qVarSelH: Selection of Variables for Clustering or Data Dimension...

In qVarSel: Select Variables for Optimal Clustering

Selection of Variables for Clustering or Data Dimension Reduction

Description

The function implements the q-Vars heuristic described in the reference below. Given a 3-dimension matrix D, with d[i,j,k] being the distance between statistic unit i and prototype j measured through variable k, the function calculates the set of variables of cardinality q that mostly explains the prototypes.

Usage

qVarSelH(d,
         q,
         maxit = 100)

Arguments

d	A numeric 3-dimensional matrix where elements d(i,j,k) are the distances between observation i and cluster center/prototype j, that are measured through variable k.
q	A positive scalar, that is the number of variables to select
maxit	A positive scalar, that is the maximum number of iteration allowed

Details

The heuristic repeatedly selects a set of variables and then allocates units to prototypes, while a local optimum is reached. Random restart is used to continue the search until the maximum number of iteration is reached.

Value

obj	The value of the objective function
x	A 0-1 vector describing wheter variable k is selected: If x[k] = 1 then k is selected
ass	A vector of assignment of units to clusters: if ass[i] = j then unit i is assigned to the cluster represented by center/prototype j
bestit	The iteration in which the optimal solution is found

Note

The methodology is heuristic and some steps are random. It may be the case that different runs provide different solutions.

Author(s)

Stefano Benati

References

S. Benati, S. Garcia Quiles, J. Puerto "Mixed Integer Linear Programming and heuristic methods for feature selection in clustering", Journal of the Operational Research Society, 69:9, (2018), pp. 1379-1395

See Also

qVarSelLP

Examples

# Simulated data with 100 units, 10 true variables,
# 10 masking variables, 2 hidden clusters

n1 = 50
n2 = 50
n_true_var = 10
n_mask_var = 10
g1 = matrix(rnorm(n1*n_true_var, 0, 1), ncol = n_true_var)
g2 = matrix(rnorm(n2*n_true_var, 2, 1), ncol = n_true_var)
m1 = matrix(runif((n1 + n2)*n_mask_var, min = 0, max = 5), ncol = n_mask_var)
a = cbind(rbind(g1, g2), m1)

## calculate data prototypes using k-means

sl2 <- kmeans(a, 2, iter.max = 100, nstart = 2)
p = sl2$centers

## calculate distances between observations and prototypes
## Remark: d is a 3-dimensions matrix

d = PrtDist(a, p)

## Select 10 most representative variables, use heuristic

lsH <- qVarSelH(d, 10, maxit = 200)

qVarSel documentation built on June 8, 2025, 12:45 p.m.