knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) library(knitr) library(rgl) knit_hooks$set(webgl = hook_webgl)
Hyperoverlap can be used to detect and visualise overlap in n-dimensional space.
To explore the functions in hyperoverlap, we'll use the
iris dataset. This dataset contains 150 observations of three species of iris ("setosa", "versicolor" and "virginica"). These data are four-dimensional (Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) and are documented in
?iris. We'll set up five test datasets to explore the different functions:
test1 two entities (setosa, virginica); three dimensions (Sepal.Length, Sepal.Width, Petal.Length)
test2 two entities (versicolor, virginica); three dimensions (as above)
test3 two entities (setosa, virginica); four dimensions
test4 two entities (versicolor, virginica); four dimensions
test5 all entities, all dimensions
test1 <- iris[which(iris$Species!="versicolor"),c(1:3,5)] test2 <- iris[which(iris$Species!="setosa"),c(1:3,5)] test3 <- iris[which(iris$Species!="versicolor"),] test4 <- iris[which(iris$Species!="setosa"),] test5 <- iris
Note that entities may be species, genera, populations etc.
To plot the decision boundary using
hyperoverlap_plot, the data cannot exceed three dimensions. For high-dimensional visualisation, see
library(hyperoverlap) setosa_virginica3d <- hyperoverlap_detect(test1[,1:3], test1$Species) versicolor_virginica3d <- hyperoverlap_detect(test2[,1:3], test2$Species)
To examine the result:
setosa_virginica3d@result #gives us the result: overlap or non-overlap? versicolor_virginica3d@result setosa_virginica3d@shape #for the non-overlapping pair, was the decision boundary linear or curvilinear? hyperoverlap_plot(setosa_virginica3d) #plot the data and the decision boundary in 3d
Note the points on the 'wrong side' of the boundary when comparing versicolor and virginica
To visualise overlap in n-dimensions, we need to use ordination techniques. The function
hyperoverlap_lda uses a combination of linear discriminant analysis (LDA) and principal components analysis (PCA) to choose the best two (or three) axes for visualisation. To plot these using other methods (e.g.
ggplot2), the point coordinates are returned as output, here named
setosa_virginica4d <- hyperoverlap_detect(test3[,1:4], test3$Species) versicolor_virginica4d <- hyperoverlap_detect(test4[,1:4], test4$Species)
To examine the result:
setosa_virginica4d@result #gives us the result: overlap or non-overlap? versicolor_virginica4d@result setosa_virginica4d@shape #for the non-overlapping pair, was the decision boundary linear or curvilinear? transformed_data <- hyperoverlap_lda(setosa_virginica4d) #plots the best two dimensions for visualising overlap transformed_data <- hyperoverlap_lda(versicolor_virginica4d)
In three dimensions:
rgl.close() #close previous device transformed_data <- hyperoverlap_lda(setosa_virginica4d, visualise3d=TRUE)
rgl.close() #close previous device transformed_data <- hyperoverlap_lda(versicolor_virginica4d, visualise3d=TRUE) #plots the best three dimensions for visualising overlap
We might want to know which species overlap in certain variables from an entire genus. To do this, we can use
hyperoverlap_set and visualise the results using
all_spp <- hyperoverlap_set(test5[,1:4],test5$Species) all_spp_plot <- hyperoverlap_pairs_plot(all_spp) all_spp_plot
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