Clustering

GHC(k, λ; nmax=2000, kern=:epanechnikov, link=:ward, as=:cluster)

A transform for partitioning geospatial data into k clusters according to a range λ using Geostatistical Hierarchical Clustering (GHC). The larger the range the more connected are nearby samples.

Parameters

• k - Approximate number of clusters
• λ - Approximate range of kernel function in length units

Options

• nmax - Maximum number of observations to use in dissimilarity matrix
• kern - Kernel function (:uniform, :triangular or :epanechnikov)
• link - Linkage function (:single, :average, :complete, :ward or :ward_presquared)
• as - Variable name used to store clustering results

References

• Fouedjio, F. 2016. A hierarchical clustering method for multivariate geostatistical data

Notes

• The range parameter controls the sparsity pattern of the pairwise distances, which can greatly affect the computational performance of the GHC algorithm. We recommend choosing a range that is small enough to connect nearby samples. For example, clustering data over a 100x100 Cartesian grid with unit spacing is possible with λ=1.0 or λ=2.0 but the problem starts to become computationally unfeasible around λ=10.0 due to the density of points.

GSC(k, m; σ=1.0, tol=1e-4, maxiter=10, weights=nothing, as=:cluster)

A transform for partitioning geospatial data into k clusters using Geostatistical Spectral Clustering (GSC).

Parameters

• k - Desired number of clusters
• m - Multiplicative factor for adjacent weights

Options

• σ - Standard deviation for exponential model (default to 1.0)
• tol - Tolerance of k-means algorithm (default to 1e-4)
• maxiter - Maximum number of iterations (default to 10)
• weights - Dictionary with weights for each attribute (default to nothing)
• as - Variable name used to store clustering results

References

• Romary et al. 2015. Unsupervised classification of multivariate geostatistical data: Two algorithms

Notes

• The algorithm implemented here is slightly different than the algorithm

described in Romary et al. 2015. Instead of setting Wᵢⱼ = 0 when i <-/-> j, we simply magnify the weight by a multiplicative factor Wᵢⱼ *= m when i <–> j. This leads to dense matrices but also better results in practice.

SLIC(k, m; tol=1e-4, maxiter=10, weights=nothing, as=:cluster)

A transform for clustering geospatial data into approximately k clusters using Simple Linear Iterative Clustering (SLIC).

The transform produces clusters of samples that are spatially connected based on a distance dₛ and that, at the same time, are similar in terms of vars with distance dᵥ. The tradeoff is controlled with a hyperparameter m in an additive model dₜ = √(dᵥ² + m²(dₛ/s)²).

Parameters

• k - Approximate number of clusters
• m - Hyperparameter of SLIC model

Options

• tol - Tolerance of k-means algorithm (default to 1e-4)
• maxiter - Maximum number of iterations (default to 10)
• weights - Dictionary with weights for each attribute (default to nothing)
• as - Variable name used to store clustering results

References

• Achanta et al. 2011. SLIC superpixels compared to state-of-the-art superpixel methods