Distances of Distances

PortfolioOptimisers.DistanceDistance Type

struct DistanceDistance{T1, T2, T3, T4, T5} <: AbstractDistanceEstimator
    dist::T1
    args::T2
    kwargs::T3
    power::T4
    alg::T5
end

Distance-of-distances estimator for portfolio optimization.

DistanceDistance wraps a distance metric from Distances.jl and a distance algorithm, allowing you to compute a "distance of distances" matrix. If power is not nothing, it computes the generalised distance matrix, which is then used to compute the distances of distances matrix.

$$\begin{array}{rl}{}_g{\tilde{d}}_{i,j}& ={\Vert }_g\text{bm}{D}_i{-}_g\text{bm}{D}_j\Vert ,\end{array}$$

where ${}_g\tilde{d}$ is the general distance of distances, ${}_g\text{bm}{D}_i$ is the row corresponding to asset $i$ of the general distance matrix computed using the specified distance algorithm AbstractDistanceAlgorithm, $\Vert \cdot \Vert$ 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

DistanceDistance(; dist::Distances.Metric = Distances.Euclidean(), args::Tuple = (),
                 kwargs::NamedTuple = (;), power::Union{Nothing, <:Integer} = 1,
                 alg::AbstractDistanceAlgorithm = SimpleDistance())

Keyword arguments correspond to the fields above.

Validation

• power >= 1.

Examples

julia> DistanceDistance()
DistanceDistance
    dist ┼ Distances.Euclidean: Distances.Euclidean(0.0)
    args ┼ Tuple{}: ()
  kwargs ┼ @NamedTuple{}: NamedTuple()
   power ┼ nothing
     alg ┴ SimpleDistance()

Related

• DistanceDistance

• distance

• Distances.jl

source

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 Distance with the specified power and 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

• DistanceDistance

• Distance

• distance

source

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 Distance with the specified power and 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 (ignored).

• kwargs...: Additional keyword arguments passed to the base distance computation.

Returns

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

Related

• DistanceDistance

• Distance

• distance

source

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 using Distance, 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}, D::Matrix{<:Real}): Tuple of correlation matrix and distance-of-distances matrix.

Related

• DistanceDistance

• Distance

• cor_and_dist

source