Package 'adproclus'

Constructor for a (low dimensional) ADPROCLUS solution object

Description

Yields an object of class adpc, which can be printed, plotted and summarized by the corresponding methods. Mandatory input are the membership matrix $A$ and the profile matrix $P$ (where the number of columns from $A$ corresponds to the number of rows in $P$), if the object is to represent a full dimensional ADPROCLUS model. For a low dimensional ADPROCLUS model, the matrices $C$ and $B$ have to be provided and $P$ can be inferred from those. All other inputs are optional but may be included so that the output from the summary(), print(), plot() is complete. For further details on the (low dimensional) ADPROCLUS model and what every element of the objects means see adproclus and adproclus_low_dim.

Usage

adpc(
  A,
  P,
  sse = NULL,
  totvar = NULL,
  explvar = NULL,
  iterations = NULL,
  timer = NULL,
  timer_one_run = NULL,
  initial_start = NULL,
  C = NULL,
  B = NULL,
  runs = NULL,
  parameters = NULL
)

Arguments

A	Membership matrix A.
P	Profile matrix P.
sse	Sum of Squared Error.
totvar	Total variance.
explvar	Explained variance.
iterations	Number of iterations.
timer	Time needed to run the complete algorithm.
timer_one_run	Time to complete this single algorithm start.
initial_start	List containing type of start and start_allocation matrix.
C	Low dimensional profiles matrix C.
B	Matrix of base vectors connecting low dimensional components with original variables B.
runs	List of suboptimal models.
parameters	List of algorithm parameters.

Value

Object of class adpc.

Examples

# Create the information needed for a minimal object of class adpc
x <- stackloss
result <- adproclus(x, 3)
A <- result$A
P <- result$P

# Use constructor to obtain object of class adpc
result_object <- adpc(A, P)

---

Additive profile clustering

Description

Perform additive profile clustering (ADPROCLUS) on object-by-variable data. Creates a model that assigns the objects to overlapping clusters which are characterized in terms of the variables by the so-called profiles.

Usage

adproclus(
  data,
  nclusters,
  start_allocation = NULL,
  nrandomstart = 3,
  nsemirandomstart = 3,
  algorithm = "ALS2",
  save_all_starts = FALSE,
  seed = NULL
)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
nclusters	Number of clusters to be used. Must be a positive integer.
start_allocation	Optional matrix of binary values as starting allocation for first run. Default is NULL.
nrandomstart	Number of random starts (see get_random). Can be zero. Increase for better results, though longer computation time. Some research finds 500 starts to be a useful reference.
nsemirandomstart	Number of semi-random starts (see get_semirandom)). Can be zero. Increase for better results, though longer computation time. Some research finds 500 starts to be a useful reference.
algorithm	Character string "ALS1" (default) or "ALS2", denoting the type of alternating least squares algorithm. Can be abbreviated with "1" or "2".
save_all_starts	Logical. If TRUE, the results of all algorithm starts are returned. By default, only the best solution is retained.
seed	Integer. Seed for the random number generator. Default: NULL, meaning no reproducibility.

Details

In this function, Mirkin's (1987, 1990) Additive Profile Clustering (ADPROCLUS) method is used to obtain an unrestricted overlapping clustering model of the object by variable data provided by data.

The ADPROCLUS model approximates an $I \times J$ object by variable data matrix $X$ by an $I \times J$ model matrix $M$ that can be decomposed into an $I \times K$ binary cluster membership matrix $A$ and a $K \times J$ real-valued cluster profile matrix $P$, with $K$ indicating the number of overlapping clusters. In particular, the aim of an ADPROCLUS analysis is therefore, given a number of clusters $K$, to estimate a model matrix $M = AP$ which reconstructs the data matrix $X$ as close as possible in a least squares sense (i.e. sum of squared residuals). For a detailed illustration of the ADPROCLUS model and associated loss function, see Wilderjans et al. (2011).

The alternating least squares algorithms ("ALS1" and "ALS2") that can be used for minimization of the loss function were proposed by Depril et al. (2008). In "ALS2", starting from an initial random or rational estimate of $A$ (see get_random and get_semirandom), $A$ and $P$ are alternately re-estimated conditionally upon each other until convergence. The "ALS1" algorithm differs from the previous one in that each row in $A$ is updated independently and that the conditionally optimal $P$ is recalculated after each row update, instead of the end of the matrix. For a discussion and comparison of the different algorithms, see Depril et al., 2008.

Warning: Computation time increases exponentially with increasing number of clusters, $K$. We recommend to determine the computation time of a single start for each specific dataset and $K$ before increasing the number of starts.

Value

adproclus() returns a list with the following components, which describe the best model (from the multiple starts):

model

matrix. The obtained overlapping clustering model M of the same size as data.

A

matrix. The membership matrix A of the clustering model. Clusters are sorted by size.

P

matrix. The profile matrix P of the clustering model.

sse

numeric. The residual sum of squares of the clustering model, which is minimized by the ALS algorithm.

totvar

numeric. The total sum of squares of data.

explvar

numeric. The proportion of variance in data that is accounted for by the clustering model.

iterations

numeric. The number of algorithm iterations until convergence of the relevant single start.

timer_one_run

numeric. The amount of time (in seconds) the relevant single start ran for.

initial_start

list. Containing the initial membership matrix, as well as the type of start that was used to obtain the clustering solution. (as returned by get_random or get_semirandom)

runs

list. Each element represents one model obtained from one of the multiple starts. Each element contains all of the above information for the respective start.

parameters

list. Contains the parameters used for the model.

timer

numeric. The amount of time (in seconds) the complete algorithm ran for.

References

Wilderjans, T. F., Ceulemans, E., Van Mechelen, I., & Depril, D. (2011S). ADPROCLUS: a graphical user interface for fitting additive profile clustering models to object by variable data matrices. Behavior Research Methods, 43(1), 56-65.

Depril, D., Van Mechelen, I., & Mirkin, B. (2008). Algorithms for additive clustering of rectangular data tables. Computational Statistics and Data Analysis, 52, 4923-4938.

Mirkin, B. G. (1987). The method of principal clusters. Automation and Remote Control, 10:131-143.

Mirkin, B. G. (1990). A sequential fitting procedure for linear data analysis models. Journal of Classification, 7(2):167-195.

See Also

adproclus_low_dim

for low dimensional ADPROCLUS

get_random

for generating random starts

get_semirandom

for generating semi-random starts

get_rational

for generating rational starts

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Quick clustering with K = 2 clusters
clust <- adproclus(data = x, nclusters = 2)

# Clustering with K = 3 clusters,
# using the ALS2 algorithm,
# with 2 random and 2 semi-random starts
clust <- adproclus(x, 3,
  nrandomstart = 2, nsemirandomstart = 2, algorithm = "ALS2"
)

# Saving the results of all starts
clust <- adproclus(x, 3,
  nrandomstart = 2, nsemirandomstart = 2, save_all_starts = TRUE
)

# Clustering using a user-defined rational start profile matrix
# (here the first 4 rows of the data)
start <- get_rational(x, x[1:4, ])$A
clust <- adproclus(x, 4, start_allocation = start)

---

Low dimensional ADPROCLUS

Description

Perform low dimensional additive profile clustering (ADPROCLUS) on object by variable data. Use case: data to cluster consists of a large set of variables, where it can be useful to interpret the cluster profiles in terms of a smaller set of components that represent the original variables well.

Usage

adproclus_low_dim(
  data,
  nclusters,
  ncomponents,
  start_allocation = NULL,
  nrandomstart = 3,
  nsemirandomstart = 3,
  save_all_starts = FALSE,
  seed = NULL
)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
nclusters	Number of clusters to be used. Must be a positive integer.
ncomponents	Number of components (dimensions) to which the profiles should be restricted. Must be a positive integer.
start_allocation	Optional matrix of binary values as starting allocation for first run. Default is NULL.
nrandomstart	Number of random starts (see get_random). Can be zero. Increase for better results, though longer computation time. Some research finds 500 starts to be a useful reference.
nsemirandomstart	Number of semi-random starts (see get_semirandom)). Can be zero. Increase for better results, though longer computation time. Some research finds 500 starts to be a useful reference.
save_all_starts	logical. If TRUE, the results of all algorithm starts are returned. By default, only the best solution is retained.
seed	Integer. Seed for the random number generator. Default: NULL, meaning no reproducibility

Details

In this function, an extension by Depril et al. (2012) of Mirkins (1987, 1990) additive profile clustering method is used to obtain a low dimensional overlapping clustering model of the object by variable data provided by data. More precisely, the low dimensional ADPROCLUS model approximates an $I \times J$ object by variable data matrix $X$ by an $I \times J$ model matrix $M$. For $K$ overlapping clusters, $M$ can be decomposed into an $I \times K$ binary cluster membership matrix $A$ and a $K \times J$ real-valued cluster profile matrix $P$ s.t. $M = AP.$ With the simultaneous dimension reduction, $P$ is restricted to be of reduced rank $S < min(K,J)$, such that it can be decomposed into $P = CB',$ with $C$ a $K \times S$ matrix and $B$ a $J \times S$ matrix. Now, a row in $C$ represents the profile values associated with the respective cluster in terms of the $S$ components, while the entries of $B$ can be used to interpret the components in terms of the complete set of variables. In particular, the aim of an ADPROCLUS analysis is therefore, given a number of clusters $K$ and a number of dimensions $S$, to estimate a model matrix $M$ that reconstructs data matrix $X$ as close as possible in a least squares sense and simultaneously reduce the dimensions of the data. For a detailed illustration of the low dimensional ADPROCLUS model and associated loss function, see Depril et al. (2012).

Warning: Computation time increases exponentially with increasing number of clusters, $K$. We recommend to determine the computation time of a single start for each specific dataset and $K$ before increasing the number of starts.

Value

adproclus_low_dim() returns a list with the following components, which describe the best model (from the multiple starts):

model

matrix. The obtained overlapping clustering model $M$ of the same size as data.

model_lowdim

matrix. The obtained low dimensional clustering model $AC$ of size $I \times S$

A

matrix. The membership matrix $A$ of the clustering model. Clusters are sorted by size.

P

matrix. The profile matrix $P$ of the clustering model.

c

matrix. The profile values in terms of the low dimensional components.

B

Variables-by-components matrix. Base vectors connecting low dimensional components with original variables. matrix. Warning: for computing $P$ use $B'$.

sse

numeric. The residual sum of squares of the clustering model, which is minimized by the ALS algorithm.

totvar

numeric. The total sum of squares of data.

explvar

numeric. The proportion of variance in data that is accounted for by the clustering model.

iterations

numeric. The number of algorithm iterations until convergence of the relevant single start.

timer_one_run

numeric. The amount of time (in seconds) the relevant single start ran for.

initial_start

list. A list containing the initial membership matrix, as well as the type of start that was used to obtain the clustering solution. (as returned by get_random or get_semirandom)

runs

list. Each element represents one model obtained from one of the multiple starts. Each element contains all of the above information.

parameters

list. Containing the parameters used for the model.

timer

numeric. The amount of time (in seconds) the complete algorithm ran for.

References

Depril, D., Van Mechelen, I., & Wilderjans, T. F. (2012). Lowdimensional additive overlapping clustering. Journal of classification, 29, 297-320.

See Also

adproclus

for full dimensional ADPROCLUS

get_random

for generating random starts

get_semirandom

for generating semi-random starts

get_rational

for generating rational starts

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Low dimensional clustering with K = 3 clusters
# where the resulting profiles can be characterized in S = 1 dimensions
clust <- adproclus_low_dim(x, 3, ncomponents = 1)

---

Randomly generated data with underlying overlapping clusters.

Description

A computer generated object-by-variable dataset with an underlying nonrestricted overlapping clustering structure. For illustrative purposes within the ADPROCLUS package only.

Usage

CGdata

Format

A data frame with 100 rows and 15 variables

---

Cluster Means based on Original Variables

Description

Obtain a cluster-by-variable dataframe where the values are the cluster means for the given variables. Takes as input a (low dimensional) ADPROCLUS model of class adpc and a dataset. This dataset must have the same number of rows as the cluster membership matrix $A$ of the model. The variables can be different from the ones the model was trained on. The function uses the cluster membership matrix of the model to computer per cluster the mean of the variables in the dataset. In the output matrix of cluster means, the last row Cl0 corresponds to the baseline cluster consisting of all the observations that were not assigned to a cluster, if this cluster is not empty. This function effectively computes column means of the dataset separately for each cluster.

Usage

cluster_means(data, model, digits = 3)

Arguments

data	Object-by-variable matrix. Can contain other variables than the ADPROCLUS model. IMPORTANT: The number of rows must be equal to the number of observations in the ADPROCLUS model.
model	ADPROCLUS solution (class: adpc). Low dimensional model possible.
digits	Integer. The number of decimal places that all decimal numbers will be rounded to.

Details

It is worth noting that the output of this function is different from the last output matrix in the summary() method applied to an ADPROCLUS model. The former computes the means over the original variable values while the latter computes them over the approximated model variable values.

Value

Cluster-by-variable dataframe where the values are the cluster means for the given variable.

Examples

# Obtain data, compute model, report cluster means
x <- CGdata
model <- adproclus(x, 3)
cluster_means(data = x, model = model)

---

Generate initial random start

Description

Generate an initial random start for the (low dimensional) Additive Profile Clustering algorithm (see adproclus and adproclus_low_dim).

Usage

get_random(data, nclusters, seed = NULL)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
nclusters	Number of clusters to be used. Must be a positive integer.
seed	Integer. Seed for the random number generator. Default: NULL

Details

get_random generates a random initial binary membership matrix A such that each entry is an independen draw from a Bernoulli Distribution with $\pi = 0.5$.

For generating an initial start from random draws from the data, see get_semirandom. For generating an initial start based on a specific set of initial cluster centers, see get_rational.

Warning: This function does not obtain an ADPRCOLUS model. To perform aditive profile clustering, see adproclus.

Value

get_random() returns a list with the following components:

type

A character string denoting the type of start ('Random Start')

A

A randomly generated initial Membership matrix

References

Wilderjans, T. F., Ceulemans, E., Van Mechelen, I., & Depril, D. (2010). ADPROCLUS: a graphical user interface for fitting additive profile clustering models to object by variable data matrices. Behavior Research Methods, 43(1), 56-65.

Depril, D., Van Mechelen, I., & Mirkin, B. (2008). Algorithms for additive clustering of rectangular data tables. Computational Statistics and Data Analysis, 52, 4923-4938.

Depril, D., Van Mechelen, I., & Wilderjans, T. F. (2012). Lowdimensional additive overlapping clustering. Journal of classification, 29, 297-320.

See Also

adproclus, adproclus_low_dim

for details about membership and profile matrices

get_semirandom

for generating semi-random starts

get_rational

for generating rational starts

Examples

# Obtain data from data set "Stackloss" and generate start allocation
start_allocation <- get_random(stackloss, 3)$A

---

Generate start allocation based on a priori profiles

Description

If cluster profiles are given a priori, this function can be used to compute the conditionally optimal cluster membership matrix A which can then be used as a rational starting allocation for the (low dimensional) ADPROCLUS procedure (see adproclus and adproclus_low_dim).

Usage

get_rational(data, starting_profiles)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
starting_profiles	A matrix where each row represents the profile values for a cluster. Needs to be of same dimensions as $P$.

Details

The function uses the same quadratic loss function and minimization method as the (low dimensional) ADPROCLUS procedure does to find the next conditionally optimal membership matrix A. (for details, see Depril et al., 2012). For the full dimensional ADPROCLUS it uses the algorithm ALS2 and not ALS1.

Warning: This function does not obtain an ADPRCOLUS model. To perform additive profile clustering, see adproclus.

Value

get_rational() returns a list with the following components:

type

A character string denoting the type of start ('Rational Start')

A

An initial Membership matrix

References

Depril, D., Van Mechelen, I., & Wilderjans, T. F. (2012). Lowdimensional additive overlapping clustering. Journal of classification, 29, 297-320.

See Also

adproclus, adproclus_low_dim

for details about membership and profile matrices

get_random

for generating random starts

get_semirandom

for generating semi-random starts

Examples

# Obtain data from standard data set "Stackloss"
x <- stackloss

# Obtaining a user-defined rational start profile matrix
# (here the first 4 rows of the data)
start_allocation <- get_rational(x, x[1:4, ])$A

---

Generate initial semi-random start

Description

Generate an initial semi-random start for the (low dimensional) Additive Profile Clustering algorithm (see adproclus and adproclus_low_dim).

Usage

get_semirandom(data, nclusters, seed = NULL)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
nclusters	Number of clusters to be used. Must be a positive integer.
seed	Integer. Seed for the random number generator. Default: NULL

Details

An initial cluster membership matrix $A$ is generated by finding the best $A$ conditional on an initial profile matrix $P$ generated by drawing k randomly chosen, distinct, rows from data (for details, see Depril et al., 2012).

Warning: This function does not obtain an ADPRCOLUS model. To perform aditive profile clustering, see adproclus.

Value

get_semirandom returns a list with the following components:

type

A character string denoting the type of start ('Semi-random Start')

A

An initial Membership matrix

References

Wilderjans, T. F., Ceulemans, E., Van Mechelen, I., & Depril, D. (2010). ADPROCLUS: a graphical user interface for fitting additive profile clustering models to object by variable data matrices. Behavior Research Methods, 43(1), 56-65.

Depril, D., Van Mechelen, I., & Mirkin, B. (2008). Algorithms for additive clustering of rectangular data tables. Computational Statistics and Data Analysis, 52, 4923-4938.

#' Depril, D., Van Mechelen, I., & Wilderjans, T. F. (2012). Lowdimensional additive overlapping clustering. Journal of classification, 29, 297-320.

See Also

adproclus, adproclus_low_dim

for details about membership and profile matrices

get_random

for generating random starts

get_rational

for generating rational starts

Examples

# Obtain data from data set "Stackloss" and generate start allocation
start_allocation <- get_semirandom(stackloss, 3)$A

---

Model selection helper for ADPROCLUS

Description

Performs ADPROCLUS for the number of clusters from min_nclusters to max_nclusters. This replaces the need to manually estimate multiple models to select the best number of clusters and returns the results in a format compatible with plot_scree_adpc to obtain a scree plot. Output is also compatible with select_by_CHull to automatically select a suitable number of clusters. The compatibility with both functions is only given if return_models = FALSE.

Usage

mselect_adproclus(
  data,
  min_nclusters,
  max_nclusters,
  return_models = FALSE,
  unexplvar = TRUE,
  start_allocation = NULL,
  nrandomstart = 1,
  nsemirandomstart = 1,
  algorithm = "ALS2",
  save_all_starts = FALSE,
  seed = NULL
)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
min_nclusters	Minimum number of clusters to estimate.
max_nclusters	Maximum number of clusters to estimate.
return_models	Boolean. If FALSE a vector of model fit scores is returned, which is compatible with the plot_scree_adpc function. If TRUE the list of actually estimated models is returned.
unexplvar	Boolean. If TRUE the model fit is specified in terms of unexplained variance. Otherwise it will be specified in terms of Sum of Squared Errors (SSE). This propagates through to the scree plots.
start_allocation	Optional starting cluster membership matrix to be passed to the ADPROCLUS procedure. See get_rational for more information.
nrandomstart	Number of random starts computed for each model.
nsemirandomstart	Number of semi-random starts computed for each model.
algorithm	Character string "ALS1" or "ALS2" (default), denoting the type of alternating least squares algorithm. Can be abbreviated with "1" or "2".
save_all_starts	Logical. If TRUE and return_models = TRUE, the results of all algorithm starts are returned. By default, only the best solution is retained.
seed	Integer. Seed for the random number generator. Default: NULL, meaning no reproducibility.

Value

Matrix with one column of SSE or unexplained variance scores for all estimated models. Row names are the value of the cluster parameter for the relevant model. Depends on the choice of return_models. If TRUE a list of estimated models is returned.

See Also

adproclus

for the actual ADPROCLUS procedure

plot_scree_adpc

for plotting the model fits

select_by_CHull

for automatic model selection via CHull method

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Estimating models with cluster parameter values ranging from 1 to 4
model_fits <- mselect_adproclus(data = x, min_nclusters = 1, max_nclusters = 4, seed = 10)

# Plot the results as a scree plot to select the appropriate number of clusters
plot_scree_adpc(model_fits)

---

Model selection helper for low dimensional ADPROCLUS

Description

Performs low dimensional ADPROCLUS for the number of clusters from min_nclusters to max_nclusters and the number of components from min_ncomponents to max_ncomponents. This replaces the need to manually estimate multiple models to select the best number of clusters and components and returns the results in a format compatible with plot_scree_adpc to obtain a scree plot / multiple scree plots. Output is also compatible with select_by_CHull to automatically select a suitable number of components for each number of clusters. The compatibility with both functions is only given if return_models = FALSE.

Usage

mselect_adproclus_low_dim(
  data,
  min_nclusters,
  max_nclusters,
  min_ncomponents,
  max_ncomponents,
  return_models = FALSE,
  unexplvar = TRUE,
  start_allocation = NULL,
  nrandomstart = 1,
  nsemirandomstart = 1,
  save_all_starts = FALSE,
  seed = NULL
)

Arguments

data	Object-by-variable data matrix of class matrix or data.frame.
min_nclusters	Minimum number of clusters to estimate.
max_nclusters	Maximum number of clusters to estimate.
min_ncomponents	Minimum number of components to estimate. Must be smaller or equal than min_nclusters.
max_ncomponents	Maximum number of components to estimate. Must be smaller or equal than max_nclusters.
return_models	Boolean. If FALSE a matrix of model fit scores is returned, which is compatible with the plot_scree_adpc function. If TRUE the list of actually estimated models is returned.
unexplvar	Boolean. If TRUE the model fit is specified in terms of unexplained variance. Otherwise it will be specified in terms of Sum of Squared Errors (SSE). This propagates through to the scree plots.
start_allocation	Optional starting cluster membership matrix to be passed to the low dimensional ADPROCLUS procedure. See get_rational for more information.
nrandomstart	Number of random starts computed for each model.
nsemirandomstart	Number of semi-random starts computed for each model.
save_all_starts	Logical. If TRUE and return_models = TRUE, the results of all algorithm starts are returned. By default, only the best solution is retained.
seed	Integer. Seed for the random number generator. Default: NULL, meaning no reproducibility.

Value

Number of clusters by number of components matrix where the values are SSE or unexplained variance scores for all estimated models. Row names are the value of the cluster parameter for the relevant model. Column names contain the value of the components parameter. Depends on the choice of return_models. If TRUE a list of estimated models is returned.

See Also

adproclus_low_dim

for the actual low dimensional ADPROCLUS procedure

plot_scree_adpc

for plotting the model fits

select_by_CHull

for automatic model selection via CHull method

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Estimating models with cluster parameter values ranging from 1 to 4
# and component parameter values also ranging from 1 to 4
model_fits <- mselect_adproclus_low_dim(data = x, 1, 4, 1, 4, seed = 1)

# Plot the results as a scree plot to select the appropriate number of clusters
plot_scree_adpc(model_fits)

---

Network plot of a (low dimensional) ADPROCLUS solution

Description

Produce a representation of a (low dimensional) ADPROCLUS solution, where each cluster is a vertex and the edge between two vertices represents the overlap between the corresponding clusters. The size of a vertex corresponds to the cluster size. The overlap is represented through color, width and numerical label of the edge. The numerical edge labels can be relative (number of overlap observations / total observations) or absolute (number of observations in both clusters). NOTE: This function can be called through the plot(model, type = "network") function with model an object of class adpc.

Usage

plot_cluster_network(
  model,
  title = NULL,
  relative_overlap = TRUE,
  filetype = NULL,
  filename = "network_plot",
  ...
)

Arguments

model	ADPROCLUS solution (class: adpc). Low dimensional model possible.
title	String. Optional title.
relative_overlap	Logical. If TRUE (default), the number of observations belonging to two clusters is divided by the total number of observations. If FALSE the number of observations in a cluster overlap will be displayed on the edges.
filetype	Optional. Choose type of file to save the plot. Possible choices: "R", "pdf", "svg", "tex", "jpg", "tiff", "png", "" Default: NULL does not create a file.
filename	Optional. Name of the file without extension. Default: "network_plot"
...	Additional arguments passing to the qgraph::qgraph() function, to customize the graph visualization.

Value

Invisibly returns the input model.

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Quick low dimensional clustering with K = 3 clusters and S = 1 dimensions
clust <- adproclus_low_dim(x, 3, 1)

# Plot the overlapping the clusters
plot_cluster_network(clust)

---

Plot profile matrix of ADPROCLUS solution

Description

Produce a representation of profile matrix $P$ (or $C$ for low dimensional solution) of an ADPROCLUS solution of class adpc. The plot displays the profiles in the style of a correlation plot. NOTE: This function can also be called through the plot(model, type = "profiles") function with model an object of class adpc.

Usage

plot_profiles(model, title = NULL, label_color = "black", ...)

Arguments

model	Object of class adpc. (Low dimensional) ADPROCLUS solution
title	String. Optional title.
label_color	String. The color of the text labels. Default: "black"
...	Additional arguments passing to the corrplot::corrplot() function, to customize the plot.

Value

Invisibly returns the input model.

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Quick clustering with K = 3 clusters
clust <- adproclus(x, 3)

# Plot the profile scores of each cluster
plot_profiles(clust)

---

Scree plot of (low dimensional) ADPROCLUS models

Description

Used for scree-plot based model selection. Visualizes a set of ADPROClUS models in terms of their number of clusters and model fit (SSE or unexplained variance). For low dimensional ADPROCLUS models plots are made with the number of components on the x-axis for each given number of clusters. One can then choose to have them displayed all in one plot (grid = FALSE) or next to each other in separate plots (grid = TRUE).

Usage

plot_scree_adpc(model_fit, title = NULL, grid = FALSE, digits = 3)

Arguments

model_fit	Matrix of SSE or unexplained variance scores as given by the output of mselect_adproclus or mselect_adproclus_low_dim.
title	String. Optional title.
grid	Boolean. FALSE means for low dimensional ADPROCLUS all lines will be in one plot. TRUE means separate plots.
digits	Integer. The number of decimal places to display.

Value

Invisibly returns the ggplot2 object.

See Also

mselect_adproclus

to obtain the model_fit input from the possible ADPROCLUS models

mselect_adproclus_low_dim

to obtain the model_fit input from the possible low dimensional ADPROCLUS models

select_by_CHull

for automatic model selection via CHull method

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Estimating models with cluster parameter values ranging from 1 to 4
model_fits <- mselect_adproclus(data = x, min_nclusters = 1, max_nclusters = 4, seed = 1)

# Plot the results as a scree plot to select the appropriate number of clusters
plot_scree_adpc(model_fits)

# Estimating models with cluster parameter values ranging from 1 to 4
# and component parameter values also ranging from 1 to 4
model_fits <- mselect_adproclus_low_dim(data = x, 1, 4, 1, 4, seed = 1)

# Plot the results as a scree plot to select the appropriate number of clusters
plot_scree_adpc(model_fits)

---

Scree plot of a pre-selection of low dimensional ADPROCLUS models

Description

To be used when one has selected a number of components for each number of clusters. Plots the remaining sets of models to compare SSE or unexplained variances. The input model_fit is supposed to be the output from the select_by_CHull function applied to the output from the mselect_adproclus_low_dim function.

Usage

plot_scree_adpc_preselected(model_fit, title = NULL, digits = 3)

Arguments

model_fit	Matrix with SSE or unexplained variance values. Can be obtained from select_by_CHull.
title	String. Optional title.
digits	Integer. The number of decimal places to display.

Value

Returns the ggplot2 object.

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Estimating models with cluster parameter values ranging from 1 to 4
# and component parameter values also ranging from 1 to 4
model_fits <- mselect_adproclus_low_dim(data = x, 1, 4, 1, 4, seed = 1)

# Choosing for each number of cluster the best number of components
model_fits_preselected <- select_by_CHull(model_fits)

# Plot the results as a scree plot to select the appropriate number of clusters
plot_scree_adpc_preselected(model_fits_preselected)

---

Plot variable to component matrix of ADPROCLUS solution

Description

Produce a representation of variable to component matrix $B'$ of a low dimensional ADPROCLUS solution of class adpc. The plot displays the scores in the style of a correlation plot. NOTE: This function can be called through the plot(model, type = "vars_by_comp") function with model an object of class adpc.

Usage

plot_vars_by_comp(model, title = NULL, label_color = "black", ...)

Arguments

model	Object of class adpc. Must be Low dimensional ADPROCLUS solution
title	String. Optional title.
label_color	String. The color of the text labels. Default: "black"
...	Additional arguments passing to the corrplot::corrplot() function, to customize the plot

Value

Invisibly returns the input model.

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Quick low dimensional clustering with K = 3 clusters and S = 1 dimensions
clust <- adproclus_low_dim(x, 3, 1)

# Plot the matrix B', connecting components with variables
plot_vars_by_comp(clust)

---

Plotting a (low dimensional) ADPROCLUS solution

Description

When passing a (low dimensional) ADPROCLUS solution of class adpc to the generic plot(), this method plots the solution in one of the following three ways:

Network

Each cluster is a vertex and the edge between two vertices represents the overlap between the corresponding clusters. The size of a vertex corresponds to the cluster size. The overlap is represented through color, width and numerical label of the edge. The numerical edge-labels can be relative (number of overlap observations / total observations) or absolute (number of observations in both clusters).

Profiles

Plot the profile matrix ($P$ for full dimensional model, $C$ for low dimensional model) in the style of a correlation plot to visualize the relation of each cluster with each variable.

Variables by components

Plot the low dimensional component-by-variable matrix $B'$ in the style of a correlation plot to visualize the relation of each component with each original variable. NOTE: Only works for low dimensional ADPROCLUS.

Usage

## S3 method for class 'adpc'
plot(x, type = "network", ...)

Arguments

x	Object of class adpc. (Low dimensional) ADPROCLUS solution
type	Choice for type of plot: one of "network", "profiles", "vars_by_comp". Default: "network". Partial matching allowed.
...	additional arguments will be passed on to the functions plot_cluster_network(), plot_profiles(), plot_vars_by_comp()

Value

Invisibly returns the input model.

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Quick low dimensional clustering with K = 3 clusters and S = 1 dimensions
clust <- adproclus_low_dim(x, 3, 1)

# Produce three plots of the model
plot(clust, type = "network")
plot(clust, type = "profiles")
plot(clust, type = "vars_by_comp")

---

Print basic information on ADPROCLUS solution

Description

For an object of class adpc as input, this method prints basic information about the ADPROCLUS solution represented by the object. Works for both full and low dimensional solutions. Adjust the parameters digits, matrix_rows, matrix_cols to change the level of detail printed.

Usage

## S3 method for class 'adpc'
print(
  x,
  title = "ADPROCLUS solution",
  digits = 3,
  matrix_rows = 10,
  matrix_cols = 15,
  ...
)

Arguments

x	ADPROCLUS solution (class: adpc)
title	String. Default: "ADPROCLUS solution"
digits	Integer. The number of decimal places that all decimal numbers will be rounded to.
matrix_rows	Integer. The number of matrix rows to display. OPTIONAL
matrix_cols	Integer. The number of matrix columns to display. OPTIONAL
...	ignored

Value

No return value, called for side effects.

Examples

# Obtain data, compute model, print model
x <- stackloss
model <- adproclus(x, 3)
print(model)

---

Print (low dimensional) ADPROCLUS summary

Description

Prints an object of class summary.adpc to represent and summarize a (low dimensional) ADPROCLUS solution. A number of parameters for how the results should be printed can be passed as an argument to summary.adpc() which then passes it on to this method. This method does not take a model of class adpc directly as input.

Usage

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

Arguments

x	Object of class summary.adpc
...	ignored

Value

Invisibly returns object of class summary.adpc.

Examples

# Obtain data, compute model, print summary of model
x <- stackloss
model <- adproclus(x, 3)
print(summary(model))

---

Automatic Model Selection for ADPROCLUS with CHull Method

Description

For a set of full dimensional ADPROCLUS models (each with different number of clusters), this function finds the "elbow" in the scree plot by using the CHull procedure (Wilderjans, Ceuleman & Meers, 2013) implemented in the multichull package. For a matrix of low dimensional ADPROCLUS models (each with different number of cluster and components), this function finds the "elbow" in the scree plot for each number of clusters with the CHull methods. That is, it reduces the number of model to choose from to the number of different cluster parameter values by choosing the "elbow" number of components for a given number of clusters. The resulting list can in turn be visualized with plot_scree_adpc_preselected. For this procedure to work, the SSE or unexplained variance values must be decreasing in the number of clusters (components). If that is not the case increasing the number of (semi-) random starts can help.

Usage

select_by_CHull(model_fit, percentage_fit = 1e-04, ...)

Arguments

model_fit	Matrix containing SSEs or unexplained variance of all models as in the output of mselect_adproclus or mselect_adproclus_low_dim.
percentage_fit	Required proportion of increase in fit of a more complex model.
...	Additional parameters to be passed on to multichull::CHull() function.

Details

This procedure cannot choose the model with the largest or smallest number of clusters (components), i.e. for a set of three models it will always choose the middle one. If for a given number of clusters exactly two models were estimated, this function chooses the model with the lower SSE/unexplained variance.

The name of the model fit criterion is propagated from the input matrix based on the first column name. It is either "SSE" or "Unexplained_Variance".

Value

For full dimensional ADPROCLUS a CHull object describing the chosen model. For low dimensional ADPROCLUS a matrix containing the list of chosen models and the relevant model parameter, compatible with plot_scree_adpc_preselected.

References

Wilderjans, T. F., Ceulemans, E., & Meers, K. (2012). CHull: A generic convex hull based model selection method. Behavior Research Methods, 45, 1-15

See Also

mselect_adproclus

to obtain the model_fit input from the possible ADPROCLUS models

mselect_adproclus_low_dim

to obtain the model_fit input from the possible low dimensional ADPROCLUS models

plot_scree_adpc

for plotting the model fits

Examples

# Loading a test dataset into the global environment
x <- stackloss

# Estimating models with cluster parameter values ranging from 1 to 4
model_fits <- mselect_adproclus(data = x, min_nclusters = 1, max_nclusters = 4)

# Use and visualize CHull method
selected_model <- select_by_CHull(model_fits)
selected_model
plot(selected_model)

# Estimating low dimensional models with cluster parameter values
# ranging from 1 to 4 and component parameter values also ranging from 1 to 4
model_fits <- mselect_adproclus_low_dim(data = x, 1, 4, 1, 4, nsemirandomstart = 10, seed = 1)

# Using the CHull method
pre_selection <- select_by_CHull(model_fits)

# Visualize pre-selected models
plot_scree_adpc_preselected(pre_selection)

---

Summary of ADPROCLUS solution

Description

For an object of class adpc as input, this method yields a summary object of class summary.adpc including group characteristics of the clusters in the solution in terms of the model variables. Works for both full and low dimensional solutions. Adjust the parameters digits, matrix_rows, matrix_cols to change the level of detail for the printing of the summary.

Usage

## S3 method for class 'adpc'
summary(
  object,
  title = "ADPROCLUS solution",
  digits = 3,
  matrix_rows = 10,
  matrix_cols = 5,
  ...
)

Arguments

object	ADPROCLUS solution (class: adpc). Low dimensional model possible.
title	String. Default: "ADPROCLUS solution"
digits	Integer. The number of decimal places that all decimal numbers will be rounded to.
matrix_rows	Integer. The number of matrix rows to display. OPTIONAL
matrix_cols	Integer. The number of matrix columns to display. OPTIONAL
...	ignored

Value

Invisibly returns object of class summary.adpc.

Examples

# Obtain data, compute model, summarize model
x <- stackloss
model <- adproclus(x, 3)
model_summary <- summary(model)

---