Ordering

Ordering

Implements the maximin ordering and other geometric algorithms.

KernelDist{K<:Kernel} <: Metric

Correlation distance based on a kernel function for covariances.

This implements the Distances.jl Metric interface.

Arguments

• kernel::K: base kernel function. This should be a KernelFunctions.jl Kernel.

(k::KernelDist)(p, q)

Distance between points p and q using the KernelDist metric.

The correlation distance for a kernel function $k(\cdot, \cdot)$ is defined as

\[\mathsf{dist}(p, q) \coloneqq \sqrt{1 - \left \lvert \rho \right \rvert}\]

where the correlation coefficient $\rho$ is defined as

\[\rho(p, q) \coloneqq \frac{k(p, q)}{\sqrt{k(p, p) k(q, q)}}.\]

maximin_ordering(
    kernel::Kernel,
    x::AbstractMatrix,
    k_neighbors=1;
    init_distances=fill(typemax(eltype(x)), (k_neighbors, size(x, 2))),
    Tree=BallTree,
)

Maximin ordering of x using k_neighbors for robustness.

The current implementation is directly copied from the maximin_ordering of KoLesky.jl.