dispca {drclust}

Disjoint Principal Components Analysis

Description

Performs disjoint PCA, that is, a simplified version of PCA. Computes each one of the Q principal components from a different subset of the J variables (resulting thus, in a simplified, easier to interpret loading matrix A).

Usage

dispca(X, Q, Rndstart, verbose, maxiter, tol, prep, print, constr)

Arguments

X

Units x variables numeric data matrix.

Q

Number of factors.

Rndstart

Number of runs to be performed (Defaults is 20).

verbose

Outputs basic summary statistics for each run (1 = enabled; 0 = disabled, default option).

maxiter

Maximum number of iterations allowed (if convergence is not yet reached. Default is 100).

tol

Tolerance threshold (maximum difference between the values of the objective function of two consecutive iterations such that convergence is assumed). Default is 1e-6.

prep

Pre-processing of the data. 1 performs the z-score transform (default choice); 2 performs the min-max transform; 0 leaves the data un-pre-processed.

print

Prints summary statistics of the results (1 = enabled; 0 = disabled, default option).

constr

is a vector of length J = nr. of variables, pre-specifying to which cluster some of the variables must be assigned. Each component of the vector can assume integer values from 1 o Q (See example for more details), or 0 if no constraint on the variable is imposed (i.e., it will be assigned based on the plain algorithm).

Value

returns a list of estimates and some descriptive quantities of the final results.

V

Variables x factors membership matrix (binary and row-stochastic). Each row is a dummy variable indicating to which cluster it has been assigned.

A

Variables x components loading matrix.

betweenss

Amount of deviance captured by the model (scalar).

totss

total amount of deviance (scalar).

size

Number of variables assigned to each column-cluster (vector).

loop

The index of the (best) run from which the results have been chosen.

it

the number of iterations performed during the (best) run.

Author(s)

Ionel Prunila, Maurizio Vichi

References

Vichi M., Saporta G. (2009) "Clustering and disjoint principal component analysis" <doi:10.1016/j.csda.2008.05.028>

Examples

# Iris data 
# Loading the numeric variables of iris data
iris <- as.matrix(iris[,-5]) 

# No constraint on variables
out <- dispca(iris, Q = 2)

# Constraint: the first two variables must contribute to the same factor.
outc <- dispca(iris, Q = 2, constr = c(1,1,0,0))