Detects the holes in an observed hypervolume relative to an expectation
The observed hypervolume whose holes are to be detected
The expected hypervolume that provides a baseline expectation geometry
Maximum number of points to be used for set operations comparing
This algorithm has a good Type I error rate (rarely detects holes that do not actually exist). However it can have a high Type II error rate (failure to find holes when they do exist). To reduce this error rate, make sure to re-run the algorithm with input hypervolumes with higher values of
@PointDensity, or increase
The algorithm performs the set difference between the observed and expected hypervolumes, then removes stray points in this hypervolume by deleting any random point whose distance from any other random point is greater than expected.
A 'rule of thumb' is that algorithm has acceptable statistical performance when log_e(m) > n, where m is the number of data points and n is the dimensionality.
Hypervolume object containing a uniformly random set of points describing the holes in
hv_obs. Note that the point density of this object is likely to be much lower than that of the input hypervolumes due to the stochastic geometry algorithms used.
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# generate annulus data data_annulus <- data.frame(matrix(data=runif(4000),ncol=2)) names(data_annulus) <- c("x","y") data_annulus <- subset(data_annulus, sqrt((x-0.5)^2+(y-0.5)^2) > 0.4 & sqrt((x-0.5)^2+(y-0.5)^2) < 0.5) # MAKE HYPERVOLUME (low reps for fast execution) hv_annulus <- hypervolume(data_annulus,bandwidth=0.1,name='annulus',reps=500) # GET CONVEX EXPECTATION hv_convex <- expectation_convex(hv_annulus, check_memory=FALSE) # DETECT HOLES (low npoints for fast execution) features_annulus <- hypervolume_holes( hv_obs=hv_annulus, hv_exp=hv_convex, set_check_memory=FALSE) # CLEAN UP RESULTS features_segmented <- hypervolume_segment(features_annulus) features_segmented_pruned <- hypervolume_prune(features_segmented, minvol=0.01) # PLOT RETAINED HOLE(S) plot(hypervolume_join(hv_annulus, features_segmented_pruned))
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