Deriving the MST criteria

Description

Compute both the mean and the standard deviation of the Minimal Spanning Tree (MST)

Usage

mstCriteria(design,plot2d="FALSE")

Arguments

Details

In our context, a MST is a tree whose the sum of the lengthes of the edges is minimal. Even if unicity does not hold, the overall length is stable. The mean and the standard deviation of the lengthes of the edges are usually derived to analyze the geometric profile of the design. A large mean and a small standard deviation characterize a so-called quasi-periodic design.

Value

A list containing two components:

Author(s)

G.Damblin & B.Iooss

References

Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of space filling designs: optimization of Latin hypercube samples and subprojection properties, Journal of Simulation, 7:276-289, 2013. http://www.gdr-mascotnum.fr/doku.php?id=iooss1

Dussert, C., Rasigni, G., Rasigni, M., and Palmari, J. (1986). Minimal spanning tree: A new approach for studying order and disorder. Physical Review B, 34(5):3528-3531.

Franco J. (2008). Planification d'experiences numerique en phase exploratoire pour la simulation des phenomenes complexes, PhD thesis, Ecole Nationale Superieure des Mines de Saint Etienne.

Franco, J., Vasseur, O., Corre, B., and Sergent, M. (2009). Minimum spanning tree: A new approach to assess the quality of the design of computer experiments. Chemometrics and Intelligent Laboratory Systems, 97:164-169.

Prim, R.C. (1957). Shortest connection networks and some generalizations, in Bell System Technical Journal 36:1389-1401.

Examples

dimension <- 2
n <- 40
X <- matrix(runif(n*dimension),n,dimension)
mstCriteria(X,plot2d=TRUE)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(DiceDesign)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DiceDesign/mstCriteria.Rd_%03d_medium.png", width=480, height=480)
> ### Name: mstCriteria
> ### Title: Deriving the MST criteria
> ### Aliases: mstCriteria
> ### Keywords: design
> 
> ### ** Examples
> 
> dimension <- 2
> n <- 40
> X <- matrix(runif(n*dimension),n,dimension)
> mstCriteria(X,plot2d=TRUE)
$tree
$tree[[1]]
[1] 25  3

$tree[[2]]
[1] 31

$tree[[3]]
[1]  1 24

$tree[[4]]
[1] 36

$tree[[5]]
[1] 13 37

$tree[[6]]
[1] 40

$tree[[7]]
[1] 33 11

$tree[[8]]
[1] 14

$tree[[9]]
[1] 29 34

$tree[[10]]
[1] 35 13

$tree[[11]]
[1]  7 19

$tree[[12]]
[1] 39 23

$tree[[13]]
[1] 10 26  5

$tree[[14]]
[1] 30  8

$tree[[15]]
[1] 34 38 40

$tree[[16]]
[1] 27

$tree[[17]]
[1] 25 32

$tree[[18]]
[1] 30

$tree[[19]]
[1] 11

$tree[[20]]
[1] 28

$tree[[21]]
[1] 37

$tree[[22]]
[1] 23

$tree[[23]]
[1] 12 22 28

$tree[[24]]
[1] 3

$tree[[25]]
[1]  1 17 39

$tree[[26]]
[1] 13 30

$tree[[27]]
[1] 34 16 31

$tree[[28]]
[1] 23 35 20

$tree[[29]]
[1] 37  9 36

$tree[[30]]
[1] 26 14 18

$tree[[31]]
[1] 27  2

$tree[[32]]
[1] 17 33

$tree[[33]]
[1] 32  7

$tree[[34]]
[1]  9 15 27

$tree[[35]]
[1] 28 10

$tree[[36]]
[1] 29  4

$tree[[37]]
[1]  5 29 21

$tree[[38]]
[1] 15

$tree[[39]]
[1] 25 12

$tree[[40]]
[1] 15  6


$stats
[1] 0.10776380 0.05868935

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>