Multidimensional Scaling for Big Data.

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 six algorithms, being two of them original proposals:

• Landmark MDS proposed by De Silva V. and JB. Tenenbaum (2004).
• Interpolation MDS proposed by Delicado P. and C. Pachón-García (2021) \<arXiv:2007.11919\> (original proposal).
• Reduced MDS proposel by Paradis E (2018).
• Pivot MDS prposed by Brandes U. and C. Pich (2007)
• Divide-and-conquer MDS proposed by Delicado P. and C. Pachón-García (2021) \<arXiv:2007.11919\> (original proposal).
• Fast MDS, proposed by Yang, T., J. Liu, L. McMillan and W. Wang (2006).

To obtain more information, please read this paper.

Installation

You can install the development version of bigmds 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:

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

landmark_mds_conf <- landmark_mds(x = x, num_landmarks = 200, r = 2)
head(landmark_mds_conf$points)
#>           [,1]       [,2]
#> [1,] -5.365249  0.7337736
#> [2,]  3.306016 -4.5927014
#> [3,] -7.294365  8.3014463
#> [4,] 15.699140  4.6770914
#> [5,] 14.089091  8.1901709
#> [6,]  9.108796  2.6281555
landmark_mds_conf$eigen
#> [1] 93.04856 16.24862

interpolation_mds_conf <- interpolation_mds(x = x, l = 200, r = 2, n_cores = 1)
head(interpolation_mds_conf$points)
#>            [,1]       [,2]
#> [1,]   5.318333  0.7392544
#> [2,]  -3.298290 -4.5693209
#> [3,]   7.265958  8.2536291
#> [4,] -15.606589  4.6378296
#> [5,] -14.014565  8.1367691
#> [6,]  -9.061479  2.6155918
interpolation_mds_conf$eigen
#> [1] 86.61081 16.94258

reduced_mds_conf <- reduced_mds(x = x, l = 200, r = 2, n_cores = 1)
head(reduced_mds_conf$points)
#>           [,1]       [,2]
#> [1,] -5.351389  0.7611677
#> [2,]  3.304342 -4.5616023
#> [3,] -7.302640  8.3011158
#> [4,] 15.673700  4.7006125
#> [5,] 14.069313  8.2312053
#> [6,]  9.110989  2.6164607
reduced_mds_conf$eigen
#> [1] 81.83749 17.31284

pivot_mds_conf <- pivot_mds(x = x, num_pivots = 200, r = 2)
head(pivot_mds_conf$points)
#>            [,1]      [,2]
#> [1,]   5.394381  0.653598
#> [2,]  -3.538906 -4.580966
#> [3,]   7.730890  8.216092
#> [4,] -15.382590  4.823825
#> [5,] -13.580535  8.303857
#> [6,]  -8.941668  2.738167
pivot_mds_conf$eigen
#> [1] 80.62164 16.28707

divide_mds_conf <- divide_conquer_mds(x = x, l = 200, c_points = 5 * 2, r = 2, n_cores = 1)
head(divide_mds_conf$points)
#>            [,1]      [,2]
#> [1,]   5.600940  1.016067
#> [2,]  -3.697173 -4.910147
#> [3,]   5.899926  8.319883
#> [4,] -15.286603  2.617717
#> [5,] -13.690950  8.371893
#> [6,]  -9.687884  2.328566
divide_mds_conf$eigen
#> [1] 84.41986 16.86691

fast_mds_conf <- fast_mds(x = x, l = 200, s_points = 2*2, r = 2, n_cores = 1)
head(fast_mds_conf$points)
#>            [,1]       [,2]
#> [1,]   4.802321  0.5703175
#> [2,]  -3.555341 -4.0507039
#> [3,]   6.766592  8.0851116
#> [4,] -16.051768  4.3472176
#> [5,] -14.437049  8.4028915
#> [6,]  -9.422427  2.4428193
fast_mds_conf$eigen
#> [1] 80.70308 16.11917