Aleph is a C++ library for exploring and extending usages of persistent homology. Its main goal is to provide users with a versatile, simple-to-use implementation that quickly permits building prototype applications.
Aleph is inspired by DIPHA and
PHAT. In particular, Aleph
borrowed the idea of keeping the representation of a boundary matrix
separate from the implementation.
For more information, please read the original paper describing
PHAT.
Since its inception in late 2016, Aleph has been used to support the following papers:
- Clique Community Persistence: A Topological Visual Analysis Approach for Complex Networks
- Persistence Concepts for 2D Skeleton Evolution Analysis
- Hierarchies and Ranks for Persistence Pairs
- Shall I compare thee to a network?—Visualizing the Topological Structure of Shakespeare’s plays
Please refer to the list of publications in the documentation of Aleph for more details. The documentation covers how to reproduce a subset of the results reported in the papers above.
If you want to contribute, please see the contribution guidelines for more details.
Aleph contains numerous algorithms and helper classes that simplify working with persistent homology. Here is a brief selection of the most important ones:
- Easy-to-use and expressive simplex and simplicial complex class
- Support for different input formats to read simplicial complexes from
a variety of input files
- 1D functions
- Edge lists
- GraphML
- GML
- HDF5
- Lexicographic triangulations
- Matrices
- NET (Pajek graphs)
- PLY
- VTK
- Standard algorithm and twisted reduction algorithm for calculating persistent homology
- Support for dualized variants of both algorithms
- Support for different boundary matrix representations
- Persistence diagram class
- Distance and kernel measures
- Bottleneck distance
- Multi-scale smoothing kernel
- Wasserstein distance
- Algorithms for computing intersection homology and persistent intersection homology
- Basic support for Čech complexes
- Support for Dowker complexes
Documentation of the main
features, including some tutorials, is available on GitHub. If you want
to delve into the code, the examples subdirectory is a good starting
point.
Aleph uses the MIT license. Please see the file LICENSE.md
in the main directory of the repository for more details.
- A recent C++ compiler with support for C++11
CMake, preferably a recent version >= 3.2- Several
Boostdependencies for some of the data structures:Boost.FunctionalBoost.IteratorBoost.MultiIndex
Eigen3for some auxiliary mathematical functionsFLANNfor fast nearest-neighbour queriesHDF5for parsingHDF5input filespybind11for building the Python bindingsRapidJSONfor parsing JSON input filesTinyXML2for parsing GraphML input files
Aleph is meant to be used as a header-only library on top of which you can develop your own projects based on persistent homology. However, Aleph ships with numerous unit tests, some example programs, and tools required for my current research. For building them, please clone the repository to some local directory on your computer. Running the following commands within this directory should be sufficient in most cases:
$ mkdir build
$ cd build
$ cmake ../
$ make
It is advisable to test that Aleph works correctly on your system, so you can run the unit tests with:
$ make test
Please submit any issues you may encounter.
For more information, including how to run tests, please refer to the detailed build instructions in the documentation.
If you want to install Aleph from source, simply issue
$ make install
from the compilation directory. In general, this will require root
privileges, unless you change the CMAKE_INSTALL_PREFIX variable to
a local directory.
It is easier to install Aleph as a package. Currently, only packages for Arch Linux are available. Use your favourite AUR helper tool for installing Aleph:
$ pacaur -S aleph-git # pacaur (deprecated)
$ trizen -S aleph-git # trizen
$ yaourt -S aleph-git # yaourt
If you want to volunteer and submit a package for your favourite Linux distribution, please take a look at issue #27 and add your comments.
If your build instructions are configured to build the Python bindings,
i.e. BUILD_PYTHON_BINDINGS follow these instructions to install them:
$ cd build/bindings/python/aleph
$ python3 setup.py install
Note that this uses the old setuptools approach for installing the
package. A simpler installation based on pip is forthcoming.
For general discussion, questions, and comments, please contact the principal developer and maintainer Bastian Rieck ([email protected]).
The following people have contributed code to Aleph:
- ExpectationMax (Max Horn): fixes and improvements to the Python bindings
- Filco306 (Filip Cornell):
pybind11documentation, Docker tutorial - macjohnny (Esteban Gehring): documentation updates
- Pseudomanifold (Bastian Rieck): principal developer
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