Local correlation dimension

CHANGELOG.md

@@ -1,3 +1,9 @@
+# 1.9
+
+- New function `local_correlation_dimension`.
+- Functions that were already exported as public are now also in the documentation:
+  `pointwise_dimensions, pointwise_correlationsums`
+
 # 1.8
 
 - New way to estimate extreme value theory dimensions based on block maxima.

Project.toml

@@ -1,7 +1,7 @@
 name = "FractalDimensions"
 uuid = "4665ce21-e117-4649-aed8-08bbe5ccbead"
 authors = ["George Datseris <datseris.george@gmail.com>", "Ignacio Del Amo <@PythagoreanCult>", "Anton P Braun"]
-version = "1.8.2"
+version = "1.9.0"
 
 [deps]
 ComplexityMeasures = "ab4b797d-85ee-42ba-b621-05d793b346a2"

docs/src/index.md

@@ -86,6 +86,12 @@ The whole above pipeline we went through is bundled in [`grassberger_proccacia_d
     They are more like convenient bundles with on-average good defaults, rather than precise functions. You should be careful
     when considering the validity of the returned number!
 
+
+## Index (contents)
+
+```@index
+```
+
 ## Linear scaling regions
 
 ```@docs
@@ -145,6 +151,14 @@ fixedmass_correlationsum
 takens_best_estimate_dim
 ```
 
+## Pointwise (local) correlation dimensions
+
+```@docs
+pointwise_dimensions
+local_correlation_dimension
+```
+
+
 ## Kaplan-Yorke dimension
 
 ```@docs

src/corrsum_based/correlationsum_vanilla.jl

@@ -4,7 +4,7 @@ using Distances: evaluate, Euclidean, pairwise, Metric
 
 export correlationsum, boxed_correlationsum
 export grassberger_proccacia_dim
-export pointwise_dimensions, pointwise_correlationsums
+export pointwise_dimensions, pointwise_correlationsums, local_correlation_dimension
 
 """
     grassberger_proccacia_dim(X::AbstractStateSpaceSet, εs = estimate_boxsizes(data); kwargs...)
@@ -163,7 +163,7 @@ versus ``\\epsilon``. `Δloc[i]` is the exponential scaling (deduced by a call t
 
 Keywords are the same as in [`correlationsum`](@ref).
 To obtain the inner correlation sums without doing the exponential scaling fit
-use `pointwise_correlationsums`.
+use `FractalDimensions.pointwise_correlationsums` with same inputs.
 """
 function pointwise_dimensions(X, εs::AbstractVector = estimate_boxsizes(X); kw...)
     Cs = pointwise_correlationsums(X, εs; kw...)
@@ -218,4 +218,49 @@ end
         out[j+lr1] = norm(v, X[ξ])
     end
     return out
-end
+end
+
+"""
+    local_correlation_dimension(X, ζ [, εs]; kw...) → Δ_ζ
+
+Return the local dimension `Δ_ζ` around state space point `ζ` given a set of state space
+points `X` which is assumed to surround (or be sufficiently near to) `ζ`.
+The local dimension is the exponential scaling of the correlation sum for point `ζ` versus
+some radii `εs`. `εs` can be a vector of reals, or it can be an integer,
+in which space that many points are equi-spaced logarithmically between the minimum and
+maximum distance of `X` to `ζ`.
+
+## Keyword arguments
+
+- `q = 2, norm = Euclidean()`: same as in [`correlationsum`](@ref).
+- `fit = LinearRegression()`: given to [`slopefit`](@ref) to estimate the dimension.
+  This default assumes that the set `X` is already sufficiently close to `ζ`.
+"""
+function local_correlation_dimension(args...; fit = LinearRegression(), kw...)
+    C, es = local_correlation_sum(args...; kw...)
+    ΔGP = slopefit(log2.(es), log2.(C), fit)[1]
+    return ΔGP
+end
+
+function local_correlation_sum(X, ζ, k = 8; norm = Euclidean(), q = 2)
+    # First estimate distances
+    dists = map(x -> norm(x, ζ), X)
+    εs = _generate_boxsizes(k, dists)
+    C = zeros(Int, length(εs))
+    # Then convert to correlation sum
+    for i in eachindex(εs)
+        C[i] = count(<(εs[i]), dists)^(q-1)
+    end
+    return C/length(dists), εs
+end
+
+function _generate_boxsizes(k::Int, dists)
+    dmax = maximum(dists)
+    dmin = partialsort!(dists, 2) # second smallest
+    base = MathConstants.e
+    lower = log(base, dmin)
+    upper = log(base, dmax)
+    return float(base) .^ range(lower, upper; length = k)
+end
+
+_generate_boxisizes(es::AbstractVector, dists) = es

test/correlationdim.jl

@@ -171,3 +171,11 @@ end
     @test all(c -> c[end] > 0, Csums)
 
 end
+
+@testset "local corrsum dimension" begin
+    rng = Xoshiro(1234)
+    F = [0.5rand(rng, 2) .+ [0.25, 0.25] for _ in 1:10_000]
+    z = SVector(0.5, 0.5)
+    d = local_correlation_dimension(F, z)
+    test_value(d, 1.9, 2.1)
+end