# Introduction

An R package implementing a Projection Pursuit algorithm based on finite Gaussian Mixtures Models for density estimation using Genetic Algorithms (PPGMMGA) to maximise an approximated 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.

library(ppgmmga)
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# Banknote data

library(mclust)
data("banknote")
X <- banknote[,-1]
Class <- banknote$Status table(Class) ## Class ## counterfeit genuine ## 100 100 Class_color <- ggthemes::tableau_color_pal("Classic 10")(2) clPairs(X, classification = Class, colors = Class_color) # 1-dimensional ppgmmga pp1D <- ppgmmga(data = X, d = 1, approx = "UT", seed = 1) pp1D ## Call: ## ppgmmga(data = X, d = 1, approx = "UT", seed = 1) ## ## 'ppgmmga' object containing: ## [1] "data" "d" "approx" "GMM" "GA" ## [6] "Negentropy" "basis" "Z" summary(pp1D) ## ── ppgmmga ───────────────────────────── ## ## Data dimensions = 200 x 6 ## Data transformation = center & scale ## Projection subspace dimension = 1 ## GMM density estimate = (VEE,4) ## Negentropy approximation = UT ## GA optimal negentropy = 0.6345935 ## GA encoded basis solution: ## x1 x2 x3 x4 x5 ## [1,] 3.268902 2.373044 1.051365 0.3131285 0.531718 ## ## Estimated projection basis: ## PP1 ## Length -0.01196531 ## Left -0.09347750 ## Right 0.16021052 ## Bottom 0.57406981 ## Top 0.34503463 ## Diagonal -0.71892026 plot(pp1D) plot(pp1D, class = Class) # 2-dimensional ppgmmga pp2D <- ppgmmga(data = X, d = 2, approx = "UT", seed = 1) summary(pp2D, check = TRUE) ## ── ppgmmga ───────────────────────────── ## ## Data dimensions = 200 x 6 ## Data transformation = center & scale ## Projection subspace dimension = 2 ## GMM density estimate = (VEE,4) ## Negentropy approximation = UT ## GA optimal negentropy = 1.13624 ## GA encoded basis solution: ## x1 x2 x3 x4 x5 x6 x7 ## [1,] 2.268667 2.929821 1.061407 1.084929 0.3044298 3.85462 0.9832903 ## x8 x9 x10 ## [1,] 1.11377 0.1671738 1.668403 ## ## Estimated projection basis: ## PP1 PP2 ## Length -0.03726866 -0.07183191 ## Left 0.03125553 -0.11981164 ## Right -0.15480788 0.06300918 ## Bottom -0.08569311 0.86390485 ## Top -0.10249897 0.46037272 ## Diagonal 0.97766012 0.13505761 ## ## Monte Carlo Negentropy approximation check: ## UT ## Approx Negentropy 1.136240194 ## MC Negentropy 1.137260367 ## MC se 0.003527379 ## Relative accuracy 0.999102956 summary(pp2D$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
##
## Clustering table:
##  1  2  3  4
## 16 99 47 38
plot(pp2D$GA) plot(pp2D) plot(pp2D, class = Class, drawAxis = FALSE) # 3-dimensional ppgmmga pp3D <- ppgmmga(data = X, d = 3, center = TRUE, scale = FALSE, gatype = "gaisl", options = ppgmmga.options(numIslands = 2), seed = 1) summary(pp3D, check = TRUE) ## ── ppgmmga ───────────────────────────── ## ## Data dimensions = 200 x 6 ## Data transformation = center ## Projection subspace dimension = 3 ## GMM density estimate = (VVE,3) ## Negentropy approximation = UT ## GA optimal negentropy = 1.16915 ## GA encoded basis solution: ## x1 x2 x3 x4 x5 x6 x7 ## [1,] 4.306147 2.435962 1.072888 1.02168 1.039589 4.934657 2.005115 ## x8 x9 x10 ... x14 x15 ## [1,] 2.047029 1.950543 2.200697 1.534584 2.504773 ## ## Estimated projection basis: ## PP1 PP2 PP3 ## Length -0.3849309 0.5240368 -0.5116536 ## Left -0.1655861 -0.1697583 -0.3109141 ## Right 0.2462001 0.5001222 -0.4154481 ## Bottom 0.2973840 0.3653894 0.3867856 ## Top 0.3097231 0.4873071 0.3130374 ## Diagonal -0.7612025 0.2747140 0.4704789 ## ## Monte Carlo Negentropy approximation check: ## UT ## Approx Negentropy 1.169149621 ## MC Negentropy 1.173876686 ## MC se 0.004294694 ## Relative accuracy 0.995973116 plot(pp3D$GA)

plot(pp3D)

plot(pp3D, class = Class)

plot(pp3D, dim = c(1,2))

plot(pp3D, dim = c(1,3), class = Class)

# A rotating 3D plot can be obtained using
if(!require("msir")) install.packages("msir")
msir::spinplot(pp3D\$Z, markby = Class,
pch.points = c(19,17),
col.points = Class_color)

# References

Scrucca L, Serafini A (2019). “Projection pursuit based on Gaussian mixtures and evolutionary algorithms.” Journal of Computational and Graphical Statistics. doi: 10.1080/10618600.2019.1598871 (URL: https://doi.org/10.1080/10618600.2019.1598871).

sessionInfo()
## R version 3.6.0 (2019-04-26)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Mojave 10.14.5
##
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
## [1] mclust_5.4.3 ppgmmga_1.2  knitr_1.23
##
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.1       GA_3.2           compiler_3.6.0   pillar_1.4.1
##  [5] iterators_1.0.10 tools_3.6.0      digest_0.6.19    evaluate_0.14
##  [9] tibble_2.1.3     gtable_0.3.0     pkgconfig_2.0.2  rlang_0.4.0
## [13] foreach_1.4.4    cli_1.1.0        yaml_2.2.0       xfun_0.8
## [17] stringr_1.4.0    dplyr_0.8.1      grid_3.6.0       tidyselect_0.2.5
## [21] glue_1.3.1       R6_2.4.0         rmarkdown_1.13   ggplot2_3.2.0
## [25] purrr_0.3.2      magrittr_1.5     scales_1.0.0     codetools_0.2-16
## [29] htmltools_0.3.6  ggthemes_4.2.0   assertthat_0.2.1 colorspace_1.4-1
## [33] labeling_0.3     stringi_1.4.3    lazyeval_0.2.2   munsell_0.5.0
## [37] crayon_1.3.4`