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DADApy is a Python package for the characterization of manifolds in high-dimensional spaces.

Homepage

For more details and tutorials, visit the homepage at: https://dadapy.readthedocs.io/

Quick Example

import numpy as np
from dadapy.data import Data

# Generate a simple 3D gaussian dataset
X = np.random.normal(0, 1, (1000, 3))

# initialize the "Data" class with the set of coordinates
data = Data(X)

# compute distances up to the 100th nearest neighbor
data.compute_distances(maxk=100)

# compute the intrinsic dimension using 2nn estimator
id, id_error, id_distance = data.compute_id_2NN()

# compute the intrinsic dimension up to the 64th nearest neighbors using Gride
id_list, id_error_list, id_distance_list = data.return_id_scaling_gride(range_max=64)

# compute the density using PAk, a point adaptive kNN estimator
log_den, log_den_error = data.compute_density_PAk()

# find the peaks of the density profile through the ADP algorithm
cluster_assignment = data.compute_clustering_ADP()

# compute the neighborhood overlap with another dataset
X2 = np.random.normal(0, 1, (1000, 5))
overlap_x2 = data.return_data_overlap(X2)

# compute the neighborhood overlap with a set of labels
labels = np.repeat(np.arange(10), 100)
overlap_labels = data.return_label_overlap(labels)

Currently implemented algorithms

• Intrinsic dimension estimators

• Two-NN estimator

  Facco et al., Scientific Reports (2017)

• Gride estimator

  Denti et al., Scientific Reports (2022)

• I3D estimator (for both continuous and discrete spaces)

  Macocco et al., Physical Review Letters (2023)

• BID estimator

  Acevedo et al., Nature Communications Physics (2025)

• Density estimators

• kNN estimator

• k*NN estimator (kNN with an adaptive choice of k)

• PAk estimator

  Rodriguez et al., JCTC (2018)

• point-adaptive mean-shift gradient estimator

  Carli et al., ArXiv (2024)

• BMTI estimator

  Carli et al., ArXiv (2024)

• Density peaks clustering methods

• Density peaks clustering

  Rodriguez and Laio, Science (2014)

• Advanced density peaks clustering

  d’Errico et al., Information Sciences (2021)

• k-peak clustering

  Sormani, Rodriguez and Laio, JCTC (2020)

• Manifold comparison tools

• Neighbourhood overlap

  Doimo et al., NeurIPS (2020)

• Information imbalance

  Glielmo et al., PNAS Nexus (2022)

• Feature selection and weighting tool

• Differentiable Information Imbalance

  Wild et al., Nature Communications (2025)

• Causal analysis tools

• Imbalance Gain

  Del Tatto et al., PNAS (2024)

• Community causal graph

  Allione et al., arXiv (2025)

Installation

The package is compatible with the Python versions 3.8, 3.9, 3.10, 3.11, and 3.12. The methods of the classes DiffImbalance and CausalGraph are only compatible with Python>=3.9. We currently only support Unix-based systems, including Linux and macOS. For Windows machines, we suggest using the Windows Subsystem for Linux (WSL).

The package requires numpy, scipy, scikit-learn, jax, jaxlib and matplotlib for the visualizations.

The package contains Cython-generated C extensions that are automatically compiled during installation.

The latest release is available through pip:

pip install dadapy

To install the latest development version, clone the source code from GitHub and install it with pip as follows:

pip install git+https://github.com/sissa-data-science/DADApy

Alternatively, if you'd like to modify the implementation of some function locally you can download the repository and install the package with:

git clone https://github.com/sissa-data-science/DADApy.git
cd DADApy
python setup.py build_ext --inplace
pip install .

The methods of the classes DiffImbalance and CausalGraph can be run on GPU, using a suitable installation of JAX on a GPU platform. The code has been tested using JAX v0.4.30 with CUDA 12, which can be installed with:

pip install --upgrade "jax[cuda12_pip]==0.4.30" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html

For more information on the installation of the JAX library on GPUs see the official repository.

Citing DADApy

A description of the package is available here.

Please consider citing it if you found this package useful for your research:

@article{dadapy,
    title = {DADApy: Distance-based analysis of data-manifolds in Python},
    journal = {Patterns},
    pages = {100589},
    year = {2022},
    issn = {2666-3899},
    doi = {https://doi.org/10.1016/j.patter.2022.100589},
    url = {https://www.sciencedirect.com/science/article/pii/S2666389922002070},
    author = {Aldo Glielmo and Iuri Macocco and Diego Doimo and Matteo Carli and Claudio Zeni and Romina Wild and Maria d’Errico and Alex Rodriguez and Alessandro Laio},
    }