Clustering layers

The purpose of this vignette is to demonstrate how we can use the Clustering package to apply k-means or fuzzy C-means on layers.

This functionality is supported through an extension, which is only active when the Clustering package is loaded.

using SpeciesDistributionToolkit
using CairoMakie
using Statistics
import StatsBase
using Clustering 

The support is currently limited to clustering methods that take a matrix of features, as distance matrices for large layers risk getting extremely large. To illustrate how the integration with Clustering works, we will get data from CHELSA1:

spatial_extent = (left = 8.412, bottom = 41.325, right = 9.662, top = 43.060)
dataprovider = RasterData(CHELSA1, BioClim)
L = [SDMLayer(dataprovider; layer = i, spatial_extent...) for i in [1, 3, 8, 12]]

4-element Vector{SDMLayer{Int16}}:
 🗺️  A 209 × 151 layer (14432 Int16 cells)
 🗺️  A 209 × 151 layer (14432 Int16 cells)
 🗺️  A 209 × 151 layer (14432 Int16 cells)
 🗺️  A 209 × 151 layer (14432 Int16 cells)

It makes more sense to normalize these layers, so they all have unit variance and a mean of zero:

L = (L .- mean.(L)) ./ std.(L)

4-element Vector{SDMLayer{Float64}}:
 🗺️  A 209 × 151 layer (14432 Float64 cells)
 🗺️  A 209 × 151 layer (14432 Float64 cells)
 🗺️  A 209 × 151 layer (14432 Float64 cells)
 🗺️  A 209 × 151 layer (14432 Float64 cells)

The syntax is the exact same as the Clustering package, with the feature matrix replaced by the vector of layers. For example, k-means with k=3 on these input data is done with:

K = kmeans(L, 3)

Clustering.KmeansResult{Matrix{Float64}, Float64, Int64}([0.7562517417015148 -1.6201198968030224 -0.045597234919157986; -0.701434492801667 0.7824439293933296 0.41059858905013663; 0.7474916743128407 -1.6092990920998222 -0.041005792517508056; -0.826209494626791 1.3628684654518257 0.25800353640560847], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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Note that this will return a Clustering result object, which can therefore be validated using any measure of clustering performance.

To bring this result back to a layer, we can use the following syntax:

k = SDMLayer(K, L)

🗺️  A 209 × 151 layer with 14432 Int64 cells
   Projection: +proj=longlat +datum=WGS84 +no_defs

The last argument must be a layer (or a vector of layers), which will be used as a template to store the output values in. In the case of kmeans, this is the cluster to which each pixel is assigned.

We can get the quality of this clustering with

clustering_quality(L, K; quality_index = :davies_bouldin)

0.6611546039539016

We can visualize the result of this clustering:

Code for the figure

fig, ax, hm = heatmap(
    k,
    colormap = :Spectral,
    figure = (; size = (800, 400)),
    axis = (; aspect = DataAspect()),
)

Fuzzy C-means is also supported. We can get three fuzzy clusters (under a fuzzyness parameter of 2) with

F = fuzzy_cmeans(L, 3, 2)

FuzzyCMeansResult: 3 clusters for 14432 points in 4 dimensions (converged in 42 iterations)

This can be converted into a vector of layers with the following syntax:

f = SDMLayer(F, L)

3-element Vector{SDMLayer{Float64}}:
 🗺️  A 209 × 151 layer (14432 Float64 cells)
 🗺️  A 209 × 151 layer (14432 Float64 cells)
 🗺️  A 209 × 151 layer (14432 Float64 cells)

Each layer represents the membership of a pixel to each of the fuzzy clusters. If required, these can be passed through mosaic with argmax to get the most likely cluster.

Code for the figure

fig, ax, hm = heatmap(
    f[1],
    colormap = :bamako,
    figure = (; size = (800, 400)),
    axis = (; aspect = DataAspect()),
)
Colorbar(fig[:, end + 1], hm)