Distances of Distances

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

A distance-of-distances estimator for portfolio optimization.

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

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

where $\tilde{d}$ is the distance of distances, $\bm{D}_{i}$ is the row corresponding to asset $i$ of the 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.
  • alg::AbstractDistanceAlgorithm: The base distance algorithm to use.

Constructor

DistanceDistance(; dist::Distances.Metric = Distances.Euclidean(), args::Tuple = (),
                 kwargs::NamedTuple = (;),
                 alg::AbstractDistanceAlgorithm = SimpleDistance())

Keyword arguments correspond to the fields above.

Examples

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

Related

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

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

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

Arguments

  • de: 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

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

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

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

Arguments

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

Returns

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

Related

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

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

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

Arguments

  • de: 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}, dist::Matrix{<:Real}): Tuple of correlation matrix and distance-of-distances matrix.

Related

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