adproclus {adproclus}

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 = "ALS1",
  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 iterations of the algorithm.

timer

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

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.

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)