Mapper-like algorithms from Topological Data Analysis, implemented in Julia.

• Classical Mapper: Filter function + interval covering + DBSCAN clustering + nerve graph
• Ball Mapper: Landmark-based covering with epsilon balls
• Generic Mapper Pipeline: Pluggable cover, refiner, and nerve strategies via abstract interfaces
• Built on MetricSpaces.jl: Re-exports all metric space operations (point clouds, distances, sampling)

using Pkg
Pkg.add("TDAmapper")

using TDAmapper
using TDAmapper.ImageCovers, TDAmapper.IntervalCovers, TDAmapper.Refiners

# Generate a point cloud on a circle
X = sphere(1000, dim=2)

# Use x-coordinate as filter function
fv = first.(X)

# Create image covering: 10 overlapping intervals
ic = R1Cover(fv, Uniform(length=10, expansion=0.3))

# Run mapper with DBSCAN clustering
M = classical_mapper(X, ic, DBscan(radius=0.1))

# M.g is the mapper graph, M.C is the covering (index vectors)
println(M)  # "Mapper graph with N vertices and M edges"

using TDAmapper

# Generate data on a torus
X = torus(2000)

# Select 100 landmarks via farthest point sampling
L = farthest_points_sample_ids(X, 100)

# Build ball mapper with radius 0.8
M = ball_mapper(X, L, 0.8)

The mapper pipeline has three pluggable stages:

1. Cover (AbstractCover): How to partition/cover the data

   • R1Cover: Pullback of intervals via a filter function
   • EpsilonBall: Balls of fixed radius around landmarks

2. Refiner (AbstractRefiner): How to cluster within each cover element

   • DBscan: DBSCAN clustering
   • Trivial: No clustering (all points in one cluster)

3. Nerve (AbstractNerve): How to build the graph

   • SimpleNerve: Edge between overlapping cover elements

All mapper functions return a Mapper struct:

• M.X: The original metric space
• M.C: The covering as Vector{Vector{Int}} (indices into M.X)
• M.g: The nerve graph (from Graphs.jl)

• Singh, G., Memoli, F., & Carlsson, G. (2007). Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. Eurographics Symposium on Point-Based Graphics.
• Dlotko, P. (2019). Ball Mapper: A Shape Summary for Topological Data Analysis. arXiv:1901.07410.

• MetricSpaces.jl: Foundation layer for metric spaces and distances
• TDAplots.jl: Visualization of mapper graphs

MIT License