General Distance of Distances

PortfolioOptimisers.GeneralDistanceDistance — Type
struct GeneralDistanceDistance{T1, T2, T3, T4, T5} <: AbstractDistanceEstimator
    dist::T1
    args::T2
    kwargs::T3
    power::T4
    alg::T5
end

A general distance-of-distances estimator for portfolio optimization.

GeneralDistanceDistance wraps a distance metric from Distances.jl and a general distance algorithm, allowing you to compute a general "distance of distances" matrix.

\[\begin{align} _{g}\tilde{d}_{i,\,j} &= \lVert_{g}\bm{D}_{i} - _{g}\bm{D}_{j}\rVert\,, \end{align}\]

where $_{g}\tilde{d}$ is the general distance of distances, $_{g}\bm{D}_{i}$ is the row corresponding to asset $i$ of the general distance matrix computed using the specified distance algorithm AbstractDistanceAlgorithm, $\lVert \cdot \rVert$ is the metric used to compute the distance of distances.

Fields

  • dist: The metric to use for the second-level distance from Distances.jl.
  • args: Positional arguments to pass to the metric.
  • kwargs: Keyword arguments to pass to the metric.
  • power: The integer power to which the base correlation or distance matrix is raised.
  • alg: The base distance algorithm to use.

Constructor

GeneralDistanceDistance(; dist::Distances.Metric = Distances.Euclidean(), args::Tuple = (),
                        kwargs::NamedTuple = (;), power::Integer = 1,
                        alg::AbstractDistanceAlgorithm = SimpleDistance())

Keyword arguments correspond to the fields above.

Validation

  • power >= 1.

Examples

julia> GeneralDistanceDistance()
GeneralDistanceDistance
    dist | Distances.Euclidean: Distances.Euclidean(0.0)
    args | Tuple{}: ()
  kwargs | @NamedTuple{}: NamedTuple()
   power | Int64: 1
     alg | SimpleDistance()

Related

source
PortfolioOptimisers.distance — Method
distance(de::GeneralDistanceDistance, ce::StatsBase.CovarianceEstimator, X::AbstractMatrix;
         dims::Int = 1, kwargs...)

Compute the general distance-of-distances matrix from a covariance estimator and data matrix.

This method first computes a base distance matrix using GeneralDistance with the specified power and algorithm, then applies the provided metric to compute a second-level distance matrix.

Arguments

  • de: General distance-of-distances estimator.
  • ce: Covariance estimator.
  • X: Data matrix (observations × features).
  • dims: Dimension along which to compute the base distance.
  • kwargs...: Additional keyword arguments passed to the base distance computation.

Returns

  • dist::Matrix{<:Real}: Matrix of pairwise distances of distances.

Related

source
PortfolioOptimisers.distance — Method
distance(de::GeneralDistanceDistance, rho::AbstractMatrix, args...; kwargs...)

Compute the general distance-of-distances matrix from a correlation or covariance matrix.

This method first computes a base distance matrix using GeneralDistance with the specified power and algorithm, then applies the provided metric to compute a second-level distance matrix.

Arguments

  • de: General distance-of-distances estimator.
  • rho: Correlation or covariance matrix.
  • args...: Additional arguments (ignored).
  • kwargs...: Additional keyword arguments passed to the base distance computation.

Returns

  • dist::Matrix{<:Real}: Matrix of pairwise distances of distances.

Related

source
PortfolioOptimisers.cor_and_dist — Method
cor_and_dist(de::GeneralDistanceDistance, ce::StatsBase.CovarianceEstimator,
             X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute both the correlation matrix and the general distance-of-distances matrix from a covariance estimator and data matrix.

This method first computes the correlation and base distance matrices using GeneralDistance, then applies the provided metric to the base distance matrix.

Arguments

  • de: General distance-of-distances estimator.
  • ce: Covariance estimator.
  • X: Data matrix (observations × features).
  • dims: Dimension along which to compute the base distance.
  • kwargs...: Additional keyword arguments passed to the base distance computation.

Returns

  • (rho::Matrix{<:Real}, D::Matrix{<:Real}): Tuple of correlation matrix and distance-of-distances matrix.

Related

source