get_occupancy_intersection_bootstrap: Volume of the intersection of a bootstrapped occupancy object

In bblonder/hypervolume: High Dimensional Geometry, Set Operations, Projection, and Inference Using Kernel Density Estimation, Support Vector Machines, and Convex Hulls

Volume of the intersection of a bootstrapped occupancy object

Description

The get_occupancy_intersection_bootstrap() function is used to get the volume of the intersection of objects generated with hypervolume_n_occupancy_bootstrap(). It provides raw values or summary statistics for all the hypervolumes or their n_wise combinations.

Usage

get_occupancy_intersection_bootstrap(path,
                                     method = "n_wise",
                                     res_type = "summary",
                                     m = 2, 
                                     relative = FALSE,
                                     tol = 1e-10)

Arguments

path	A path to a directory of bootstrapped occupancy objects obtained with hypervolume_n_occupancy_bootstrap().
method	If all compute the volume of the intersection among all the hypervolumes for each bootstrapped occupancy object found in path. If n_wise compute the volume of the intersection for each n_wise combination of hypervolumes within the bootstrapped occupancy objects found in path.
res_type	It can be raw or pairwise. See details.
m	Number of elements to choose. Default to 2 (pairwise comparisons). This argument is ignored when method is set to all.
relative	If TRUE it computes relative instead of absolute volumes.
tol	Set the tolerance for reconstructing whole volume. See details.

Details

The function get_occupancy_intersection_bootstrap() returns the volume of the intersection for each bootstrapped occupancy object if res_type = "raw" and method = "all". When res_type = "summary" and method = "all" this function returns the mean volume as well as the standard deviation, median, minimum, maximum, 2.5% and 97.5% quantiles, skewness and kurtosis of the intersection. The same summary statistics are calculated for each n_wise combination of hypervolumes when res_type = "summary" and method = "n_wise". The number of elements of n_wise combinations is set with the argument m. The intersection is calculated by finding the set of random points shared by all or n_wise combinations of hypervolumes in each of the bootstrapped occupancy objects. More details on how the intersection is computed in occupancy_to_intersection().
The get_occupancy_intersection_bootstrap() function attempts to reconstruct the volume of the intersection from each bootstrapped occupancy object. At first, the volume of the union of hypervolumes is calculated for each hypervolume of the jth bootstrapped occupancy object as the ratio between the total number of random points and the number of random points of the ith hypervolume of the jth bootstrapped occupancy object, multiplied by the volume of the ith hypervolume of the jth bootstrapped occupancy object. This step results in a number of reconstructed volumes equal to the number of hypervolumes in the jth bootstrapped occupancy object. Reconstructed volumes are then compared among each other to ensure the consistency of the reconstruction. To do this, the distance among reconstructed volumes is calculated using the dist() function of the stats package. If at least one of the distances is greater than tol the computation is stopped and some suggestions are returned. The volume of the intersection is then calculated as the ratio between the number of random points of the intersection and the total number of random points, multiplied by the volume of the union of hypervolumes.
When relative = TRUE relative instead of absolute volumes are returned. The relative volume is calculated as the ratio between the volume of the intersection and the volume of the union of all the hypervolumes (or combination of hypervolumes when method = "n_wise"). The same approach described above is used to reconstruct the volume of the union of hypervolumes.

Value

A data.frame with bootstrapped volumes or summary statistics of the intersection.

See Also

hypervolume_n_occupancy, hypervolume_n_occupancy_bootstrap, occupancy_to_intersection

Examples

## Not run: 
data(penguins,package='palmerpenguins')
penguins_no_na = as.data.frame(na.omit(penguins))

# split the dataset on species and sex
penguins_no_na_split = split(penguins_no_na, 
paste(penguins_no_na$species, penguins_no_na$sex, sep = "_"))

# calculate the hypervolume for each element of the splitted dataset
hv_list = mapply(function(x, y) 
  hypervolume_gaussian(x[, c("bill_length_mm","bill_depth_mm","flipper_length_mm")],
                       samples.per.point=100, name = y), 
                       x = penguins_no_na_split, 
                       y = names(penguins_no_na_split))


# transform the list into an HypervolumeList
hv_list = hypervolume_join(hv_list)

# bootstrap the hypervolumes
hv_list_boot = hypervolume_n_resample(name = "example", hv_list)

# calculate occupancy on bootstrapped hypervolumes
hv_occupancy_boot_sex = hypervolume_n_occupancy_bootstrap(path = hv_list_boot,
                                    name = "example_occ",
                                    classification = rep(c("female", "male"), 3))

# get the intersection
get_occupancy_intersection_bootstrap(hv_occupancy_boot_sex)


## End(Not run)

bblonder/hypervolume documentation built on Feb. 1, 2024, 8:01 p.m.