PrtDist: Calculation of the distances between units and centers
| PrtDist | R Documentation |
Calculation of the distances between units and centers
Description
Given a data set A, with a[i,k] be the measure of variable k on unit i, and a prototype set P, with p[j,k] be the measure of variable k on prototype j, the function calculate d[i,j,k], the i,j distance according variable k.
Usage
PrtDist(a,
p)
Arguments
a |
Matrix with n rows (units) and m columns (variables) |
p |
Matrix with g rows (prototypes) and m columns (variables) |
Details
d[i,j,k] is the squared distance: d[i,j,k] = (a[i,k] - p[j,k])^2
Value
d: The 3-dimensional matrix of i,j,k distances
Note
The function has been written to simplify the code examples. It has been written as a R script with minimal vectorization, therefore it is not computationally much efficient. Moreover d(i,j,k) is the square of differences and users may prefer to employ other dissimilarity measures. In that case, they should better write their own function.
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
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)
