qVarSelLP: A Mixed Integer Linear Programming Formulation for the...

In qVarSel: Variables Selection for Clustering and Classification

Description

The function solve the mixed integer linear programming formulation of the variable selection problem.

Usage

qVarSelLP(d,
          q,
          binary = FALSE,
          write = FALSE)

Arguments

d	A 3-dimensional distance matrix, in which d[i,j,k] is the distance between unit i and prototype j, according to variable k.
q	The number of variables to selct.
binary	Set this value to TRUE if you wish to solve the problem with integer variables, or set it to FALSE if you just want to solve the continuous relaxation
write	Set this value to TRUE if you want that the optimization problem is exported in a file called qdistsel.lp

Details

The function solves the linear problem through the lpSolve solver available through the package lpSolveAPI. The linear programming formulation is the implementation of model F3 described in the paper below (without the median variables).

Value

status	The result of the optimization as output of the function solve() of library lpSolveAPI
obj	The value of the objective function
x	The value of the problem variables corresponding to the variable selection: x[j] = 1 means that variable j has been selected, 0 otherwise. If the continuous relaxation has been solved, the vector can contain fractional variables (most likely meaningless).

Note

The computational time to solve an integer programming problem can easily become exponential, therefore be carefull when set variable "binary" to TRUE, as you could wait days even to get the solution of a small scale problem. Even though the continuos version can contain fractional variables, comparing the objective functions of subroutines qVarSelH and qVarSelLP is a certificate of the solution quality.

Author(s)

Stefano Benati

References

S. Benati, S. Garcia Quiles, "A p-median model with distance selection", Working Paper, Universidad Carlos III de Madrid, 2012

See Also

lpSolveAPI

Examples

 ## Generate random cluster
  
  a <- rbind(cbind(rnorm(5, 0, 1), rnorm(5, 0, 3), rnorm(5, 0, 5)), 
            cbind(rnorm(5, 5, 1), rnorm(5, 5, 3), rnorm(5, 5, 5) ))
            
  ## 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 2 most representative variables, use heuristic  
  
  lsH <- qVarSelH(d, 2, maxit = 200)

  ## Select 2 variables, use linear relaxation
  
  require(lpSolveAPI)
  lsC <- qVarSelLP(d, 2)
  
  
  ## check optimality
  
  if (abs(lsH$obj - lsC$obj) < 0.001)
      message = "Heuristic Solution is Optimal"

Example output

Loading required package: lpSolveAPI

qVarSel documentation built on May 2, 2019, 9:28 a.m.