Distances of Distances

PortfolioOptimisers.DistanceDistance Type

struct DistanceDistance{__T_metric, __T_args, __T_kwargs, __T_power, __T_alg} <: AbstractDistanceEstimator

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

• metric: Distance metric used for the distances of distances computations.

• args: Additional positional arguments for the distances of distances metric.

• kwargs: Additional keyword arguments for the distances of distances metric.

• power: Optional matrix exponent.

• alg: Distance algorithm.

Constructors

DistanceDistance(;
    metric::Distances.Metric = Distances.Euclidean(),
    args::Tuple = (),
    kwargs::NamedTuple = (;),
    power::Option{<:Integer} = 1,
    alg::AbstractDistanceAlgorithm = SimpleDistance()
) -> DistanceDistance

Keywords correspond to the struct's fields.

Validation

• If power is not nothing, power >= 1.

Examples

julia> DistanceDistance()
DistanceDistance
  metric ┼ 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::MatNum;
         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 perform the computation.

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

Returns

• D::Matrix{<:Number}: Matrix of pairwise distances of distances.

Related

• DistanceDistance

• Distance

• distance

source

PortfolioOptimisers.distance Method

distance(de::DistanceDistance, rho::MatNum, 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

• D::Matrix{<:Number}: 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::MatNum;
             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 perform the computation.

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

Returns

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

Related

• DistanceDistance

• Distance

• cor_and_dist

source