# bigmds

MDS is a statistic tool for reduction of dimensionality, using as input a distance matrix of dimensions n × n. When n is large, classical algorithms suffer from computational problems and MDS configuration can not be obtained.

With this package, we address these problems by means of three algorithms:

• Divide-and-conquer MDS.
• Fast MDS.
• Interpolation MDS.

The main idea of these methods is based on partitioning the dataset into small pieces, where classical methods can work. Fast MDS was designed by Yang, T., J. Liu, L. McMillan, and W. Wang (2006), whereas divide-and-conquer MDS and interpolation MDS were designed by Delicado P. and C. Pachón-García (2021).

## Installation

You can install directly from CRAN with:

``# install.packages("bigmds")``

You can install the development version from GitHub with:

``````# install.packages("devtools")
devtools::install_github("pachoning/bigmds")``````

## Example

This is a basic example which shows you how to solve a common problem:

``````set.seed(42)
library(bigmds)
x <- matrix(data = rnorm(4*10000), nrow = 10000) %*% diag(c(9, 4, 1, 1))

divide_mds_conf <- divide_conquer_mds(x = x, l = 200, c_points = 2*2, r = 2, n_cores = 1, dist_fn = stats::dist)
#>             [,1]       [,2]
#> [1,] -12.0029447  4.5482795
#> [2,]   5.3135571 -0.6207096
#> [3,]  -3.0272576 -1.0857873
#> [4,]  -6.5402649 -1.9113426
#> [5,]  -3.3311073  2.8156667
#> [6,]   0.9705889 -6.5670390
divide_mds_conf\$eigen
#>  83.26941 16.27533
divide_mds_conf\$GOF
#>  0.9795777 0.9795777

fast_mds_conf <- fast_mds(x = x, l = 200, s_points = 2*2, r = 2, n_cores = 1, dist_fn = stats::dist)
#>           [,1]       [,2]
#> [1,] 13.439660  5.0882344
#> [2,] -5.180648 -0.6150152
#> [3,]  3.894922 -0.8759228
#> [4,]  5.248688 -1.6144764
#> [5,]  3.520470  3.1887151
#> [6,] -1.329876 -6.7787889
fast_mds_conf\$eigen
#>  81.72223 16.07915
fast_mds_conf\$GOF
#>  0.9796994 0.9796994

interpolation_mds_conf <- interpolation_mds(x = x, l = 200, r = 2, n_cores = 1, dist_fn = stats::dist)
#>             [,1]       [,2]
#> [1,] -12.3616929 -4.6878946
#> [2,]   4.9424093  0.7621167
#> [3,]  -3.3580614  1.1415676
#> [4,]  -5.7834592  1.5567990
#> [5,]  -3.6974408 -2.8075217
#> [6,]   0.8118489  6.4465272
interpolation_mds_conf\$eigen
#>  80.06032 16.53691
interpolation_mds_conf\$GOF
#>  0.9785652 0.9785652``````

With the implementation of classical MDS, it takes much more time to obtain a MDS configuration due to computational problems. Try it yourself!

``````x <- matrix(data = rnorm(4*10000, sd = 10), nrow = 10000)
dist_matrix <- stats::dist(x = x)
mds_result <- stats::cmdscale(d = dist_matrix, k = 2, eig = TRUE)``````