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)
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:
To obtain more information, please read this paper.
You can install the development version of bigmds from GitHub with:
# install.packages("devtools")
devtools::install_github("pachoning/bigmds")
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