JuliaTDA.jl

JuliaTDA.jl is the umbrella package for the JuliaTDA ecosystem — a coherent toolkit for Topological Data Analysis in Julia. A single

using JuliaTDA

re-exports the whole stack: metric-space geometry, the Mapper algorithm, Makie-based plotting, persistent homology, persistence-diagram tooling / vectorizations, and ToMATo clustering.

The ecosystem

Package	Role	What it brings
MetricSpaces.jl	Geometry foundation	EuclideanSpace, distances, samplers, filters (eccentricity, kde, dtm_density, knn_density), transformations (center, scale, standardize, embed), geodesic_distance, nerve_1d/nerve_2d, and the Datasets submodule (sphere, torus, mammoth, …)
TDAmapper.jl	Mapper	mapper, classical_mapper, ball_mapper; cover / refiner / nerve submodules; the Tables.jl helpers euclidean_space and node_statistics
TDAplots.jl	Plotting (Makie)	mapper_plot, metricspace_plot, the interactive mapper_explorer, persistence / barcode plots, 21 graph layouts
Ripserer.jl	Persistent homology	ripserer, Rips, Alpha, Cubical, EdgeCollapsedRips, …
PersistenceDiagrams.jl	Diagrams & ML	PersistenceDiagram, Bottleneck, Wasserstein, Landscape, PersistenceImage, BettiCurve, entropy curves, MLJ integration
ToMATo.jl	Clustering	tomato, proximity_graph

How they compose

MetricSpaces  ──►  TDAmapper  ──►  TDAplots
                                      │
Ripserer  ──►  PersistenceDiagrams ◄──┘   (Ripserer re-exports the basics)

ToMATo  (density-based clustering, built on MetricSpaces)

Quick start

using JuliaTDA
# The Mapper building blocks live in submodules; bring them into scope:
using JuliaTDA.ImageCovers, JuliaTDA.IntervalCovers, JuliaTDA.Refiners, JuliaTDA.Nerves
using Statistics: mean

# Datasets are a submodule of MetricSpaces — access them qualified:
X = JuliaTDA.MetricSpaces.Datasets.sphere(500)   # 500 points on a circle

# A per-point eccentricity filter (high for outliers, low near the centre):
f = eccentricity(X)

# Run the classical Mapper and plot it, coloured by the filter:
M = classical_mapper(X, R1Cover(f, Uniform(length = 10, expansion = 0.3)),
                     DBscan(), SimpleNerve())
mapper_plot(M; node_values = [mean(f[c]) for c in M.C])

# Persistent homology of a point cloud:
dgms = ripserer(X)        # dgms[2] holds the H₁ (loop) features

Tables.jl integration (built in)

JuliaTDA depends on Tables directly, so TDAmapper's TDAmapperTablesExt extension is always loaded for umbrella users — no extra using Tables needed. Any Tables.jl source (a NamedTuple of columns, a DataFrame, CSV rows, …) works:

tbl = (x = randn(200), y = randn(200), z = randn(200), label = rand(["a","b"], 200))
X   = euclidean_space(tbl; cols = (:x, :y, :z), standardize = true)
M   = classical_mapper(X, R1Cover(eccentricity(X), Uniform(length = 8)),
                       DBscan(), SimpleNerve())
node_statistics(M, tbl; stats = (mean, std))   # per-node summary, one row per node

A note on knn_density

Both MetricSpaces and ToMATo export a function named knn_density, with different implementations. To keep using JuliaTDA unambiguous:

• the unqualified knn_density is MetricSpaces' version (the general-purpose density filter), reached through the TDAplots re-export chain;
• ToMATo's clustering-oriented variant stays available, fully qualified, as JuliaTDA.ToMATo.knn_density.

(Separately, MetricSpaces and Graphs both export eccentricity and center; JuliaTDA pins both unqualified names to the MetricSpaces meaning.)

Installation

Development install (now)

Until the pure-Julia packages are registered in the General registry, build the environment by develop-ing the sibling repositories from their GitHub URLs:

using Pkg
Pkg.develop([
    PackageSpec(url = "https://github.com/JuliaTDA/MetricSpaces.jl"),
    PackageSpec(url = "https://github.com/JuliaTDA/TDAmapper.jl"),
    PackageSpec(url = "https://github.com/JuliaTDA/TDAplots.jl"),
    PackageSpec(url = "https://github.com/JuliaTDA/Ripserer.jl"),
    PackageSpec(url = "https://github.com/JuliaTDA/PersistenceDiagrams.jl"),
    PackageSpec(url = "https://github.com/JuliaTDA/ToMATo.jl"),
])
Pkg.develop(PackageSpec(url = "https://github.com/JuliaTDA/JuliaTDA.jl"))

If you have the repositories checked out side by side locally, you can instead develop them by path:

using Pkg
for p in ("MetricSpaces", "TDAmapper", "TDAplots", "Ripserer",
          "PersistenceDiagrams", "ToMATo")
    Pkg.develop(PackageSpec(path = "../$(p).jl"))
end

The Manifest.toml is intentionally not committed, so each developer resolves against their own local checkouts / forks.

Registry install (later)

Once the ecosystem is registered, the dev incantation above collapses to a single line:

using Pkg; Pkg.add("JuliaTDA")

Documentation

Full documentation, including three worked examples (Mapper exploration, persistent homology for ML, and ToMATo clustering), lives at https://JuliaTDA.github.io/JuliaTDA.jl/.

License

MIT. See the individual packages for their respective licenses (Ripserer and PersistenceDiagrams originate from mtsch's upstream work).