Topcat is Java library for computing and analyzing multiparameter persistence modules. It comes with a python interface and a jupyter notebook with examples of how to use it.
Input to Topcat can be given as either:
- a list of distance matrices and a list of filtration values for each parameter
- a multifiltered simplicial complex
The current implementation of Topcat has been inspired by Ulrich Bauers work on Ripser (http://ripser.org), where he uses the following optimizations (among others):
- computes the cohomology instead of homology,
- uses the combinatorial number system to index simplices,
- performs an implicit matrix reduction of the coboundary matrix .
We make heavy use of these techniques in Topcat to be able to handle millions of simplices.
A detailed description of the algorithms implemented in Topcat to compute the multiparameter persistence modules can be found in my master's thesis. A description of the theory of persistence contours, noise systems and the stable rank can be found in the following papers:
- "Multidimensional Persistence and Noise" by Scolamiero et al. (arXiv:1505.06929)
- "Stable Invariants for Multidimensional Persistence" by G and Chachólski (arXiv:1703.03632)
Future work:
- Make use of the Chunk reduction described in the paper ''Chunk Reduction for Multi-Parameter Persistent Homology'' by Fugacci and Kerber (arXiv:1812.08580),
- Implement multiparameter persistence landscapes as described in the paper ''Multiparameter Persistence Landscapes'' by Oliver Vipond (arXiv:1812.09935).
- Maven 2/3
- Java 7 or higher
- Python 2.7/3 (optional)
- py4j (optional)
In the project root folder, compile the java code with Maven using the following:
mvn clean install
The library can be accessed either within java or via the Python-interface.