A quick tour of ppgmmga
Introduction
An R package implementing a Projection Pursuit algorithm based on finite Gaussian Mixtures Models for density estimation using Genetic Algorithms (PPGMMGA) to maximise a Negentropy index. The PPGMMGA algorithm provides a method to visualise high-dimensional data in a lower-dimensional space, with special reference to reveal clustering structures.
Banknote data
library(mclust)
data("banknote")
X <- banknote[,-1]
Class <- banknote$Status
table(Class)
## Class
## counterfeit genuine
## 100 100
clPairs(X, classification = Class,
symbols = ppgmmga.options("classPlotSymbols"),
colors = ppgmmga.options("classPlotColors"))
1-dimensional PPGMMGA
PP1D <- ppgmmga(data = X, d = 1, seed = 1)
PP1D
## Call:
## ppgmmga(data = X, d = 1, seed = 1)
##
## 'ppgmmga' object containing:
## [1] "data" "d" "approx" "GMM" "GA"
## [6] "Negentropy" "basis" "Z"
summary(PP1D)
## ── ppgmmga ─────────────────────────────
##
## Data dimensions = 200 x 6
## Data transformation = center & scale
## Projection subspace dimension = 1
## GMM density estimate = (VEE,4)
## Negentropy approximation = UT
## GA optimal negentropy = 0.6345935
## GA encoded basis solution:
## x1 x2 x3 x4 x5
## [1,] 3.268902 2.373044 1.051365 0.313128 0.531718
##
## Estimated projection basis:
## PP1
## Length -0.0119653
## Left -0.0934775
## Right 0.1602105
## Bottom 0.5740698
## Top 0.3450346
## Diagonal -0.7189203
##
## Monte Carlo Negentropy approximation check:
## UT
## Approx Negentropy 0.634593544
## MC Negentropy 0.633614256
## MC se 0.002249545
## Relative accuracy 1.001545559
2-dimensional PPGMMGA
PP2D <- ppgmmga(data = X, d = 2, seed = 1)
summary(PP2D)
## ── ppgmmga ─────────────────────────────
##
## Data dimensions = 200 x 6
## Data transformation = center & scale
## Projection subspace dimension = 2
## GMM density estimate = (VEE,4)
## Negentropy approximation = UT
## GA optimal negentropy = 1.13624
## GA encoded basis solution:
## x1 x2 x3 x4 x5 x6 x7 x8
## [1,] 2.268667 2.929821 1.061407 1.084929 0.30443 3.85462 0.98329 1.11377
## x9 x10
## [1,] 0.167174 1.668403
##
## Estimated projection basis:
## PP1 PP2
## Length -0.0372687 -0.0718319
## Left 0.0312555 -0.1198116
## Right -0.1548079 0.0630092
## Bottom -0.0856931 0.8639049
## Top -0.1024990 0.4603727
## Diagonal 0.9776601 0.1350576
##
## Monte Carlo Negentropy approximation check:
## UT
## Approx Negentropy 1.136240194
## MC Negentropy 1.137260367
## MC se 0.003527379
## Relative accuracy 0.999102956
summary(PP2D$GMM)
## -------------------------------------------------------
## Density estimation via Gaussian finite mixture modeling
## -------------------------------------------------------
##
## Mclust VEE (ellipsoidal, equal shape and orientation) model with 4 components:
##
## log-likelihood n df BIC ICL
## -1191.595 200 51 -2653.405 -2666.898
3-dimensional PPGMMGA
PP3D <- ppgmmga(data = X, d = 3,
center = TRUE, scale = FALSE,
gatype = "gaisl",
options = ppgmmga.options(numIslands = 2),
seed = 1)
summary(PP3D)
## ── ppgmmga ─────────────────────────────
##
## Data dimensions = 200 x 6
## Data transformation = center
## Projection subspace dimension = 3
## GMM density estimate = (VVE,3)
## Negentropy approximation = UT
## GA optimal negentropy = 1.16915
## GA encoded basis solution:
## x1 x2 x3 x4 x5 x6 x7 x8
## [1,] 4.338173 2.52915 1.092234 1.076827 0.831164 4.978505 2.007004 2.077824
## x9 x10 ... x14 x15
## [1,] 1.994252 2.210178 1.57216 2.527153
##
## Estimated projection basis:
## PP1 PP2 PP3
## Length -0.3089258 0.5132932 -0.5708323
## Left -0.1213218 -0.1762688 -0.3272492
## Right 0.3028257 0.4912820 -0.3875035
## Bottom 0.2419392 0.3734296 0.4166151
## Top 0.2647285 0.4937701 0.3427949
## Diagonal -0.8182461 0.2843287 0.3547153
##
## Monte Carlo Negentropy approximation check:
## UT
## Approx Negentropy 1.169149622
## MC Negentropy 1.174923148
## MC se 0.004308964
## Relative accuracy 0.995086040
# A rotating 3D plot can be obtained using
if(!require("msir")) install.packages("msir")
msir::spinplot(PP3D$Z, markby = Class,
pch.points = c(20,17),
col.points = ppgmmga.options("classPlotColors")[1:2])References
Scrucca L, Serafini A (2019). “Projection pursuit based on Gaussian mixtures and evolutionary algorithms.” Journal of Computational and Graphical Statistics, 28(4), 847–860. https://doi.org/10.1080/10618600.2019.1598871.
sessionInfo()
## R version 4.4.2 (2024-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: Etc/UTC
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] mclust_6.1.1 ppgmmga_1.3 knitr_1.49 rmarkdown_2.29
##
## loaded via a namespace (and not attached):
## [1] gtable_0.3.6 jsonlite_1.8.9 compiler_4.4.2 crayon_1.5.3
## [5] Rcpp_1.0.13-1 GA_3.2.4 jquerylib_0.1.4 scales_1.3.0
## [9] yaml_2.3.10 fastmap_1.2.0 ggplot2_3.5.1 R6_2.5.1
## [13] labeling_0.4.3 iterators_1.0.14 tibble_3.2.1 maketools_1.3.1
## [17] munsell_0.5.1 bslib_0.8.0 pillar_1.9.0 rlang_1.1.4
## [21] utf8_1.2.4 cachem_1.1.0 xfun_0.49 sass_0.4.9
## [25] sys_3.4.3 cli_3.6.3 withr_3.0.2 magrittr_2.0.3
## [29] digest_0.6.37 foreach_1.5.2 grid_4.4.2 lifecycle_1.0.4
## [33] vctrs_0.6.5 evaluate_1.0.1 glue_1.8.0 farver_2.1.2
## [37] codetools_0.2-20 buildtools_1.0.0 fansi_1.0.6 colorspace_2.1-1
## [41] pkgconfig_2.0.3 tools_4.4.2 htmltools_0.5.8.1