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.
julia
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:
julia
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:
julia
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:
julia
K = kmeans(L, 3)Clustering.KmeansResult{Matrix{Float64}, Float64, Int64}([-0.024290109840419176 -1.5998492881033777 0.7563348321468751; 0.4099570007976743 0.7775766878036976 -0.7183008245307021; -0.021135554240059813 -1.5892440394418732 0.7486843999304184; 0.2375218426002975 1.3545365470755926 -0.8314611134862943], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 3, 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, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, 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0.47077387450127706, 0.487410622358726, 0.5319462280723313, 0.5304315949470535, 0.5828316948923389, 0.5974122035330218, 0.5718833822071598, 0.523422548587976, 0.49403339421504633, 0.5375869719228623, 0.5346586963995312], [5431, 2830, 6171], [5432, 2833, 6167], 20751.8717361467, 100, false)Note that this will return a Clustering result object, which can therefore be validated using any measure of clustering performance. Under the hood, the package is converting the stack of layers into a matrix, which is what Clustering handles.
But what if I want to work on a very large layer?
You can absolutely decide to extract the data from your layers, work with them in Clustering, then write them back in. In our experience, the limitation of not using clustering methods that require a distance matrix has never been a blocking point.
To bring this result back to a layer, we can use the following syntax:
julia
k = SDMLayer(K, L)🗺️ A 209 × 151 layer with 14432 Int64 cells
Spatial Reference System: +proj=longlat +datum=WGS84 +no_defsThe 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 must pass a layer here because the clustering result has no information that would allow us to re-create the layer from scratch. For example, it has no CRS, no coordinates, etc.
The layer given as the second argument here is NOT modified, and the object returned in k is a new layer.
We can get the quality of this clustering with
julia
clustering_quality(L, K; quality_index = :davies_bouldin)0.6676210012048363We can visualize the result of this clustering:
Code for the figure
julia
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
julia
F = fuzzy_cmeans(L, 3, 2)FuzzyCMeansResult: 3 clusters for 14432 points in 4 dimensions (converged in 24 iterations)This can be converted into a vector of layers with the following syntax:
julia
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
julia
fig, ax, hm = heatmap(
f[1],
colormap = :bamako,
figure = (; size = (800, 400)),
axis = (; aspect = DataAspect()),
)
Colorbar(fig[:, end + 1], hm)