Multiscale Clustering Bifiltration (MCbiF)

Code for the ICLR 2026 conference paper "MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology" by Juni Schindler and Mauricio Barahona: https://openreview.net/forum?id=E7D6uybODJ

Installation

Clone the repository and open the folder in your terminal.

git clone https://github.com/barahona-research-group/MCbiF.git
cd MCF/

Then, to install the package with pip, execute the following command:

pip install .

To install the package with support for optimial Sankey diagram plotting execute instead:

pip install ."[sankey]" 

To also install all dependencies for the experiments, execute:

pip install ."[experiments]" 

Note that this package requires an installation of the the Rivet software for multiparameter persistent homology. Installation instructions are available here: https://rivet.readthedocs.io/en/latest/installing.html

Experiments

The \experiments directory contains code for our three experiments:

• Regression Task: Minimimal Crossing Number of Sankey Layout
• Classification Task: Non-Order Preserving Sequences of Partitions
• Application to Real-World Temporal Contact Data of Free-Ranging House Mice

Cite

Please cite our paper if you use this code in your own work:

@inproceedings{schindlerMCbiFMeasuringTopological2026,
  author = {Schindler, Juni and Barahona, Mauricio},
  title = {MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology},
  booktitle = {The Fourteenth International Conference on Learning Representations},
  year = {2026},
  url = {https://openreview.net/forum?id=E7D6uybODJ}
  doi = {10.48550/arXiv.2510.14710}
}

Licence

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.