Getting the entropy matrix

For some applications, we want to place points to capture the maximum amount of information, which is to say that we want to sample a balance of entropy values, as opposed to absolute values. In this vignette, we will walk through an example using the entropize function to convert raw data to entropy values.

using BiodiversityObservationNetworks
using NeutralLandscapes
using CairoMakie

Entropy is problem-specific

The solution presented in this vignette is a least-assumption solution based on the empirical values given in a matrix of measurements. In a lot of situations, this is not the entropy that you want. For example, if your pixels are storing probabilities of Bernoulli events, you can directly use the entropy of the events in the entropy matrix.

We start by generating a random matrix of measurements:

measurements = rand(MidpointDisplacement(), (200, 200)) .* 100
heatmap(measurements)

Using the entropize function will convert these values into entropy at the pixel scale:

U = entropize(measurements)
heatmap(U)

The values closest to the median of the distribution have the highest entropy, and the values closest to its extrema have an entropy of 0. The entropy matrix is guaranteed to have values on the unit interval.

We can use entropize as part of a pipeline, and overlay the points optimized based on entropy on the measurement map:

locations =
    measurements |> entropize |> seed(BalancedAcceptance(; numpoints = 100)) |> first
heatmap(U)