| Title: | Least-Squares Bilinear Clustering for Three-Way Data |
|---|---|
| Description: | Functions for performing least-squares bilinear clustering of three-way data. The method uses the bilinear decomposition (or bi-additive model) to model two-way matrix slices while clustering over the third way. Up to four different types of clusters are included, one for each term of the bilinear decomposition. In this way, matrices are clustered simultaneously on (a subset of) their overall means, row margins, column margins and row-column interactions. The orthogonality of the bilinear model results in separability of the joint clustering problem into four separate ones. Three of these sub-problems are specific k-means problems, while a special algorithm is implemented for the interactions. Plotting methods are provided, including biplots for the low-rank approximations of the interactions. |
| Authors: | Pieter Schoonees [aut, cre], Patrick Groenen [ctb] |
| Maintainer: | Pieter Schoonees <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1 |
| Built: | 2024-11-11 04:14:29 UTC |
| Source: | https://github.com/cran/lsbclust |
Funtions for least squares latent class matrix factorizations.
Pieter C. Schoonees [aut, cre], Patrick J.F. Groenen [aut]
Van Rosmalen, J., Van Herk, H., & Groenen, P. J. F. (2010). Identifying response styles: A latent-class bilinear multinomial logit model. Journal of Marketing Research, 47(1), 157-172.
Vectorize matrix slices over a specific way of an three-way array, and
conduct kmeans on it.
akmeans(data, centers, margin = 3L, ndim = NULL, ...)akmeans(data, centers, margin = 3L, ndim = NULL, ...)
data |
Three-way data array |
centers |
Passed to |
margin |
Integer indicating which way to cluster over |
ndim |
The rank of the low dimensional approximation of the matrix
slices to construct before clustering (using |
... |
Additional arguments passed to |
set.seed(1) res <- akmeans(data = carray(dcars), margin = 3L, centers = 5, nstart = 10)set.seed(1) res <- akmeans(data = carray(dcars), margin = 3L, centers = 5, nstart = 10)
Decomposes a matrix into an overall mean matrix, row margins matrix, column margins matrix
and an interaction matrix, depending on delta.
bicomp(x, delta = c(1, 1, 1, 1), which = 0L:4L)bicomp(x, delta = c(1, 1, 1, 1), which = 0L:4L)
x |
A matrix to be decomposed. |
delta |
A vector of length four with 0/1 entries which controls the type of decomposition made. |
which |
A vector giving the elements to return, with 0 = original data, 1 = overall means, 2 = row means, 3 = column means and 4 = interactions. |
An object of class bicomp, possible also inheriting from class data.frame,
which is either a named list with the required components, or a single matrix if a single
component is requested. An additional attribute return_type gives information on the type
of matrices returned.
Double-centre the matrix slices of a three-way array.
carray(array, margin = 3L, rows = TRUE, columns = TRUE)carray(array, margin = 3L, rows = TRUE, columns = TRUE)
array |
A three-way array |
margin |
The way of the array over which the centring must be done |
rows |
Logical indicating whether to centre the rows of the matrix slices |
columns |
Logical indicating whether to centre the columns of the matrix slices |
Generic function to compare simulation results in lsbclust.
cfsim(fitted, actual, method = c("diag", "cRand"))cfsim(fitted, actual, method = c("diag", "cRand"))
fitted |
An object of class |
actual |
An object of class |
method |
The type of statistics to calculate, passed to |
This function compares cluster membership and parameter estimates for the results of
akmeans on simulated data, constructed using rlsbclust,
to the true underlying values.
## S3 method for class 'akmeans' cfsim(fitted, actual, method = c("diag", "cRand"))## S3 method for class 'akmeans' cfsim(fitted, actual, method = c("diag", "cRand"))
fitted |
An object of class |
actual |
An object of class |
method |
The method for calculating cluster agreement across random starts, passed on
to |
## Simulate LSBCLUST data, fit akmeans on double-centered data, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) dat[[1]]$data <- carray(dat[[1]]$data) res <- akmeans(data = dat[[1]]$data, centers = 5, margin = 3, ndim = 2) cfsim(res, dat[[1]])## Simulate LSBCLUST data, fit akmeans on double-centered data, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) dat[[1]]$data <- carray(dat[[1]]$data) res <- akmeans(data = dat[[1]]$data, centers = 5, margin = 3, ndim = 2) cfsim(res, dat[[1]])
This function compares cluster membership and parameter estimates for the results of
lsbclust on simulated data to the true underlying values.
## S3 method for class 'lsbclust' cfsim(fitted, actual, method = c("diag", "cRand"))## S3 method for class 'lsbclust' cfsim(fitted, actual, method = c("diag", "cRand"))
fitted |
An object of class |
actual |
An object of class |
method |
The type of statistics to calculate, passed to |
## Simulate LSBCLUST data, fit LSBCLUST, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5)) cfsim(res, dat[[1]])## Simulate LSBCLUST data, fit LSBCLUST, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5)) cfsim(res, dat[[1]])
This function compares cluster membership and parameter estimates for the results of
T3Clusf on simulated data, using rlsbclust,
to the true underlying values.
## S3 method for class 'T3Clusf' cfsim(fitted, actual, method = c("diag", "cRand"))## S3 method for class 'T3Clusf' cfsim(fitted, actual, method = c("diag", "cRand"))
fitted |
An object of class |
actual |
An object of class |
method |
The method for calculating cluster agreement across random starts, passed on
to |
## Simulate LSBCLUST data, fit T3Clusf on double-centered data, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) dat[[1]]$data <- carray(dat[[1]]$data) res <- T3Clusf(X = dat[[1]]$data, Q = 2, G = 5) cfsim(res, dat[[1]])## Simulate LSBCLUST data, fit T3Clusf on double-centered data, and compare set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) dat[[1]]$data <- carray(dat[[1]]$data) res <- T3Clusf(X = dat[[1]]$data, Q = 2, G = 5) cfsim(res, dat[[1]])
These export into the framework set out in package clue.
## S3 method for class 'int.lsbclust' cl_class_ids(x) ## S3 method for class 'int.lsbclust' is.cl_partition(x) ## S3 method for class 'int.lsbclust' is.cl_hard_partition(x) ## S3 method for class 'lsbclust_sim_part' cl_class_ids(x) ## S3 method for class 'lsbclust_sim_part' is.cl_partition(x) ## S3 method for class 'lsbclust_sim_part' is.cl_hard_partition(x) ## S3 method for class 'T3Clusf' cl_class_ids(x) ## S3 method for class 'T3Clusf' is.cl_partition(x) ## S3 method for class 'T3Clusf' is.cl_hard_partition(x) ## S3 method for class 'akmeans' cl_class_ids(x) ## S3 method for class 'akmeans' is.cl_partition(x) ## S3 method for class 'akmeans' is.cl_hard_partition(x)## S3 method for class 'int.lsbclust' cl_class_ids(x) ## S3 method for class 'int.lsbclust' is.cl_partition(x) ## S3 method for class 'int.lsbclust' is.cl_hard_partition(x) ## S3 method for class 'lsbclust_sim_part' cl_class_ids(x) ## S3 method for class 'lsbclust_sim_part' is.cl_partition(x) ## S3 method for class 'lsbclust_sim_part' is.cl_hard_partition(x) ## S3 method for class 'T3Clusf' cl_class_ids(x) ## S3 method for class 'T3Clusf' is.cl_partition(x) ## S3 method for class 'T3Clusf' is.cl_hard_partition(x) ## S3 method for class 'akmeans' cl_class_ids(x) ## S3 method for class 'akmeans' is.cl_partition(x) ## S3 method for class 'akmeans' is.cl_hard_partition(x)
x |
An object of class |
This function calculates the cluster means in vectorized form based on the current value of the clustering vector.
ClustMeans(nclust, start, data)ClustMeans(nclust, start, data)
nclust |
The number of clusters. |
start |
The current clustering vector. |
data |
The concatenated data, with J * K rows and N columns |
A numeric matrix with nclust rows and J*K columns.
A utility function for calculating centring matrices.
cmat(k)cmat(k)
k |
An integer determining the dimensions of the centring matrix. |
This data set relates to 187 Dutch households rating 10 automobile manufacturers according to 8 variables (original Dutch terms in parentheses): price (prijsniveau), design (vormgeving), safety (veiligheid), operating cost (gebruikskosten), ) sportiness (sportiviteit), size (modelgrootte), reliability (betrouwbaarheid) and feautures (uitrusting). A rating scale from 1 to 10 was used.
dcarsdcars
A three-way array with cars in the first dimension, variables in the second and consumers in the third dimension.
The items and labels for the endpoints of the scales are (original Dutch labels in parentheses):
A rating from 1 = Expensive (duur) to 10 = Cheap (goedkoop)
A rating from 1 = Ugly (lelijk) to 10 = Beautiful (mooi)
A rating from 1 = Bad (slecht) to 10 = Good (goed)
A rating from 1 = Low (laag) to 10 = High (hoog)
A rating from 1 = Slow (langzaam) to 10 = Fast (snel)
A rating from 1 = Large (groot) to 10 = Small (klein)
A rating from 1 = Bad (slecht) to 10 = Good (goed)
A rating from 1 = Simple (eenvoudig) to 10 = Luxurious (luxe)
The original sample consisted of 188 households. However, one of these households (code 87845) was discarded because it appears that they used a rating scale from 0 to 10 instead of from 1 to 10. Note that all rating scales has been reversed so that higher scores are better for most items. The exceptions are OperatingCost and Size, where larger values mean higher costs and smaller cars respectively.
Tammo Bijmolt, Michel van de Velden
data("dcars") set.seed(5448) m <- lsbclust(data = dcars, delta = c(1, 1, 1, 1), nclust = c(5, 3, 6, 8), nstart = 5, nstart.kmeans = 10, parallel = FALSE, fixed = "columns")data("dcars") set.seed(5448) m <- lsbclust(data = dcars, delta = c(1, 1, 1, 1), nclust = c(5, 3, 6, 8), nstart = 5, nstart.kmeans = 10, parallel = FALSE, fixed = "columns")
An S3 method for fitted for class "akmeans".
## S3 method for class 'akmeans' fitted(object, ...)## S3 method for class 'akmeans' fitted(object, ...)
object |
An object of class |
... |
Unimplemented |
An array approximating the original data
An S3 method for fitted for class "lsbclust".
## S3 method for class 'lsbclust' fitted(object, ...)## S3 method for class 'lsbclust' fitted(object, ...)
object |
An object of class |
... |
Unimplemented |
An array approximating the original data
An S3 method for fitted for class "T3Clusf".
## S3 method for class 'T3Clusf' fitted(object, ...)## S3 method for class 'T3Clusf' fitted(object, ...)
object |
An object of class |
... |
Unimplemented |
An array approximating the original data
This function finds K orthogonal rotation matrices so that the rotated versions of the input configurations match each other optimally in the least-squares sense. The algorithm depends on the starting values for the rotation matrices. At present identity matrices are used as starting values. Only rotations / reflections are considered – no scaling or translation factors are included.
genproc(configs, maxit = 50L, reltol = 1e-06, random = FALSE)genproc(configs, maxit = 50L, reltol = 1e-06, random = FALSE)
configs |
A list of original configuration matrices |
maxit |
The maximum number of iterations allowed |
reltol |
The relative error tolerance for determining numeric convergence. |
random |
Logical indicating whether or not to use random starts (only applicable when the dimensionality is two). |
Gower, J. C., & Dijksterhuis, G. B. (2004). Procrustes problems (Vol. 3). Oxford: Oxford University Press.
This function takes a matrix or data.frame and the number of rating categories maxcat
and produces a three-way array of m by maxcat indicator matrices, one for each of the n rows.
The input x must be a matrix or data.frame of dimensions n by m
which contains the ratings on a scale of 1 to maxcat for m items. Note that missing values
(NA's) will not appear in the columns.
indarr(x, maxcat, na.add = TRUE)indarr(x, maxcat, na.add = TRUE)
x |
a |
maxcat |
an integer indicating the maximum of the rating scale (which is assumed to start with 1) |
na.add |
logical indicating whether to add a designated category for missings or not. Defaults to TRUE. |
A list of rating by item indicator matrices.
Pieter C. Schoonees
data("lov") arr <- indarr(lov[1:10, 1:9], maxcat = 9) str(arr)data("lov") arr <- indarr(lov[1:10, 1:9], maxcat = 9) str(arr)
This function implements the interaction clustering part of the Least Squares Bilinear Clustering method of Schoonees, Groenen and Van de Velden (2014).
int.lsbclust(data, margin = 3L, delta, nclust, ndim = 2, fixed = c("none", "rows", "columns"), nstart = 50, starts = NULL, alpha = 0.5, parallel = FALSE, mc.cores = detectCores() - 1, maxit = 100, verbose = 1, method = "diag", minsize = 3L, return_data = FALSE)int.lsbclust(data, margin = 3L, delta, nclust, ndim = 2, fixed = c("none", "rows", "columns"), nstart = 50, starts = NULL, alpha = 0.5, parallel = FALSE, mc.cores = detectCores() - 1, maxit = 100, verbose = 1, method = "diag", minsize = 3L, return_data = FALSE)
data |
A three-way array representing the data. |
margin |
An integer giving the single subscript of |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
nclust |
An integer giving the desired number of clusters. If it is a vector, the algorithm will be run for each element. |
ndim |
The required rank for the approximation of the interactions (a scalar). |
fixed |
One of |
nstart |
The number of random starts to use. |
starts |
A list containing starting configurations for the cluster membership vector. If not supplied, random initializations will be generated. |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed between rows and columns. |
parallel |
Logical indicating whether to parallelize over different starts or not. |
mc.cores |
The number of cores to use in case |
maxit |
The maximum number of iterations allowed. |
verbose |
Integer controlling the amount of information printed: 0 = no information, 1 = Information on random starts and progress, and 2 = information is printed after each iteration for the interaction clustering. |
method |
The method for calculating cluster agreement across random starts, passed on
to |
minsize |
Integer giving the minimum size of cluster to uphold when reinitializing empty clusters. |
return_data |
Logical indicating whether to include the data in the return value or not |
An object of class int.lsb
data("supermarkets") out <- int.lsbclust(data = supermarkets, margin = 3, delta = c(1,1,0,0), nclust = 4, ndim = 2, fixed = "rows", nstart = 1, alpha = 0)data("supermarkets") out <- int.lsbclust(data = supermarkets, margin = 3, delta = c(1,1,0,0), nclust = 4, ndim = 2, fixed = "rows", nstart = 1, alpha = 0)
This function does a weighted K-means clustering.
ComputeMeans(cm, data, weight, nclust) AssignCluster(data, weight, M, nclust) KMeansW(nclust, start, data, weight, eps = 1e-08, IterMax = 100L)ComputeMeans(cm, data, weight, nclust) AssignCluster(data, weight, M, nclust) KMeansW(nclust, start, data, weight, eps = 1e-08, IterMax = 100L)
cm |
Numeric vector of class indicators. |
data |
The concatenated data, with N rows and M columns. Currently, the columns are clustered. |
weight |
The vector of length |
nclust |
The number of clusters. |
M |
Matrix of cluster means. |
start |
The current cluster membership vector. |
eps |
Numerical absolute convergence criteria for the K-means. |
IterMax |
Integer giving the maximum number of iterations allowed for the K-means. |
A list with the folowing values.
centers |
the |
cluster |
vector of length N with cluster memberships. |
loss |
vector of length |
iterations |
the number of iterations used (corresponding to the number
of nonzero entries in |
set.seed(1) clustmem <- sample.int(n = 10, size = 100, replace = TRUE) mat <- rbind(matrix(rnorm(30*4, mean = 3), nrow = 30), matrix(rnorm(30*4, mean = -2), nrow = 30), matrix(rnorm(40*4, mean = 0), nrow = 40)) wt <- runif(100) testMeans <- lsbclust:::ComputeMeans(cm = clustmem, data = mat, weight = wt, nclust = 3) testK <- lsbclust:::KMeansW(start = clustmem, data = mat, weight = wt, nclust = 3)set.seed(1) clustmem <- sample.int(n = 10, size = 100, replace = TRUE) mat <- rbind(matrix(rnorm(30*4, mean = 3), nrow = 30), matrix(rnorm(30*4, mean = -2), nrow = 30), matrix(rnorm(40*4, mean = 0), nrow = 40)) wt <- runif(100) testMeans <- lsbclust:::ComputeMeans(cm = clustmem, data = mat, weight = wt, nclust = 3) testK <- lsbclust:::KMeansW(start = clustmem, data = mat, weight = wt, nclust = 3)
This function calculates the loss function for the interaction clustering for all data slices and clusters means. The inputs are numeric matrices.
x |
The data matrix, with the N slices strung out as vectors in the columns. |
y |
The matrix of cluster means, with each mean represented by a row. |
A numeric matrix with nclust rows and N columns.
This is the list-of-values data set used in Van Rosmalen, Van Herk & Groenen (2010).
Column names and factor labels differ slightly from that paper. Missing values are encoded as
NA as usual. The first nine columns are items answered on a nine-point rating scale, with
rating 1 representing 'very important' and category 9 'not important at all'. The respondents
were asked how important each of these items are as a guiding principle in their lives.
data("lov")data("lov")
A data frame with 4514 observations on the following 12 variables.
a numeric vector; 'a sense of belonging'
a numeric vector
a numeric vector; 'warm relationships with others'
a numeric vector
a numeric vector; 'being well-respected'
a numeric vector; 'fun and enjoyment'
a numeric vector
a numeric vector
a numeric vector; 'a sense of accomplishment'
a factor with levels Britain, France, Germany,
Italy and Spain
a factor with levels Low and High
a factor with levels -25, 25-39, 40-54 and 55+
Joost van Rosmalen
Van Rosmalen, J., Van Herk, H., & Groenen, P. J. (2010). Identifying response styles: A latent-class bilinear multinomial logit model. Journal of Marketing Research, 47(1), 157-172.
data("lov") ## Construct array lovarr <- indarr(lov[, 1:9], maxcat = 9) ## Run analysis set.seed(13841) fit <- lsbclust(data = lovarr, margin = 3, delta = c(0, 1, 0, 0), nclust = c(NA, 11, NA, 5), fixed = "rows", nstart = 1, iter.max = 50, nstart.kmeans = 10)data("lov") ## Construct array lovarr <- indarr(lov[, 1:9], maxcat = 9) ## Run analysis set.seed(13841) fit <- lsbclust(data = lovarr, margin = 3, delta = c(0, 1, 0, 0), nclust = c(NA, 11, NA, 5), fixed = "rows", nstart = 1, iter.max = 50, nstart.kmeans = 10)
This function clusters along one way of a three-way array (as specified by margin) while
decomposing along the other two dimensions. Four types of clusterings are allowed based on the
respective two-way slices of the array: on the overall means, row margins, column margins and the
interactions between rows and columns. Which clusterings can be fit is determined by the vector
delta, with four binary elements. All orthogonal models are fitted.
The nonorthogonal case delta = (1, 1, 0, 0) returns an error. See the reference for further details.
lsbclust(data, margin = 3L, delta = c(1L, 1L, 1L, 1L), nclust, ndim = 2L, fixed = c("none", "rows", "columns"), nstart = 20L, starts = NULL, nstart.kmeans = 500L, alpha = 0.5, parallel = FALSE, maxit = 100L, verbose = 1, method = "diag", type = NULL, sep.nclust = TRUE, ...)lsbclust(data, margin = 3L, delta = c(1L, 1L, 1L, 1L), nclust, ndim = 2L, fixed = c("none", "rows", "columns"), nstart = 20L, starts = NULL, nstart.kmeans = 500L, alpha = 0.5, parallel = FALSE, maxit = 100L, verbose = 1, method = "diag", type = NULL, sep.nclust = TRUE, ...)
data |
A three-way array representing the data. |
margin |
An integer giving the single subscript of |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
nclust |
A vector of length four giving the number of clusters for the overall mean, the row margins, the column margins and the interactions (in that order) respectively. Alternatively, a vector of length one, in which case all components will have the same number of clusters. |
ndim |
The required rank for the approximation of the interactions (a scalar). |
fixed |
One of |
nstart |
The number of random starts to use for the interaction clustering. |
starts |
A list containing starting configurations for the cluster membership vector. If not
supplied, random initializations will be generated (passed to |
nstart.kmeans |
The number of random starts to use in |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed
between rows and columns (passed to |
parallel |
Logical indicating whether to parallel over different starts or not
(passed to |
maxit |
The maximum number of iterations allowed in the interaction clustering. |
verbose |
Integer controlling the amount of information printed: 0 = no information, 1 = Information on random starts and progress, and 2 = information is printed after each iteration for the interaction clustering. |
method |
The method for calculating cluster agreement across random starts, passed on
to |
type |
One of |
sep.nclust |
Logical indicating how nclust should be used across different |
... |
Additional arguments passed to |
Returns an object of S3 class lsbclust which has slots:
overall |
Object of class |
rows |
Object of class |
columns |
Object of class |
interactions |
Object of class |
call |
The function call used to create the object |
delta |
The value of |
df |
Breakdown of the degrees-of-freedom across the different subproblems |
loss |
Breakdown of the loss across subproblems |
time |
Time taken in seconds to calculate the solution |
cluster |
Matrix of cluster membership per observation for all cluster types |
Schoonees, P.C., Groenen, P.J.F., Van de Velden, M. Least-squares Bilinear Clustering of Three-way Data. Econometric Institute Report, EI2014-23.
Construct simple two-dimensional biplots given matrices representing the rows and columns of a two-dimensional matrix using ggplot2.
meanbiplot(rows, cols)meanbiplot(rows, cols)
rows |
A list of matrices representing the rows |
cols |
A list of matrices representing the columns |
set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) meanbiplot(dat[[1]]$interactions$C, dat[[1]]$interactions$D)set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) meanbiplot(dat[[1]]$interactions$C, dat[[1]]$interactions$D)
Construct a heatmap of a matrix using ggplot2.
meanheatmap(x)meanheatmap(x)
x |
Matrix or list of matrices to be plotted |
set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(6, 6), nclust = c(5, 4, 6, 5)) meanheatmap(Map(tcrossprod, dat[[1]]$interactions$C, dat[[1]]$interactions$D))set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(6, 6), nclust = c(5, 4, 6, 5)) meanheatmap(Map(tcrossprod, dat[[1]]$interactions$C, dat[[1]]$interactions$D))
This function conducts k-means on the overall mean, the row margins or column margins of a set of N matrices. These matrices are two-way slices of a three-dimensional array.
orc.lsbclust(data, margin = 3L, delta, nclust, sep.nclust = TRUE, type = NULL, verbose = 1, ...)orc.lsbclust(data, margin = 3L, delta, nclust, sep.nclust = TRUE, type = NULL, verbose = 1, ...)
data |
A three-way array representing the data. |
margin |
An integer giving the single subscript of |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
nclust |
An integer giving the desired number of clusters. In case |
sep.nclust |
Logical indicating how nclust should be used across different |
type |
One of |
verbose |
Integer controlling the amount of information printed: 0 = no information, 1 = Information on random starts and progress, and 2 = information is printed after each iteration for the interaction clustering. |
... |
Additional arguments passed to |
A list containing a subset of the classes row.kmeans, col.kmeans and
ovl.kmeans which are specific versions of class kmeans. In case type is a vector, a list
is returned containing the results for each of the (unique) elements of type, with the
same classes as before. See kmeans for an overview of the structure of these objects.
bicomp ObjectPlot method for an object of class bicomp (see bicomp).
## S3 method for class 'bicomp' plot(x, which = 0L:4L, arrange = TRUE, col = c("red4", "beige", "blue4"), strip.legend = TRUE, add.titles = FALSE, ...)## S3 method for class 'bicomp' plot(x, which = 0L:4L, arrange = TRUE, col = c("red4", "beige", "blue4"), strip.legend = TRUE, add.titles = FALSE, ...)
x |
An object of class |
which |
A numeric vector indicating which matrices to plot, with 0 = original data, 1 = overall means, 2 = row means, 3 = column means and 4 = interactions. |
arrange |
Logical indicating whether the arrange the plots side-by-side
via |
col |
A character vector of length three giving the parameters
|
strip.legend |
Logical indicating whether to strip the legend off the plot or not. |
add.titles |
Logical indicating whether to add titles to the plots or not. |
... |
Additional arguments to |
Simple plot method for object of class 'col.kmeans' as output by orc.lsbclust.
## S3 method for class 'col.kmeans' plot(x, which = 1L, ...)## S3 method for class 'col.kmeans' plot(x, which = 1L, ...)
x |
An object of class |
which |
Which type of plot to produce (only 3 types are implemented). |
... |
additional arguments passed to |
Pieter C. Schoonees
data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "columns") plot(m)data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "columns") plot(m)
Two-dimensional plot method for object of class 'int.lsbclust' as output by int.lsbclust.
## S3 method for class 'int.lsbclust' plot(x, which = seq_len(nclust), plot.type = c("biplots", "means", "estimates"), segments = NULL, biplot.axes = TRUE, nmarkers = 5, alpha = NULL, check.alpha = TRUE, fix.alpha = FALSE, probs = 0, arrange = FALSE, fix.limits = TRUE, limit.exp = 1.05, lambda.scale = TRUE, procrustes.rotation = x$fixed == "none", fix.lambda = FALSE, labs.grey = TRUE, label.0 = FALSE, tick.length = 0.0075 * diff(lims), axis.col = "grey60", label.size = 3, axis.size = 0.25, axis.title.size = 4, draw.axis = NULL, points.col = list(rows = "red", columns = "blue2"), offset.tick.labels = 3.5, offset.axis.title = list(rows = 0.015 * max(nchar(rnms)), columns = 0.015 * max(nchar(cnms))), axis.arrow = grid::arrow(angle = 20, length = grid::unit(0.0175, "npc")), ...)## S3 method for class 'int.lsbclust' plot(x, which = seq_len(nclust), plot.type = c("biplots", "means", "estimates"), segments = NULL, biplot.axes = TRUE, nmarkers = 5, alpha = NULL, check.alpha = TRUE, fix.alpha = FALSE, probs = 0, arrange = FALSE, fix.limits = TRUE, limit.exp = 1.05, lambda.scale = TRUE, procrustes.rotation = x$fixed == "none", fix.lambda = FALSE, labs.grey = TRUE, label.0 = FALSE, tick.length = 0.0075 * diff(lims), axis.col = "grey60", label.size = 3, axis.size = 0.25, axis.title.size = 4, draw.axis = NULL, points.col = list(rows = "red", columns = "blue2"), offset.tick.labels = 3.5, offset.axis.title = list(rows = 0.015 * max(nchar(rnms)), columns = 0.015 * max(nchar(cnms))), axis.arrow = grid::arrow(angle = 20, length = grid::unit(0.0175, "npc")), ...)
x |
An object of class |
which |
A vector indicating which item segments to plot. |
plot.type |
Character string giving the type of plots to produce: either |
segments |
A logical vector with two elements, indicating whether the rows and columns should be plotted as line segments or not. |
biplot.axes |
A logical indicating whether to plot calibrated biplot axes for the line
segments indicated in |
nmarkers |
Either a single integer giving the number of desired markers per biplot axis
for all axes, or a named list. This is passed as the argument |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed between rows and columns. It will trigger a recomputation of the updates if it does not correspond to the value used when fitting the model. Do not confuse this with the term "alpha" used in the context of colour transparency. |
check.alpha |
Logical indicating whether to look for a better alpha. This is only used when
|
fix.alpha |
Logical indicating whether to fix alpha across all clusters or not
when |
probs |
Argument passed to |
arrange |
Logical indicating whether to arrange the plots side-by-side
via |
fix.limits |
Logical indicating whether biplot x- and y-limits must be fixed across clusters
or not. Note that this is automatically set to |
limit.exp |
A numeric expansion factor applied multiplicatively to the plot limits, but only
when |
lambda.scale |
Logical indicating whether to apply lambda scaling to the coordinates or not. If true, the scaling is done such that the average squared distance to the origin is equal for the row and column coordinates. |
procrustes.rotation |
Logical indicating whether to do Procrustes rotations so that the
location of the axes indicated as segments (see argument |
fix.lambda |
Logical indicating whether to fix lambda across all clusters or not. |
labs.grey |
Logical indicating whether to apply greying to the text labels are well. |
label.0 |
Logical indicating whether to label the origin or not. |
tick.length |
The required tick length as a |
axis.col |
The colour of the biplot axes. |
label.size |
The size of the labels for the markers on the biplot axes. |
axis.size |
Line size for biplot axes. |
axis.title.size |
Size of biplot axis titles. |
draw.axis |
A list with up to two components which must be named |
points.col |
A named list containing the colours to use for plotting the sets of points. The
elements |
offset.tick.labels |
A numeric value giving the offset factor of the biplot axis marker labels from their respective tick marks. Higher (lower) values lead to labels being further from (nearer to) their respective tick marks. |
offset.axis.title |
A names list of (up to) two numeric values giving the fixed length offset of the
biplot axis title label from the end of the axis segment. The two elements must have names
|
axis.arrow |
An |
... |
Additional arguments passed to |
In case nmarkers is a list, it can have up to two elements. These are required to be named
"rows" and/or "columns", otherwise an error will be thrown. The elements of the list
contains either single numeric values each or numeric vectors of the appropriate lengths
indicating the n argument passed to pretty.
In some cases, the row and/or column fit values can contain non-finite values. If that occurs, colour transparency cannot and will not be used for that particular element (and this can vary between clusters). This relates to the alpha parameter in the plotting routines.
This plot method simply plots each of the components in the list of class lsbclust.
## S3 method for class 'lsbclust' plot(x, type = c("overall", "rows", "columns", "interactions"), biplot.axes = TRUE, ...)## S3 method for class 'lsbclust' plot(x, type = c("overall", "rows", "columns", "interactions"), biplot.axes = TRUE, ...)
x |
An object of class |
type |
A character vector indicating which component(s) of |
biplot.axes |
A logical indicating whether to plot calibrated biplot axes for the line
segments indicated in |
... |
additional arguments passed to the plot methods of the respective components, typically
to |
Pieter C. Schoonees
plot.int.lsbclust, plot.ovl.kmeans,
plot.row.kmeans, plot.col.kmeans
data("dcars") m <- lsbclust(data = dcars, margin = 3, delta = c(1, 1, 1, 1), nclust = 5, nstart = 1) plot(m)data("dcars") m <- lsbclust(data = dcars, margin = 3, delta = c(1, 1, 1, 1), nclust = 5, nstart = 1) plot(m)
Simple plot method for object of class 'ovl.kmeans' as output by orc.lsbclust.
## S3 method for class 'ovl.kmeans' plot(x, which = 1L, ...)## S3 method for class 'ovl.kmeans' plot(x, which = 1L, ...)
x |
An object of class |
which |
Which type of plot to produce. Currently only |
... |
additional arguments passed to |
Pieter C. Schoonees
data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "overall") plot(m)data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "overall") plot(m)
Simple plot method for object of class 'row.kmeans' as output by orc.lsbclust.
## S3 method for class 'row.kmeans' plot(x, which = 1L, ...)## S3 method for class 'row.kmeans' plot(x, which = 1L, ...)
x |
An object of class |
which |
Which type of plot to produce (only 3 types are implemented). |
... |
additional arguments passed to |
Pieter C. Schoonees
data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "rows") plot(m)data("dcars") m <- orc.lsbclust(data = dcars, margin = 3, delta = c(1,1,1,1), nclust = 5, type = "rows") plot(m)
Plot 'step.lsbclust' objects.
## S3 method for class 'step.lsbclust' plot(x, which = 1L:5L, col.all = NULL, arrange = FALSE, chull = FALSE, ...)## S3 method for class 'step.lsbclust' plot(x, which = 1L:5L, col.all = NULL, arrange = FALSE, chull = FALSE, ...)
x |
An object of class |
which |
Which type of plot to produce. |
col.all |
A character vector of length one indicating which of |
arrange |
Logical indicating whether the arrange the plots side-by-side
via |
chull |
Logical indicating whether to plot the estimated convex hull or not. |
... |
additional arguments passed to |
Pieter C. Schoonees
Two-dimensional plot method for object of class 'T3Clusf' as output by T3Clusf.
## S3 method for class 'T3Clusf' plot(x, which = seq_len(nclust), arrange = FALSE, ...)## S3 method for class 'T3Clusf' plot(x, which = seq_len(nclust), arrange = FALSE, ...)
x |
An object of class |
which |
An integer vector indicating which item segments to plot. |
arrange |
Logical indicating whether to arrange the plots on a single page or not |
... |
Additional arguments to |
Print a 'lsbclust' object.
## S3 method for class 'lsbclust' print(x, ...)## S3 method for class 'lsbclust' print(x, ...)
x |
An object of class 'lsbclust' |
... |
Unimplemented. |
Simulate three-way arrays adhering to the LSBCLUST framework (see lsbclust).
rlsbclust(ndata = 50L, nobs, size, nclust, clustsize = NULL, delta = rep(1L, 4L), ndim = 2L, alpha = 0.5, fixed = c("none", "rows", "columns"), err_sd = 1, svmins = 1, svmax = 6)rlsbclust(ndata = 50L, nobs, size, nclust, clustsize = NULL, delta = rep(1L, 4L), ndim = 2L, alpha = 0.5, fixed = c("none", "rows", "columns"), err_sd = 1, svmins = 1, svmax = 6)
ndata |
Integer giving the number of data sets to generate with the same underlying parameters. |
nobs |
Integer giving the number of observations to sample. |
size |
Vector with two elements giving the number of rows and columns respectively of each simulated observation. |
nclust |
A vector of length four giving the number of clusters for the overall mean, the row margins, the column margins and the interactions (in that order) respectively. Alternatively, a vector of length one, in which case all components will have the same number of clusters. |
clustsize |
A list of length four, with each element containing a vector
of the same length as the corresponding entry in |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
ndim |
The required rank for the approximation of the interactions (a scalar). |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed
between rows and columns (passed to |
fixed |
One of |
err_sd |
The standard deviation of the error distribution, as passed to
|
svmins |
Vector of minimum values for the singular values
(as passed to |
svmax |
The maximum possible singular value (as passed to |
## Nothing fixed, balanced classes set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5)) cfsim(res, dat[[1]]) ## Rows fixed, balanced classes set.seed(2) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5), fixed = "rows") res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5), fixed = "rows") cfsim(res, dat[[1]]) ## Rows fixed, unbalanced classes set.seed(3) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5), fixed = "columns", clustsize = list(NULL, NULL, c(40, 25, 15, 10, 5, 5), c(40, 25, 15, 10, 10))) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5), fixed = "columns") cfsim(res, dat[[1]])## Nothing fixed, balanced classes set.seed(1) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5)) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5)) cfsim(res, dat[[1]]) ## Rows fixed, balanced classes set.seed(2) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5), fixed = "rows") res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5), fixed = "rows") cfsim(res, dat[[1]]) ## Rows fixed, unbalanced classes set.seed(3) dat <- rlsbclust(ndata = 1, nobs = 100, size = c(10, 8), nclust = c(5, 4, 6, 5), fixed = "columns", clustsize = list(NULL, NULL, c(40, 25, 15, 10, 5, 5), c(40, 25, 15, 10, 10))) res <- lsbclust(data = dat[[1]]$data, nclust = c(5, 4, 6, 5), fixed = "columns") cfsim(res, dat[[1]])
Uniformly sample an orthornormal matrix from the collection of all possible orthonormal matrices of a certain size. The QR decomposition is used on a matrix containing Gaussian random numbers. The QR decomposition might not be the most efficient algorithm under some circumstances.
rorth(nrow, ncol, sd = 1)rorth(nrow, ncol, sd = 1)
nrow |
Integer giving the number of rows required. |
ncol |
Integer giving the number of columns required. |
sd |
The standard deviation passed to |
Stewart, G. W. (1980). The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM Journal on Numerical Analysis, 17(3), 403-409.
set.seed(1) rorth(5, 2)set.seed(1) rorth(5, 2)
Perform a single simulation run for the LSBCLUST model. Multiple data sets are generated for a single set of underlying parameters,
sim_lsbclust(ndata, nobs, size, nclust, clustsize = NULL, delta = rep(1L, 4L), ndim = 2L, alpha = 0.5, fixed = c("none", "rows", "columns"), err_sd = 1, svmins = 0.5, svmax = 5, seed = NULL, parallel = FALSE, parallel_data = TRUE, verbose = 0, nstart_T3 = 20L, nstart_ak = 20L, mc.cores = detectCores() - 1, include_fits = FALSE, include_data = FALSE, nstart, nstart.kmeans)sim_lsbclust(ndata, nobs, size, nclust, clustsize = NULL, delta = rep(1L, 4L), ndim = 2L, alpha = 0.5, fixed = c("none", "rows", "columns"), err_sd = 1, svmins = 0.5, svmax = 5, seed = NULL, parallel = FALSE, parallel_data = TRUE, verbose = 0, nstart_T3 = 20L, nstart_ak = 20L, mc.cores = detectCores() - 1, include_fits = FALSE, include_data = FALSE, nstart, nstart.kmeans)
ndata |
Integer giving the number of data sets to generate with the same underlying parameters. |
nobs |
Integer giving the number of observations to sample. |
size |
Vector with two elements giving the number of rows and columns respectively of each simulated observation. |
nclust |
A vector of length four giving the number of clusters for the overall mean, the row margins, the column margins and the interactions (in that order) respectively. Alternatively, a vector of length one, in which case all components will have the same number of clusters. |
clustsize |
A list of length four, with each element containing a vector
of the same length as the corresponding entry in |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
ndim |
The required rank for the approximation of the interactions (a scalar). |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed
between rows and columns (passed to |
fixed |
One of |
err_sd |
The standard deviation of the error distribution, as passed to
|
svmins |
Vector of minimum values for the singular values
(as passed to |
svmax |
The maximum possible singular value (as passed to |
seed |
An optional seed to be set for the random number generator |
parallel |
Logical indicating whether to parallelize over random starts.
Note that |
parallel_data |
Logical indicating whether to parallelize over the data sets. If
|
verbose |
Integer giving the number of iterations after which the loss values is printed. |
nstart_T3 |
The number of random starts to use for |
nstart_ak |
The number of random starts to use for |
mc.cores |
The number of cores to use, passed to |
include_fits |
Logical indicating whether to include the model fits, or or only the fit statistics |
include_data |
Logical indicating whether to include the simulated data fitted on, or only the results |
nstart |
From |
nstart.kmeans |
From |
set.seed(1) res <- sim_lsbclust(ndata = 5, nobs = 100, size = c(10, 8), nclust = rep(5, 4), verbose = 0, nstart_T3 = 2, nstart_ak = 1, parallel_data = FALSE, nstart = 2, nstart.kmeans = 5 )set.seed(1) res <- sim_lsbclust(ndata = 5, nobs = 100, size = c(10, 8), nclust = rep(5, 4), verbose = 0, nstart_T3 = 2, nstart_ak = 1, parallel_data = FALSE, nstart = 2, nstart.kmeans = 5 )
Generate random singular values for a specified number of clusters for use in simulations. A mixture distribution is used with truncation to ensure that the singular values differ between clusters, are ordered, and are nonnegative.
simsv(nclust, ndim = 2, mins = 1, max = 5)simsv(nclust, ndim = 2, mins = 1, max = 5)
nclust |
Integer giving the number of clusters for which to sample singular values. |
ndim |
Integer; the number of singular values required. |
mins |
Numeric vector of length |
max |
Numeric value giving the maximum possible value for the mean of the cluster-
specific singular value distribution, relative to the |
Fit lsbclust models for different numbers of clusters and/or different values of
delta. The resulting output can be inspected through its plot method to facilitate
model selection. Each component of the model is fitted separately.
step.lsbclust(data, margin = 3L, delta = c(1, 1, 1, 1), nclust, ndim = 2, fixed = c("none", "rows", "columns"), nstart = 20, starts = NULL, nstart.kmeans = 500, alpha = 0.5, parallel = FALSE, maxit = 100, verbose = -1, type = NULL, ...)step.lsbclust(data, margin = 3L, delta = c(1, 1, 1, 1), nclust, ndim = 2, fixed = c("none", "rows", "columns"), nstart = 20, starts = NULL, nstart.kmeans = 500, alpha = 0.5, parallel = FALSE, maxit = 100, verbose = -1, type = NULL, ...)
data |
A three-way array representing the data. |
margin |
An integer giving the single subscript of |
delta |
A four-element binary vector (logical or numeric) indicating which sum-to-zero constraints must be enforced. |
nclust |
Either a vector giving the number of clusters which will be applied to each element
of the model, that is to (a subset of) the overall mean, row margins, column margins and
interactions. If it is a list, arguments are matched by the names |
ndim |
The required rank for the approximation of the interactions (a scalar). |
fixed |
One of |
nstart |
The number of random starts to use for the interaction clustering. |
starts |
A list containing starting configurations for the cluster membership vector. If not
supplied, random initializations will be generated (passed to |
nstart.kmeans |
The number of random starts to use in |
alpha |
Numeric value in [0, 1] which determines how the singular values are distributed
between rows and columns (passed to |
parallel |
Logical indicating whether to parallelize over different starts or not
(passed to |
maxit |
The maximum number of iterations allowed in the interaction clustering. |
verbose |
The number of iterations after which information on progress is provided
(passed to |
type |
One of |
... |
Additional arguments passed to |
m <- step.lsbclust(data = dcars, margin = 3, delta = c(1, 0, 1, 0), nclust = 4:5, ndim = 2, fixed = "columns", nstart = 1, nstart.kmeans = 100, parallel = FALSE) ## For a list of all deltas delta <- expand.grid(replicate(4, c(0,1), simplify = FALSE)) delta <- with(delta, delta[!(Var1 == 0 & Var3 == 1), ]) delta <- with(delta, delta[!(Var2 == 0 & Var4 == 1),]) delta <- delta[-4,] delta <- as.list(as.data.frame(t(delta))) m2 <- step.lsbclust(data = dcars, margin = 3, delta = delta, nclust = 4:5, ndim = 2, fixed = "columns", nstart = 1, nstart.kmeans = 100, parallel = FALSE)m <- step.lsbclust(data = dcars, margin = 3, delta = c(1, 0, 1, 0), nclust = 4:5, ndim = 2, fixed = "columns", nstart = 1, nstart.kmeans = 100, parallel = FALSE) ## For a list of all deltas delta <- expand.grid(replicate(4, c(0,1), simplify = FALSE)) delta <- with(delta, delta[!(Var1 == 0 & Var3 == 1), ]) delta <- with(delta, delta[!(Var2 == 0 & Var4 == 1),]) delta <- delta[-4,] delta <- as.list(as.data.frame(t(delta))) m2 <- step.lsbclust(data = dcars, margin = 3, delta = delta, nclust = 4:5, ndim = 2, fixed = "columns", nstart = 1, nstart.kmeans = 100, parallel = FALSE)
Some goodness-of-fit diagnostics are provided for all three margins.
## S3 method for class 'int.lsbclust' summary(object, digits = 3, ...)## S3 method for class 'int.lsbclust' summary(object, digits = 3, ...)
object |
An object of class 'int.lsbclust'. |
digits |
The number of digits in the printed output. |
... |
Unimplemented. |
Summarize a lsbclust object.
## S3 method for class 'lsbclust' summary(object, digits = 3, ...)## S3 method for class 'lsbclust' summary(object, digits = 3, ...)
object |
An object of class 'lsbclust'. |
digits |
The number of digits in the printed output. |
... |
Unimplemented. |
This data set relates to 220 consumers rating 10 Dutch supermarket chains according to 8 variables. A rating scale from 1 to 10 was used.
supermarketssupermarkets
A three-way array with supermarkets in the first dimension, variables in the second and consumers in the third dimension.
Michel van de Velden
data("supermarkets") fit <- lsbclust(data = supermarkets, nclust = 6, fixed = "rows", nstart = 2)data("supermarkets") fit <- lsbclust(data = supermarkets, nclust = 6, fixed = "rows", nstart = 2)
This is an implementation of the T3Clusf algorithm of Rocci & Vichi (2005).
T3Clusf(X, Q, R = Q, G = 2, margin = 3L, alpha = 1, eps = 1e-08, maxit = 100L, verbose = 1, nstart = 1L, parallel = TRUE, mc.cores = detectCores() - 1L, minsize = 3L)T3Clusf(X, Q, R = Q, G = 2, margin = 3L, alpha = 1, eps = 1e-08, maxit = 100L, verbose = 1, nstart = 1L, parallel = TRUE, mc.cores = detectCores() - 1L, minsize = 3L)
X |
Three-way data array, with no missing values. |
Q |
Integer giving the number of dimensions required for mode B (variables).
This is the first mode of the array, excluding the mode clustered over (see |
R |
Integer giving the number of dimensions required for mode C (occasions).
This is the second mode of the array, excluding the mode clustered over (see |
G |
Integer giving the number of clusters required. |
margin |
Integer giving the margin of the array to cluster over. The remaining two
modes, in the original order, corresponds to |
alpha |
Numeric value giving the fuzziness parameter. |
eps |
Small numeric value giving the empirical convergence threshold. |
maxit |
Integer giving the maximum number of iterations allowed. |
verbose |
Integer giving the number of iterations after which the loss values are printed. |
nstart |
Integer giving the number of random starts required. |
parallel |
Logical indicating whether to parallelize over random starts if
|
mc.cores |
Argument passed to |
minsize |
Integer giving the minimum size of cluster to uphold when reinitializing empty clusters. |
Rocci, R., & Vichi, M. (2005). Three-mode component analysis with crisp or fuzzy partition of units. Psychometrika, 70(4), 715-736.
data("dcars") set.seed(13) res <- T3Clusf(X = carray(dcars), Q = 3, R = 2, G = 3, alpha = 1)data("dcars") set.seed(13) res <- T3Clusf(X = carray(dcars), Q = 3, R = 2, G = 3, alpha = 1)