sigfur: SIgFUR

Description

SIgFUR applies Seed-Based Iteration, Greedy Algorithm, and FUR in sequence for each element of subit_len_list_sbi. The mean seed ranking is used as the input to Seed-Based Iteration. The best of all output rankings from FUR is considered as the consensus ranking.

Usage

sigfur(
  input_rkgs,
  subit_len_list_sbi,
  omega_sbi,
  subit_len_list_fur,
  search_radius,
  objNames = c(),
  wt = c()
)

Value

A list containing the consensus ranking (expressed as ordering), total Kemeny distance, and average tau correlation coefficient corresponding to the consensus ranking.

Arguments

input_rkgs: a n by k matrix of k rankings of n objects, where each column is a complete ranking.
subit_len_list_sbi: a vector containing positive integer(s) for the subiteration lengths to Seed-Based Iteration. Recommended values are between 2 and 8. Smaller subiteration lengths result in shorter run-time.
omega_sbi: a positive integer for the number of repetitions of perturbing the seed ranking in Seed-Based Iteration. An omega_sbi value of 1 corresponds to a single application of Subiterative Convergence.
subit_len_list_fur: a vector containing positive integer(s) for the subiteration lengths to FUR.
search_radius: a positive integer for the maximum change in the rank of each object in the Greedy Algorithm and FUR. The default value of 0 considers all possible rank changes for each object. It is recommended to use a search radius of less than or equal to \(\min(30, \lfloor \mbox{n}/2 \rfloor)\).
objNames: a n-length vector containing object names. An optional parameter.
wt: a k-length vector containing weights for each judge or attribute. An optional parameter.

References

Badal, P. S., & Das, A. (2018). Efficient algorithms using subiterative convergence for Kemeny ranking problem. Computers & Operations Research, 98, 198-210. tools:::Rd_expr_doi("10.1016/j.cor.2018.06.007")

Examples

Run this code

## Four input rankings of five objects
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 2, 4, 5, 3),
    byrow = FALSE, ncol = 4)
subit_len_list_sbi <- c(2:3)
omega_sbi <- 10
subit_len_list_fur <- c(2:3)
search_radius <- 1
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius)
# Determined the consensus ranking, total Kemeny distance, and average tau correlation coefficient

## Five input rankings with five objects
## 2nd ranking == 3rd ranking, so if a third object is weighted as zero,
## we should get the same answer as the first examples
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 
                       2, 4, 5, 3),byrow = FALSE, ncol = 5)
subit_len_list_sbi <- c(2:3)
omega_sbi <- 10
subit_len_list_fur <- c(2:3)
search_radius <- 1
wt = c(1,1,0,1,1)
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius, wt=wt)
# Determined the consensus ranking, total Kemeny distance, and average tau correlation coefficient

## Using five input rankings with five objects with prepare_data to 
## automatically prepare the weight vector
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 
                       2, 4, 5, 3),byrow = FALSE, ncol = 5)
out = prepare_data(input_rkgs) 
input_rkgs = out$input_rkgs
wt = out$wt
subit_len_list_sbi <- c(2:3)
omega_sbi <- 10
subit_len_list_fur <- c(2:3)
search_radius <- 1
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius, wt=wt)
# Determined the consensus ranking, total Kemeny distance, and average tau correlation coefficient

## Included dataset of 15 input rankings of 50 objects
data(data50x15)
input_rkgs <- as.matrix(data50x15[, -1])
subit_len_list_sbi <- c(3)
omega_sbi <- 5
subit_len_list_fur <- c(2:3)
search_radius <- 1
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius)