12  Clustering with ToMATo

Let’s play with some known datasets.

12.1 Spiral dataset

Import data from this file and extract a subset of 10000 points

using DelimitedFiles, Random;
using AlgebraOfGraphics, GLMakie;
import GeometricDatasets as gd;
using ToMATo

X = readdlm("datasets/spiral.txt");
seed = MersenneTwister(0);
ids = rand(seed, 1:size(X)[1], 15_000)
X = X[ids, :]' |> Matrix;

X

2×15000 Matrix{Float64}:
 937.984  1517.26   814.057  1377.31   …  1343.56  1703.04   478.709  1406.98
 259.679   989.4   1721.36    242.761      485.03   928.448  611.633  1726.12

plot \(X\)

scatter(X)

calculate the density

ds = gd.density_estimation(X, h = 100)

df = (x1 = X[1, :], x2 = X[2, :], ds = ds)
plt = data(df) * mapping(:x1, :x2, color = :ds)
draw(plt)

plot it in 3d

axis = (type = Axis3, width = 800, height = 450)
df = (x1 = X[1, :], x2 = X[2, :], ds = ds)
plt = data(df) * mapping(:x1, :x2, :ds, color = :ds)
draw(plt; axis = axis)

calculate the proximity graph \(g\)

g = proximity_graph(
    X
    , epsilon_ball_or_knn(30, min_ball_points = 10, max_ball_points = 25, knn_points = 10)
    )

{15000, 150840} undirected simple Int64 graph

estimate \(\tau\)

_, births_and_deaths = tomato(X, g, ds, Inf)
plot_births_and_deaths(births_and_deaths)

choose \(\tau = 0.01\), calculate the ToMATo clustering

τ = 0.01
clusters, _ = tomato(X, g, ds, τ, max_cluster_height = τ);

and plot it

axis = (type = Axis, width = 800, height = 450)
df = (x1 = X[1, :], x2 = X[2, :], cluster = clusters .|> string)
plt = data(df) * mapping(:x1, :x2, color = :cluster)
draw(plt; axis = axis)

12.2 Toy example

The next example can be found in this link

X = readdlm("datasets/toy_example.txt");
X = X' |> Matrix;

X

2×10000 Matrix{Float64}:
 0.392345  5.40588  0.215228  2.55846  …  8.62843  2.99077  1.11412  5.19651
 1.24778   2.40142  1.26093   7.2899      9.36162  7.13162  8.71054  7.12939

scatter(X)

ds = gd.density_estimation(X, h = 0.5)

df = (x1 = X[1, :], x2 = X[2, :], ds = ds)
plt = data(df) * mapping(:x1, :x2, color = :ds)
draw(plt)

axis = (type = Axis3, width = 800, height = 450)
df = (x1 = X[1, :], x2 = X[2, :], ds = ds)
plt = data(df) * mapping(:x1, :x2, :ds, color = :ds)
draw(plt; axis = axis)

g = proximity_graph(
    X
    , epsilon_ball_or_knn(0.2, min_ball_points = 5, max_ball_points = 10, knn_points = 5)
    )

{10000, 68200} undirected simple Int64 graph

_, births_and_deaths = tomato(X, g, ds, Inf)
plot_births_and_deaths(births_and_deaths)

τ = 0.005
clusters, _ = tomato(X, g, ds, τ, max_cluster_height = τ);

axis = (type = Axis, width = 800, height = 450)
df = (x1 = X[1, :], x2 = X[2, :], cluster = clusters .|> string)
plt = data(df) * mapping(:x1, :x2, color = :cluster)
draw(plt; axis = axis)