linjianma / fast_random_tensor_decompositions Goto Github PK

This library contains the implementation of the paper "Fast and accurate randomized algorithms for low-rank tensor decompositions".

Run

pip install -r requirements.txt

to install necessary packages.

Run

python run_als.py -h

to see the existing input arguments and their functions.

To run Tucker decomposition on the dense random tensor (tensor 1 or tensor 2 in the paper), run

python run_als.py --s 500 --R 5 --epsilon 0.25 --seed 1 --tensor random --hosvd 3 --decomposition Tucker --rank-ratio 1.2 --fix-percentage 0. --num-iter 10 --method Leverage

The input tensor will have size s x s x s, Tucker rank is based on --hosvd-core-dim, the sketch size is (R/epsilon)**2. --hosvd 0 means random initialization, 1 means initialize with HOSVD, and 3 means initialize with RRF detailed in the paper.

To run tensor 2 in the paper, set --tensor random_bias.

Method can be ALS, means the traditional ALS algorithm, or Leverage, meaning leverage score sampling (when setting --fix-percentage 0 it's random sampling, when setting --fix-percentage 1 it's deterministic sampling), or Tensorsketch, meaning using the TensorSketch algorithm, or Tensorsketch-ref, meaning running the algorithm proposed in Melik and Becker, NeurIPS 2018.

To run Tucker decomposition on the real image dataset, run

python run_als.py --R 5 --epsilon 0.25 --seed 1 --tensor coil100 --hosvd 3 --decomposition Tucker --fix-percentage 0. --num-iter 10 --method Leverage

where --tensor can also be timelapse.

To run Tucker decomposition on sparse random tensors (detailed in the appendix), run

python run_als.py --s 500 --R 5 --epsilon 0.25 --seed 1 --tensor random --hosvd 3 --decomposition Tucker_simulate --rank-ratio 1.2 --fix-percentage 0. --num-iter 10 --method Leverage --sparsity 0.2

where --sparsity denotes the p parameter in the paper.

To run CP decomposition on sparse random tensors, run

python run_als.py --s 500 --R 5 --epsilon 0.25 --seed 1 --tensor random --hosvd 3 --decomposition CP_simulate --rank-ratio 1.2 --fix-percentage 0. --num-iter 10 --method Leverage --sparsity 0.2

For this case, method can be ALS, meaning traditional ALS algorithm, or Leverage, meaning CP-ALS with leverage score sampling, or Tucker, meaning run the Tucker+CP algorithm, or Leverage_tucker, meaing run the leverage sampling based Tucker+CP algorithm.