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hopkins

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Homepage: https://kwstat.github.io/hopkins

Repository: https://github.com/kwstat/hopkins

Key features

The hopkins() function:

  • Can assess the spatial distribution of points for randomness.
  • Correctly calculates Hopkins statistic using exponents d=D.
  • Is very fast for method="simple".
  • Can use method="torus" to correct for edge effects in higher dimensions.

We believe that most software implementations of Hopkins statistics are incorrect because they use “d=1” as the exponent of the distances in the calculation instead of “d=2” for 2-dimensional data or the more general “d=D” for D-dimensional data.

For full details, see Wright (2023), “Will the Real Hopkins Statistic Please Stand Up”, https://journal.r-project.org/articles/RJ-2022-055/

Installation 

# Install the released version from CRAN:
install.packages("hopkins")

# Install the development version from GitHub:
install.packages("devtools")
devtools::install_github("kwstat/hopkins")

Usage 

library(hopkins)
hopkins(iris[, -5], m=15) # .9952293
hopkins.pval(0.21, 10) # .00466205

Guidelines for using Hopkins statistic

It is easy to mis-use Hopkins statistic. Here are some things you MUST think about. See the vignettes for more details.

  1. Does the data need to be centered and scaled to unit variance??
  2. Is the number of events n > 100 and the number of randomly-sampled events at most 10% of n?
  3. Is spatial randomness of the events even possible? If the events are known or suspected to be correlated, this violates the null hypothesis of spatial uniformity, and may also mean that the sampling frame is not shaped like a hypercube.
  4. Could nearest-neighbor events have occurred outside the boundary of the sampling frame? If yes, it may be appropriate to calculate nearest-neighbor distances using a torus geometry.
  5. Is the sampling frame non-rectangular? If yes, then be extremely careful with the use of Hopkins statistic in how points are samples from UU.
  6. Is the dimension of the data much greater than 2? Edge effects are more common in higher dimensions.
  7. Is the dimension of the data large? It is difficult to detect spatial randomness in a large number of dimensions.

The Hopkins statistic attempts to assess the spatial distribution of points. Prairie dogs cluster together in burrows, while the burrows are spaced somewhat evenly apart from each other. Also, prairie dogs (sort of) “hop”, and “kins” is both “endearing” and “a group with similar characteristics”. So “hopkins” could mean “a cute group of hoppers” (prairie dogs).