Pairwise Perturbation for Tensor Decomposition

Pairwise Perturbation (PP) is an efficient numerical algorithm for alternating least squares (ALS) in CP and Tucker decompositions.

PP uses perturbative corrections to the ALS subproblems rather than recomputing the tensor contractions.

This repository implements PP in C++, and is based on the parallel numerical library Cyclops Tensor Framework.

Building

To correctly run the code, CTF should be installed at first. See CTF repository for detailed instructions.

Modify config.mk based on your local information.

Run coil-100 real data test:

Use the scripts in the script folder as follows to download the coil-100 dataset and change the data into binary file:

./get_coil.sh
python imageloader.py

Then run test_ALS with following command:

mpirun n -model CP -tensor o1 -pp 0 -dim 4 -rank 10 -maxiter 250

Run time-lapse real data test:

Use the scripts in the script folder as follows to download the time-lapse dataset and change the data into binary file:

./get_time_lapse.sh
./unzip_time_lapse.sh
python matloader.py

Then run test_ALS with following command:

mpirun n -model CP -tensor o2 -pp 0 -dim 4 -rank 10 -maxiter 250

Benchmark experiments and tests on synthetic data

Commands for these tests are in script_strongscaling.py, script_weakscaling.py, script_synthetic.py, script_real.py in the script folder.

Visualization with Visdom

For now visdom can fetch all the csv files following the particular format and plot them.

Go to the Visdom folder then execute the following commands:

visdom -port XXXXX

python visdom_pull_server.py -port XXXXX

Acknowledging Usage

The source code is available to everyone. If you would like to acknowledge the usage of the code, please cite the following paper:

Linjian Ma and Edgar Solomonik; Accelerating Alternating Least Squares for Tensor Decomposition by Pairwise Perturbation; arXiv:1811.10573 [math.NA], November 2018.