This code implements the Sparse-TDA method that integrates QR pivoting-based sparse sampling algorithm into persistence images to transform topological features into image pixels and identify discriminative pixel samples in the presence of noisy and redundant information.

Pipeline of Sparse-TDA method for multi-way classification

Please cite the following paper if you make use of the code.

@article{guo2018sparse,
  title={Sparse-TDA: Sparse realization of topological data analysis for multi-way classification},
  author={Guo, Wei and Manohar, Krithika and Brunton, Steven L and Banerjee, Ashis G},
  journal={IEEE Transactions on Knowledge and Data Engineering},
  volume={30},
  number={7},
  pages={1403--1408},
  year={2018},
  publisher={IEEE}
}

• Setup
  • Compiling DIPHA
  • Additional 3rd party tools
  • Compiling dipha-pss (optional)
• Usage

First, clone this repository and all the submodules via

git clone https://github.com/w-guo/Sparse-TDA.git
cd Sparse-TDA
git submodule update --init --recursive   

The persistence diagrams (PDs) are computed using DIPHA which requires MPI support. You can install, e.g., OpenMPI. On MacOS, this can be simply done via

brew install open-mpi

Once this has finished, change into the code/external/dipha directory and create a build directory, then use cmake to configure the build process, e.g.,

cd code/external/dipha
mkdir build
cd build
cmake ..
make

For the full pipeline to work, we also need

1. libsvm
2. PersistenceImages (nonlinear weighting function is added to our fork)
3. iso2mesh
4. (Scale-Invariant) Heat-Kernel Signature
5. Completed Local Binary Pattern

where libsvm, PersistenceImages and iso2mesh should have been downloaded during the git submodule update into code/external. Please follow the libsvm documentation on how to compile the MATLAB interface. Then download the last two packages and put them under code/external.

This repository also contains the code for the persistence scale space (PSS) kernel method that is used for comparison in our paper. The core code for computing the kernel is provided by Roland Kwitt, and we include a copy under code. In case you want to replicate the results using the PSS kernel method, you also need to compile dipha-pss via

cd code/dipha-pss
mkdir build
cd build
cmake ..
make

Create a data folder under this repository. The data sets used in our paper can be found at

• Download SHREC14
• Download Outex_TC_00000

Unpack the downloaded datasets to /data. The essential results from our paper can be reproduced by the main scripts in the SHREC and Outex folders

• run_*_kernel.m
• run_*_sparse.m
• run_*_sparse_multiple_samples.m

For example, if you want to generate the results from the Outex data set using the Spase-TDA method in Table 1 & 2, just run

cd code/matlab
setup % load required packages
cd Outex
run_Outex_sparse