 1, 1, drop = FALSE], is.relabelled = FALSE))

Linkage Clustering Ensemble

Description

Generate a cluster assignment from a CTS, SRS, or ASRS similarity matrix.

Usage

LCE(E, k, dc = 0.8, R = 10, sim.mat = c("cts", "srs", "asrs"))

Arguments

Value

a vector containing the cluster assignment from either the CTS, SRS, or ASRS similarity matrices

Author(s)

Johnson Liu

See Also

Other consensus functions: CSPA(), LCA(), k_modes(), majority_voting()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
x <- consensus_cluster(dat, nk = 4, reps = 4, algorithms = c("km", "hc"),
progress = FALSE)
## Not run: 
LCE(E = x, k = 4, sim.mat = "asrs")

## End(Not run)

x <- apply(x, 2:4, impute_knn, data = dat, seed = 1)
x_imputed <- impute_missing(x, dat, nk = 4)
LCE(E = x_imputed, k = 4, sim.mat = "cts")

Proportion of Ambiguous Clustering

Description

Given a consensus matrix, returns the proportion of ambiguous clusters (PAC). This is a robust way to assess clustering performance.

Usage

PAC(cm, lower = 0, upper = 1)

Arguments

Details

Since a consensus matrix is symmetric, we only look at its lower (or upper) triangular matrix. The proportion of entries strictly between lower and upper is the PAC. In a perfect clustering, the consensus matrix would consist of only 0s and 1s, and the PAC assessed on the (0, 1) interval would have a perfect score of 0. Using a (0.1, 0.9) interval for defining ambiguity is common as well.

The PAC is not, strictly speaking, an internal validity index. Originally used to choose the optimal number of clusters, here we use it to assess cluster stability. However, PAC is still agnostic any gold standard clustering result so we use it like an internal validity index.

Value

the PAC is a score used in clustering performance. The lower it is the better, because we want minimal ambiguity amongst the consensus.

Author(s)

Derek Chiu

References

Senbabaoglu, Y., Michailidis, G., & Li, J. Z. (2014). Critical limitations of consensus clustering in class discovery. Scientific reports, 4.

Examples

set.seed(1)
x <- replicate(100, rbinom(100, 4, 0.2))
y <- consensus_matrix(x)
PAC(y, lower = 0.05, upper = 0.95)

Compactness Measure

Description

Compute the compactness validity index for a clustering result.

Usage

compactness(data, labels)

Arguments

Details

This index is agnostic to any reference clustering results, calculating cluster performance on the basis of compactness and separability. Smaller values indicate a better clustering structure.

Value

the compactness score

Author(s)

Derek Chiu

References

MATLAB function valid_compactness by Simon Garrett in LinkCluE

Examples

set.seed(1)
E <- matrix(rep(sample(1:4, 1000, replace = TRUE)), nrow = 100, byrow =
              FALSE)
set.seed(1)
dat <- as.data.frame(matrix(runif(1000, -10, 10), nrow = 100, byrow = FALSE))
compactness(dat, E[, 1])

Consensus clustering

Description

Runs consensus clustering across subsamples of the data, clustering algorithms, and cluster sizes.

Usage

consensus_cluster(
  data,
  nk = 2:4,
  p.item = 0.8,
  reps = 1000,
  algorithms = NULL,
  nmf.method = c("brunet", "lee"),
  hc.method = "average",
  xdim = NULL,
  ydim = NULL,
  rlen = 200,
  alpha = c(0.05, 0.01),
  minPts = 5,
  distance = "euclidean",
  abs = TRUE,
  prep.data = c("none", "full", "sampled"),
  scale = TRUE,
  type = c("conventional", "robust", "tsne"),
  min.var = 1,
  progress = TRUE,
  seed.nmf = 123456,
  seed.data = 1,
  file.name = NULL,
  time.saved = FALSE
)

Arguments

Details

See examples for how to use custom algorithms and distance functions. The default clustering algorithms provided are:

• "nmf": Nonnegative Matrix Factorization (using Kullback-Leibler Divergence or Euclidean distance; See Note for specifications.)

• "hc": Hierarchical Clustering

• "diana": DIvisive ANAlysis Clustering

• "km": K-Means Clustering

• "pam": Partition Around Medoids

• "ap": Affinity Propagation

• "sc": Spectral Clustering using Radial-Basis kernel function

• "gmm": Gaussian Mixture Model using Bayesian Information Criterion on EM algorithm

• "block": Biclustering using a latent block model

• "som": Self-Organizing Map (SOM) with Hierarchical Clustering

• "cmeans": Fuzzy C-Means Clustering

• "hdbscan": Hierarchical Density-based Spatial Clustering of Applications with Noise (HDBSCAN)

The progress bar increments on every unit of reps.

Value

An array of dimension nrow(x) by reps by length(algorithms) by length(nk). Each cube of the array represents a different k. Each slice of a cube is a matrix showing consensus clustering results for algorithms. The matrices have a row for each sample, and a column for each subsample. Each entry represents a class membership.

When "hdbscan" is part of algorithms, we do not include its clustering array in the consensus result. Instead, we report two summary statistics as attributes: the proportion of outliers and the number of clusters.

Note

The nmf.method options are "brunet" (Kullback-Leibler Divergence) and "lee" (Euclidean distance). When "hdbscan" is chosen as an algorithm to use, its results are excluded from the rest of the consensus clusters. This is because there is no guarantee that the cluster assignment will have every sample clustered; more often than not there will be noise points or outliers. In addition, the number of distinct clusters may not even be equal to nk.

Author(s)

Derek Chiu, Aline Talhouk

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]

# Custom distance function
manh <- function(x) {
  stats::dist(x, method = "manhattan")
}

# Custom clustering algorithm
agnes <- function(d, k) {
  return(as.integer(stats::cutree(cluster::agnes(d, diss = TRUE), k)))
}

assign("agnes", agnes, 1)

cc <- consensus_cluster(dat, reps = 6, algorithms = c("pam", "agnes"),
distance = c("euclidean", "manh"), progress = FALSE)
str(cc)

Combine algorithms

Description

Combines results for multiple objects from consensus_cluster() and outputs either the consensus matrices or consensus classes for all algorithms.

Usage

consensus_combine(..., element = c("matrix", "class"))

Arguments

Details

This function is useful for collecting summaries because the original results from consensus_cluster were combined to a single object. For example, setting element = "class" returns a matrix of consensus cluster assignments, which can be visualized as a consensus matrix heatmap.

Value

consensus_combine returns either a list of all consensus matrices or a data frame showing all the consensus classes

Author(s)

Derek Chiu

Examples

# Consensus clustering for multiple algorithms
set.seed(911)
x <- matrix(rnorm(500), ncol = 10)
CC1 <- consensus_cluster(x, nk = 3:4, reps = 10, algorithms = "ap",
progress = FALSE)
CC2 <- consensus_cluster(x, nk = 3:4, reps = 10, algorithms = "km",
progress = FALSE)

# Combine and return either matrices or classes
y1 <- consensus_combine(CC1, CC2, element = "matrix")
str(y1)
y2 <- consensus_combine(CC1, CC2, element = "class")
str(y2)

Evaluate, trim, and reweigh algorithms

Description

Evaluates algorithms on internal/external validation indices. Poor performing algorithms can be trimmed from the ensemble. The remaining algorithms can be given weights before use in consensus functions.

Usage

consensus_evaluate(
  data,
  ...,
  cons.cl = NULL,
  ref.cl = NULL,
  k.method = NULL,
  plot = FALSE,
  trim = FALSE,
  reweigh = FALSE,
  n = 5,
  lower = 0,
  upper = 1
)

Arguments

Details

This function always returns internal indices. If ref.cl is not NULL, external indices are additionally shown. Relevant graphical displays are also outputted. Algorithms are ranked across internal indices using Rank Aggregation. Only the top n algorithms are kept, the rest are trimmed.

Value

consensus_evaluate returns a list with the following elements

• k: if ref.cl is not NULL, this is the number of distinct classes in the reference; otherwise the chosen k is determined by the one giving the largest mean PAC across algorithms

• pac: a data frame showing the PAC for each combination of algorithm and cluster size

• ii: a list of data frames for all k showing internal evaluation indices

• ei: a data frame showing external evaluation indices for k

• trim.obj: A list with 4 elements

  • alg.keep: algorithms kept

  • alg.remove: algorithms removed

  • rank.matrix: a matrix of ranked algorithms for every internal evaluation index

  • top.list: final order of ranked algorithms

  • E.new: A new version of a consensus_cluster data object

Examples

# Consensus clustering for multiple algorithms
set.seed(911)
x <- matrix(rnorm(500), ncol = 10)
CC <- consensus_cluster(x, nk = 3:4, reps = 10, algorithms = c("ap", "km"),
progress = FALSE)

# Evaluate algorithms on internal/external indices and trim algorithms:
# remove those ranking low on internal indices
set.seed(1)
ref.cl <- sample(1:4, 50, replace = TRUE)
z <- consensus_evaluate(x, CC, ref.cl = ref.cl, n = 1, trim = TRUE)
str(z, max.level = 2)

Consensus matrix

Description

Returns the (weighted) consensus matrix given a data matrix

Usage

consensus_matrix(data, weights = NULL)

Arguments

Details

Given a vector of cluster assignments, we first calculate the connectivity matrix and indicator matrix. A connectivity matrix has a 1 if both samples are in the same cluster, and 0 otherwise. An indicator matrix has a 1 if both samples were selected to be used in a subsample of a consensus clustering algorithm, and 0 otherwise. Summation of connectivity matrices and indicator matrices is performed over different subsamples of the data. The consensus matrix is calculated by dividing the aggregated connectivity matrices by the aggregated indicator matrices.

If a meta-consensus matrix is desired, where consensus classes of different clustering algorithms are aggregated, we can construct a weighted meta-consensus matrix using weights.

Value

a consensus matrix

Note

When consensus is calculated over bootstrap samples, not every sample is used in each replication. Thus, there will be scenarios where two samples are never chosen together in any bootstrap samples. This typically happens when the number of replications is small. The coordinate in the consensus matrix for such pairs of samples is NaN from a 0 / 0 computation. These entries are coerced to 0.

Author(s)

Derek Chiu

Examples

set.seed(2)
x <- replicate(100, rbinom(100, 4, 0.2))
w <- rexp(100)
w <- w / sum(w)
cm1 <- consensus_matrix(x)
cm2 <- consensus_matrix(x, weights = w)

Diverse Clustering Ensemble

Description

Runs consensus clustering across subsamples, algorithms, and number of clusters (k).

Usage

dice(
  data,
  nk,
  p.item = 0.8,
  reps = 10,
  algorithms = NULL,
  k.method = NULL,
  nmf.method = c("brunet", "lee"),
  hc.method = "average",
  distance = "euclidean",
  cons.funs = c("kmodes", "majority", "CSPA", "LCE", "LCA"),
  sim.mat = c("cts", "srs", "asrs"),
  prep.data = c("none", "full", "sampled"),
  min.var = 1,
  seed = 1,
  seed.data = 1,
  trim = FALSE,
  reweigh = FALSE,
  n = 5,
  evaluate = TRUE,
  plot = FALSE,
  ref.cl = NULL,
  progress = TRUE,
  verbose = TRUE
)

Arguments

Details

There are three ways to handle the input data before clustering via argument prep.data. The default is to use the raw data as-is ("none"). Or, we can enact prepare_data() on the full dataset ("full"), or the bootstrap sampled datasets ("sampled").

Value

A list with the following elements

Author(s)

Aline Talhouk, Derek Chiu

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
ref.cl <- strsplit(rownames(dat), "_") |>
  purrr::map_chr(2) |>
  factor() |>
  as.integer()
dice.obj <- dice(dat, nk = 4, reps = 5, algorithms = "hc", cons.funs =
"kmodes", ref.cl = ref.cl, progress = FALSE, verbose = FALSE)
str(dice.obj, max.level = 2)

External validity indices

Description

External validity indices compare a predicted clustering result with a reference class or gold standard.

Usage

ev_nmi(pred.lab, ref.lab, method = "emp")

ev_confmat(pred.lab, ref.lab)

Arguments

Details

ev_nmi calculates the normalized mutual information

ev_confmat calculates a variety of statistics associated with confusion matrices. Accuracy, Cohen's kappa, and Matthews correlation coefficient have direct multiclass definitions, whereas all other metrics use macro-averaging.

Value

ev_nmi returns the normalized mutual information.

ev_confmat returns a tibble of the following summary statistics using yardstick::summary.conf_mat():

• accuracy: Accuracy

• kap: Cohen's kappa

• sens: Sensitivity

• spec: Specificity

• ppv: Positive predictive value

• npv: Negative predictive value

• mcc: Matthews correlation coefficient

• j_index: Youden's J statistic

• bal_accuracy: Balanced accuracy

• detection_prevalence: Detection prevalence

• precision: alias for ppv

• recall: alias for sens

• f_meas: F Measure

Note

ev_nmi is adapted from infotheo::mutinformation()

Author(s)

Johnson Liu, Derek Chiu

References

Strehl A, Ghosh J. Cluster ensembles: a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 2002;3:583-617.

Examples

set.seed(1)
E <- matrix(rep(sample(1:4, 1000, replace = TRUE)), nrow = 100, byrow =
              FALSE)
x <- sample(1:4, 100, replace = TRUE)
y <- sample(1:4, 100, replace = TRUE)
ev_nmi(x, y)
ev_confmat(x, y)

Graphical Displays

Description

Graph cumulative distribution function (CDF) graphs, relative change in area under CDF curves, heatmaps, and cluster assignment tracking plots.

Usage

graph_cdf(mat)

graph_delta_area(mat)

graph_heatmap(mat, main = NULL)

graph_tracking(cl)

graph_all(x)

Arguments

Details

graph_cdf plots the CDF for consensus matrices from different algorithms. graph_delta_area calculates the relative change in area under CDF curve between algorithms. graph_heatmap generates consensus matrix heatmaps for each algorithm in x. graph_tracking tracks how cluster assignments change between algorithms. graph_all is a wrapper that runs all graphing functions.

Value

Various plots from graph_*{} functions. All plots are generated using ggplot, except for graph_heatmap, which uses NMF::aheatmap(). Colours used in graph_heatmap and graph_tracking utilize RColorBrewer::brewer.pal() palettes.

Author(s)

Derek Chiu

References

https://stackoverflow.com/questions/4954507/calculate-the-area-under-a-curve

Examples

# Consensus clustering for 3 algorithms
library(ggplot2)
set.seed(911)
x <- matrix(rnorm(80), ncol = 10)
CC1 <- consensus_cluster(x, nk = 2:4, reps = 3,
algorithms = c("hc", "pam", "km"), progress = FALSE)

# Plot CDF
p <- graph_cdf(CC1)

# Change y label and add colours
p + labs(y = "Probability") + stat_ecdf(aes(colour = k)) +
scale_color_brewer(palette = "Set2")

# Delta Area
p <- graph_delta_area(CC1)

# Heatmaps with column side colours corresponding to clusters
CC2 <- consensus_cluster(x, nk = 3, reps = 3, algorithms = "hc", progress =
FALSE)
graph_heatmap(CC2)

# Track how cluster assignments change between algorithms
p <- graph_tracking(CC1)

Gene expression data for High Grade Serous Carcinoma from TCGA

Description

There are 489 samples measured on 321 genes. Sample IDs are in the row names and gene names are in the column names. This data set is used for clustering HGSC into subtypes with prognostic significance. The cluster assignments obtained by TCGA are indicated by the last six characters of each row name in hgsc: MES.C1, IMM.C2, DIF.C4, and PRO.C5

Usage

hgsc

Format

A data frame with 489 rows and 321 columns.

K-Nearest Neighbours imputation

Description

The non-missing cases indicate the training set, and missing cases indicate the test set.

Usage

impute_knn(x, data, seed = 123456)

Arguments

Value

An object with (potentially not all) missing values imputed with K-Nearest Neighbours.

Note

We consider 5 nearest neighbours and the minimum vote for definite decision is 3.

Author(s)

Aline Talhouk

See Also

Other imputation functions: impute_missing()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
x <- consensus_cluster(dat, nk = 4, reps = 4, algorithms = c("km", "hc",
"diana"), progress = FALSE)
x <- apply(x, 2:4, impute_knn, data = dat, seed = 1)

Impute missing values

Description

Impute missing values from bootstrapped subsampling

Usage

impute_missing(E, data, nk)

Arguments

Details

The default output from consensus_cluster will undoubtedly contain NA entries because each replicate chooses a random subset (with replacement) of all samples. Missing values should first be imputed using impute_knn(). Not all missing values are guaranteed to be imputed by KNN. See class::knn() for details. Thus, any remaining missing values are imputed using majority voting.

Value

If flattened matrix consists of more than one repetition, i.e. it isn't a column vector, then the function returns a matrix of clusterings with complete cases imputed using majority voting, and relabelled, for chosen k.

Author(s)

Aline Talhouk

See Also

Other imputation functions: impute_knn()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
E <- consensus_cluster(dat, nk = 3:4, reps = 10, algorithms = c("hc", "km",
"sc"), progress = FALSE)
sum(is.na(E))
E_imputed <- impute_missing(E, dat, 4)
sum(is.na(E_imputed))

K-modes

Description

Combine clustering results using K-modes.

Usage

k_modes(E, is.relabelled = TRUE, seed = 1)

Arguments

Details

Combine clustering results generated using different algorithms and different data perturbations by k-modes. This method is the categorical data analog of k-means clustering. Complete cases are needed: i.e. no NAs. If the matrix contains NAs those are imputed by majority voting (after class relabeling).

Value

a vector of cluster assignments based on k-modes

Author(s)

Aline Talhouk

References

Luo, H., Kong, F., & Li, Y. (2006, August). Combining multiple clusterings via k-modes algorithm. In International Conference on Advanced Data Mining and Applications (pp. 308-315). Springer, Berlin, Heidelberg.

See Also

Other consensus functions: CSPA(), LCA(), LCE(), majority_voting()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
cc <- consensus_cluster(dat, nk = 4, reps = 6, algorithms = "pam", progress =
FALSE)
table(k_modes(cc[, , 1, 1, drop = FALSE], is.relabelled = FALSE))

Majority voting

Description

Combine clustering results using majority voting.

Usage

majority_voting(E, is.relabelled = TRUE)

Arguments

Details

Combine clustering results generated using different algorithms and different data perturbations by majority voting. The class of a sample is the cluster label which was selected most often across algorithms and subsamples.

Value

a vector of cluster assignments based on majority voting

Author(s)

Aline Talhouk

See Also

Other consensus functions: CSPA(), LCA(), LCE(), k_modes()

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
cc <- consensus_cluster(dat, nk = 4, reps = 6, algorithms = "pam", progress =
FALSE)
table(majority_voting(cc[, , 1, 1, drop = FALSE], is.relabelled = FALSE))

Minimize Frobenius norm for between two matrices

Description

Finds a permutation of a matrix such that its Frobenius norm with another matrix is minimized.

Usage

min_fnorm(A, B = diag(nrow(A)))

Arguments

Details

Finds the permutation P of A such that ⁠||PA - B||⁠ is minimum in Frobenius norm. Uses the linear-sum assignment problem (LSAP) solver in the package clue. The default B is the identity matrix of same dimension, so that the permutation of A maximizes its trace. This procedure is useful for constructing a confusion matrix when we don't know the true class labels of a predicted class and want to compare to a reference class.

Value

Permuted matrix such that it is the permutation of A closest to B

Author(s)

Ravi Varadhan: https://stat.ethz.ch/pipermail/r-help/2010-April/236664.html

Examples

set.seed(1)
A <- matrix(sample(1:25, size = 25, rep = FALSE), 5, 5)
min_fnorm(A)

Simulate and select null distributions on empirical gene-gene correlations

Description

Using a principal component constructed from the sample space, we simulate null distributions with univariate Normal distributions using pcn_simulate. Then a subset of these distributions is chosen using pcn_select.

Usage

pcn_simulate(data, n.sim = 50)

pcn_select(data.sim, cl, type = c("rep", "range"), int = 5)

Arguments

Value

pcn_simulate returns a list of length n.sim. Each element is a simulated matrix using this "Principal Component Normal" (pcn) procedure.

pcn_select returns a list with elements

• ranks: When type = "range", ranks of each extracted dataset shown

• ind: index of representative simulation

• dat: simulation data representation of all in pcNormal

Author(s)

Derek Chiu

Examples

set.seed(9)
A <- matrix(rnorm(300), nrow = 20)
pc.dat <- pcn_simulate(A, n.sim = 50)
cl <- sample(1:4, 20, replace = TRUE)
pc.select <- pcn_select(pc.dat, cl, "rep")

Prepare data for consensus clustering

Description

Perform feature selection or dimension reduction to remove noise variables.

Usage

prepare_data(
  data,
  scale = TRUE,
  type = c("conventional", "robust", "tsne"),
  min.var = 1
)

Arguments

Details

We can apply a basic filtering method of feature selection that removes variables with low signal and (optionally) scales before consensus clustering. Or, we can use t-SNE dimension reduction to transform the data to just two variables. This lower-dimensional embedding allows algorithms such as hierarchical clustering to achieve greater performance.

Value

dataset prepared for usage in consensus_cluster

Author(s)

Derek Chiu

Examples

set.seed(2)
x <- replicate(10, rnorm(100))
x.prep <- prepare_data(x)
dim(x)
dim(x.prep)

Relabel classes to a standard

Description

Relabel clustering categories to match to a standard by minimizing the Frobenius norm between the two labels.

Usage

relabel_class(pred.cl, ref.cl)

Arguments

Value

A vector of relabeled cluster assignments

Author(s)

Aline Talhouk

Examples

set.seed(2)
pred <- sample(1:4, 100, replace = TRUE)
true <- sample(1:4, 100, replace = TRUE)
relabel_class(pred, true)

Significant Testing of Clustering Results

Description

Uses the SigClust K-Means algorithm to assess significance of clustering results.

Usage

sigclust(x, k, nsim, nrep = 1, labflag = 0, label = 0, icovest = 2)

Arguments

Details

This function is a wrapper for the original sigclust::sigclust(), except that an additional parameter k is allows testing against any number of clusters. In addition, the default type of covariance estimation is also different.

Value

An object of class sigclust. See sigclust::sigclust() for details.

Author(s)

Hanwen Huang: hanwenh@email.unc.edu; Yufeng Liu: yfliu@email.unc.edu; J. S. Marron: marron@email.unc.edu

References

Liu, Yufeng, Hayes, David Neil, Nobel, Andrew and Marron, J. S, 2008, Statistical Significance of Clustering for High-Dimension, Low-Sample Size Data, Journal of the American Statistical Association 103(483) 1281–1293.

Examples

data(hgsc)
dat <- hgsc[1:100, 1:50]
nk <- 4
cc <- consensus_cluster(dat, nk = nk, reps = 5, algorithms = "pam",
progress = FALSE)
cl.mat <- consensus_combine(cc, element = "class")
lab <- cl.mat$`4`[, 1]
set.seed(1)
str(sigclust(x = dat, k = nk, nsim = 50, labflag = 1, label = lab))

Similarity Matrices

Description

cts computes the connected triple based similarity matrix, srs computes the simrank based similarity matrix, and asrs computes the approximated simrank based similarity matrix.

Usage

cts(E, dc)

srs(E, dc, R)

asrs(E, dc)

Arguments

Value

an N by N CTS, SRS, or ASRS matrix

Author(s)

Johnson Liu, Derek Chiu

References

MATLAB functions cts, srs, asrs in package LinkCluE by Simon Garrett

Examples

set.seed(1)
E <- matrix(rep(sample(1:4, 800, replace = TRUE)), nrow = 100)
CTS <- cts(E = E, dc = 0.8)
SRS <- srs(E = E, dc = 0.8, R = 3)
ASRS <- asrs(E = E, dc = 0.8)
purrr::walk(list(CTS, SRS, ASRS), str)