tda-mapper

This Python package provides a simple and efficient implementation of Mapper algorithm.

• Installation: pip install tda-mapper

• Documentation: https://tda-mapper.readthedocs.io/en/main/

About Mapper

The Mapper algorithm is a well-known technique in the field of topological data analysis that allows data to be represented as a graph. Mapper is used in various fields such as machine learning, data mining, and social sciences, due to its ability to preserve topological features of the underlying space, providing a visual representation that facilitates exploration and interpretation. For an in-depth coverage of Mapper you can read the original paper.

Step 1	Step 2	Step 3	Step 4
Chose a lens	Cover the image of the lens	Perform clustering on the pullback cover	Build the Mapper graph

Usage

Here you can find an example to use to kickstart your analysis. In this toy-example we use a two-dimensional dataset of two concentric circles. The Mapper graph is a topological summary of the whole point cloud.

import numpy as np

from sklearn.datasets import make_circles
from sklearn.decomposition import PCA
from sklearn.cluster import DBSCAN

from tdamapper.core import MapperAlgorithm
from tdamapper.cover import CubicalCover
from tdamapper.plot import MapperPlot

X, y = make_circles(                # load a labelled dataset
    n_samples=5000,
    noise=0.05,
    factor=0.3,
    random_state=42)
lens = PCA(2).fit_transform(X)

mapper_algo = MapperAlgorithm(
    cover=CubicalCover(
        n_intervals=10,
        overlap_frac=0.3),
    clustering=DBSCAN())
mapper_graph = mapper_algo.fit_transform(X, lens)

mapper_plot = MapperPlot(
    X, mapper_graph,
    colors=y,                       # color according to categorical values
    cmap='jet',                     # Jet colormap, for classes
    agg=np.nanmean,                 # aggregate on nodes according to mean
    dim=2,
    iterations=60,
    seed=42)
fig_mean = mapper_plot.plot(
    width=600,
    height=600)
fig_mean.show(config={'scrollZoom': True})

fig_std = mapper_plot.with_colors(  # reuse the plot with the same positions
    colors=y,
    cmap='viridis',                 # viridis colormap, for ranges
    agg=np.nanstd,                  # aggregate on nodes according to std
).plot(
    width=600,
    height=600)
fig_std.show(config={'scrollZoom': True})

Dataset	Mapper graph (average)	Mapper graph (deviation)