Using a distance matrix

Generating data

For this example we will generate evenly distributed points on a circle then compute the distance matrix of those points. In practice it makes little sense to go through this song and dance unless your data is given as a distance matrix.

import matplotlib.pyplot as plt
import numpy as np
from sklearn.metrics import pairwise_distances

theta = np.linspace(0, 2 * np.pi, 50)
circle = np.c_[np.cos(theta), np.sin(theta)]
data = pairwise_distances(circle)

plt.matshow(data)
plt.show()

Projecting our data

From here we will pretend that we don’t know the underlying data which generated the distance matrix. We pick [MDS](https://scikit-learn.org/stable/modules/generated/sklearn.manifold.MDS.html) as our lense function as it plays nicely with distance matrices.

from sklearn.manifold import MDS

projection: np.ndarray = MDS(
    n_components=1,
    metric="precomputed",
    n_init=1,  # type: ignore
    init="classical_mds",
).fit_transform(data)

plt.scatter(circle[:, 0], circle[:, 1], label="data")
plt.scatter(projection, np.zeros_like(projection), label="projection")
plt.legend()
plt.show()

Defining a clusterer

This is the last place where we need to do something different to facilitate running mapper on a distance matrix. All we have to do is tell the base clusterer that the metric is precomputed. From there the adapter should be clever enough to detect this fact.

from sklearn.cluster import AgglomerativeClustering

import zen_mapper as zm

sk = AgglomerativeClustering(
    linkage="single",
    n_clusters=None,  # type: ignore
    distance_threshold=0.2,
    metric="precomputed",
)
clusterer = zm.sk_learn(sk)

Computing the mapper graph

cover_scheme = zm.Width_Balanced_Cover(n_elements=3, percent_overlap=0.4)

result = zm.mapper(
    data=data,
    projection=projection,
    cover_scheme=cover_scheme,
    clusterer=clusterer,
    dim=1,
)

Visualizing the mapper graph

import networkx as nx

graph = zm.to_networkx(result.nerve)
nx.draw(graph)