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* oganize files for Datasets * add metric-based dataset distance * clarify a bit * add Hausdorff distance * address PR comments * changelog * use `main` in CI * add a test with different metric * woops forgot an include * [wipwip] start sets of datasets distance * port over the proximity version for sets of datasets * doc and finish set dataset function * passing tests for sets of datasets! * optimzie for brute force or not way to compute distances * add hasudroff sets distance,needs tests * allow custom user function in sets datasets * add changelog * fix missing `end` * comment out all delay embedding tests for now
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| # TODO: This will become its own package | ||
| # after merging of DynamicalSystems.jl subrepos | ||
| include("dataset.jl") | ||
| include("subdataset.jl") | ||
| include("neighborhoods.jl") | ||
| include("dataset_distance.jl") | ||
| include("utils.jl") |
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| export dataset_distance, Hausdorff, datasets_sets_distances | ||
| ########################################################################################### | ||
| # Dataset distance | ||
| ########################################################################################### | ||
| """ | ||
| dataset_distance(dataset1, dataset2 [, method]) | ||
| Calculate a distance between two `AbstractDatasets`, | ||
| i.e., a distance defined between sets of points, as dictated by `method`. | ||
| `method` defaults to `Euclidean()`. | ||
| ## Description | ||
| If `method isa Metric` from Distances.jl, then the distance is the minimum | ||
| distance of all the distances from a point in one set to the closest point in | ||
| the other set. The distance is calculated with the given metric. | ||
| In this case there is an internal heuristic: if `length(dataset1)*length(dataset2) ≥ 1000` | ||
| the algorithm switches to a KDTree-based version, otherwise it uses brute force. | ||
| You can overwrite this by explicitly setting the `brute` boolean keyword | ||
| or calling `dataset_distance_brute` directly. | ||
| `method` can also be [`Hausdorff`](@ref) (a name provided by this module). | ||
| """ | ||
| function dataset_distance(d1, d2::AbstractDataset, metric::Metric = Euclidean(); | ||
| brute = length(d1)*length(d2) < 1000) | ||
| if brute | ||
| return dataset_distance_brute(d1, d2, metric) | ||
| else | ||
| tree = KDTree(d2, metric) | ||
| return dataset_distance(d1, tree) | ||
| end | ||
| end | ||
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| function dataset_distance(d1, tree::KDTree) | ||
| # Notice that it is faster to do a bulksearch of all points in `d1` | ||
| # rather than use the internal inplace method `NearestNeighbors.knn_point!`. | ||
| _, vec_of_ds = bulksearch(tree, d1, NeighborNumber(1)) | ||
| return minimum(vec_of_ds)[1] | ||
| # For future benchmarking reasons, we leave the code here | ||
| ε = eltype(d2)(Inf) | ||
| dist, idx = [ε], [0] | ||
| for p in d1 # iterate over all points of dataset | ||
| Neighborhood.NearestNeighbors.knn_point!( | ||
| tree, p, false, dist, idx, Neighborhood.alwaysfalse | ||
| ) | ||
| @inbounds dist[1] < ε && (ε = dist[1]) | ||
| end | ||
| return ε | ||
| end | ||
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| function dataset_distance_brute(d1, d2::AbstractDataset, metric = Euclidean()) | ||
| ε = eltype(d2)(Inf) | ||
| for x ∈ d1 | ||
| for y ∈ d2 | ||
| εnew = metric(x, y) | ||
| εnew < ε && (ε = εnew) | ||
| end | ||
| end | ||
| return ε | ||
| end | ||
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| """ | ||
| Hausdorff(metric = Euclidean()) | ||
| A dataset distance that can be used in [`dataset_distance`](@ref). | ||
| The [Hausdorff distance](https://en.wikipedia.org/wiki/Hausdorff_distance) is the | ||
| greatest of all the distances from a point in one set to the closest point in the other set. | ||
| The distance is calculated with the metric given to `Hausdorff` which defaults to Euclidean. | ||
| `Hausdorff` is a proper metric in the space of sets of datasets. | ||
| """ | ||
| struct Hausdorff{M<:Metric} | ||
| metric::M | ||
| end | ||
| Hausdorff() = Hausdorff(Euclidean()) | ||
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| function dataset_distance(d1::AbstractDataset, d2, h::Hausdorff, | ||
| # trees given for a natural way to call this function in `datasets_sets_distances` | ||
| tree1 = KDTree(d1, h.metric), | ||
| tree2 = KDTree(d2, h.metric), | ||
| ) | ||
| # This yields the minimum distance between each point | ||
| _, vec_of_distances12 = bulksearch(tree1, vec(d2), NeighborNumber(1)) | ||
| _, vec_of_distances21 = bulksearch(tree2, vec(d1), NeighborNumber(1)) | ||
| # get max of min distances (they are vectors of length-1 vectors, hence the [1]) | ||
| max_d12 = maximum(vec_of_distances12)[1] | ||
| max_d21 = maximum(vec_of_distances21)[1] | ||
| return max(max_d12, max_d21) | ||
| end | ||
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| ########################################################################################### | ||
| # Sets of datasets distance | ||
| ########################################################################################### | ||
| """ | ||
| datasets_sets_distances(a₊, a₋ [, metric/method]) → distances | ||
| Calculate distances between sets of `Dataset`s. Here `a₊, a₋` are containers of | ||
| `Dataset`s, and the returned distances are dictionaries of | ||
| of distances. Specifically, `distances[i][j]` is the distance of the dataset in | ||
| the `i` key of `a₊` to the `j` key of `a₋`. Notice that distances from `a₋` to | ||
| `a₊` are not computed at all (assumming symmetry in the distance function). | ||
| The `metric/method` can be as in [`dataset_distance`](@ref), in which case | ||
| both sets must have equal-dimension datasets. | ||
| However, `method` can also be any arbitrary user function that takes as input | ||
| two datasets and returns any positive-definite number as their "distance". | ||
| """ | ||
| function datasets_sets_distances(a₊, a₋, method = Euclidean()) | ||
| ids₊, ids₋ = keys(a₊), keys(a₋) | ||
| gettype = a -> eltype(first(values(a))) | ||
| T = promote_type(gettype(a₊), gettype(a₋)) | ||
| distances = Dict{eltype(ids₊), Dict{eltype(ids₋), T}}() | ||
| _datasets_sets_distances!(distances, a₊, a₋, method) | ||
| end | ||
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| function _datasets_sets_distances!(distances, a₊, a₋, metric::Metric) | ||
| @assert keytype(a₊) == keytype(a₋) | ||
| search_trees = Dict(m => KDTree(vec(att), metric) for (m, att) in pairs(a₋)) | ||
| @inbounds for (k, A) in pairs(a₊) | ||
| distances[k] = pairs(valtype(distances)()) | ||
| for (m, tree) in search_trees | ||
| # Internal method of `dataset_distance` for non-brute way | ||
| d = dataset_distance(A, tree) | ||
| distances[k][m] = d | ||
| end | ||
| end | ||
| return distances | ||
| end | ||
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| function _datasets_sets_distances!(distances, a₊, a₋, method::Hausdorff) | ||
| @assert keytype(a₊) == keytype(a₋) | ||
| metric = method.metric | ||
| trees₊ = Dict(m => KDTree(vec(att), metric) for (m, att) in pairs(a₊)) | ||
| trees₋ = Dict(m => KDTree(vec(att), metric) for (m, att) in pairs(a₋)) | ||
| @inbounds for (k, A) in pairs(a₊) | ||
| distances[k] = pairs(valtype(distances)()) | ||
| tree1 = trees₊[k] | ||
| for (m, tree2) in trees₋ | ||
| # Internal method of `dataset_distance` for non-brute way | ||
| d = dataset_distance(A, a₋[m], method, tree1, tree2) | ||
| distances[k][m] = d | ||
| end | ||
| end | ||
| return distances | ||
| end | ||
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| function _datasets_sets_distances!(distances, a₊, a₋, f::Function) | ||
| @inbounds for (k, A) in pairs(a₊) | ||
| distances[k] = pairs(valtype(distances)()) | ||
| for (m, B) in pairs(a₋) | ||
| distances[k][m] = f(A, B) | ||
| end | ||
| end | ||
| return distances | ||
| end |
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| using Test, DelayEmbeddings | ||
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| println("\nTesting Dataset distance...") | ||
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| @testset "Dataset Distances" begin | ||
| d1 = float.(range(1, 10; length = 11)) | ||
| d2 = d1 .+ 10 | ||
| @test dataset_distance(Dataset(d1), Dataset(d2)) == 1.0 | ||
| @test dataset_distance(Dataset(d1), Dataset(d2); brute = false) == 1.0 | ||
| @test dataset_distance(Dataset(d1), Dataset(d2); brute = true) == 1.0 | ||
| @test dataset_distance(Dataset(d1), Dataset(d2), Hausdorff()) == 10.0 | ||
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| d1 = Dataset([SVector(0.0, 1)]) | ||
| d2 = Dataset([SVector(1.0, 2)]) | ||
| @test dataset_distance(d1, d2, Chebyshev()) == 1.0 | ||
| d2 = Dataset([SVector(1.0, 2), SVector(1.0, 3)]) | ||
| @test dataset_distance(d1, d2, Hausdorff(Chebyshev())) == 2.0 | ||
| end | ||
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| @testset "Sets of Dataset Distances" begin | ||
| d1 = range(1, 10; length = 11) | ||
| d2 = d1 .+ 10 | ||
| d3 = d2 .+ 10 | ||
| set1 = Dataset.([d1, d2, d3]) | ||
| r = range(1, 10; length = 11) | ||
| D = 6 | ||
| makedata = x -> (y = zeros(D); y[1] = x; y) | ||
| d1 = Dataset([makedata(x) for x in r]) | ||
| d2 = Dataset([makedata(x+10) for x in r]) | ||
| d3 = Dataset([makedata(x+20) for x in r]) | ||
| set2 = Dataset.([d1, d2, d3]) | ||
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| @testset "$method" for method in (Euclidean(), Hausdorff()) | ||
| for set in (set1, set2) | ||
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| offset = method isa Hausdorff ? 9 : 0 | ||
| dsds = datasets_sets_distances(set, set, method) | ||
| for i in 1:3 | ||
| @test dsds[i][i] == 0 | ||
| end | ||
| @test dsds[2][1] == dsds[2][3] == 1 + offset | ||
| @test dsds[3][1] == dsds[1][3] == 11 + offset | ||
| end | ||
| end | ||
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| @testset "user function" begin | ||
| d4 = d3[1:3] | ||
| set3 = Dataset.([d1, d2, d4]) | ||
| f = (d1, d2) -> abs(length(d1) - length(d2)) | ||
| dsds = datasets_sets_distances(set3, set3, f) | ||
| @test dsds[2][3] == dsds[3][2] == 8 | ||
| @test dsds[2][1] == dsds[1][2] == 0 | ||
| end | ||
| end |
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