An R package implementing a Projection Pursuit algorithm based on finite Gaussian mixtures models for density estimation using Genetic Algorithms to maximise an approximated Negentropy index. The ppgmmga algorithm provides a method to visualise high-dimensional data in a lower-dimensional space.
library(ppgmmga)
## ___ ___ ___ ___ _ __ _ ___ ____ _
## / _ \/ _ \/ _ `/ ' \/ ' \/ _ `/ _ `/
## / .__/ .__/\_, /_/_/_/_/_/_/\_, /\_,_/
## /_/ /_/ /___/ /___/ version 1.0
library(mclust)
## Package 'mclust' version 5.4.1
## Type 'citation("mclust")' for citing this R package in publications.
data("banknote")
X <- banknote[,-1]
Class <- banknote$Status
table(Class)
## Class
## counterfeit genuine
## 100 100
clPairs(X, classification = Class)
pp1D <- ppgmmga(data = X, d = 1, approx = "UT", seed = 1)
pp1D
## Call:
## ppgmmga(data = X, d = 1, approx = "UT", seed = 1)
##
## 'ppgmmga' object containing:
## [1] "data" "d" "approx" "GMM" "GA"
## [6] "Negentropy" "basis" "Z"
summary(pp1D)
## ── ppgmmga ─────────────────────────────
##
## Data dimensions = 200 x 6
## Data transformation = center & scale
## Projection subspace dimension = 1
## GMM density estimate = (VEE,4)
## Negentropy approximation = UT
## GA optimal negentropy = 0.6345935
## GA encoded basis solution:
## x1 x2 x3 x4 x5
## [1,] 0.127318 0.7685482 2.090227 2.828462 2.609874
##
## Estimated projection basis:
## PP1
## Length -0.01196616
## Left -0.09347799
## Right 0.16021148
## Bottom 0.57406937
## Top 0.34503416
## Diagonal -0.71892054
plot(pp1D)
plot(pp1D, class = Class)
pp2D <- ppgmmga(data = X, d = 2, approx = "UT", seed = 1)
summary(pp2D, check = TRUE)
## ── ppgmmga ─────────────────────────────
##
## Data dimensions = 200 x 6
## Data transformation = center & scale
## Projection subspace dimension = 2
## GMM density estimate = (VEE,4)
## Negentropy approximation = UT
## GA optimal negentropy = 1.13624
## GA encoded basis solution:
## x1 x2 x3 x4 x5 x6 x7
## [1,] 1.972386 2.97614 1.231153 1.590697 0.3159946 3.859221 0.9727494
## x8 x9 x10
## [1,] 1.114576 0.167687 1.683149
##
## Estimated projection basis:
## PP1 PP2
## Length -0.044409969 -0.06764246
## Left 0.018859484 -0.12241338
## Right -0.147571751 0.07854225
## Bottom 0.003090167 0.86813545
## Top -0.054869445 0.46843261
## Diagonal 0.986343980 0.03438478
##
## Monte Carlo Negentropy approximation check:
## UT
## Approx Negentropy 1.136240193
## MC Negentropy 1.134698923
## MC se 0.003533358
## Relative accuracy 1.001358307
summary(pp2D$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$GA)
plot(pp2D)
plot(pp2D, class = Class, drawAxis = FALSE)
gmm <- densityMclust(data = scale(X, center = TRUE, scale = FALSE), G = 2)
pp3D <- ppgmmga(data = X, d = 3,
center = TRUE, scale = FALSE, gmm = gmm,
gatype = "gaisl",
options = ppgmmga.options(numIslands = 2),
seed = 1)
summary(pp3D$GA)
## ── Islands Genetic Algorithm ───────────
##
## GA settings:
## Type = real-valued
## Number of islands = 2
## Islands pop. size = 50
## Migration rate = 0.1
## Migration interval = 10
## Elitism = 1
## Crossover probability = 0.8
## Mutation probability = 0.1
## Search domain =
## x1 x2 x3 x4 x5 x6 x7
## lower 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## upper 6.283185 3.141593 3.141593 3.141593 3.141593 6.283185 3.141593
## x8 x9 x10 x11 x12 x13 x14
## lower 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## upper 3.141593 3.141593 3.141593 6.283185 3.141593 3.141593 3.141593
## x15
## lower 0.000000
## upper 3.141593
##
## GA results:
## Iterations = 120
## Epochs = 12
## Fitness function values = 0.8572447 0.8572447
## Solutions =
## x1 x2 x3 x4 x5 x6 x7
## [1,] 1.851015 1.178840 0.9667885 0.5621497 0.4874974 4.149389 0.9175687
## [2,] 1.851015 1.178839 0.9667894 0.5621510 0.4874959 4.149388 0.9175686
## x8 x9 x10 x11 x12 x13 x14
## [1,] 1.951967 1.57328 2.37529 0.6113169 0.8308838 1.753269 1.942719
## [2,] 1.951967 1.57328 2.37529 0.6113156 0.8308834 1.753269 1.942719
## x15
## [1,] 1.541154
## [2,] 1.541153
plot(pp3D$GA)
plot(pp3D)
plot(pp3D, class = Class)
plot(pp3D, dim = c(1,2))
plot(pp3D, dim = c(1,3), class = Class)
Scrucca, L. and Serafini, A. (2018) Projection pursuit based on Gaussian mixtures and evolutionary algorithms. Under review.