Subspace power method

An implementation of the subspace power method, in MATLAB and Python, for decomposing symmetric tensors, as described in

J. Kileel, J. M. Pereira, Subspace power method for symmetric tensor decomposition, arXiv:1912.04007

Matlab

Required External Packages

To compare performance with other tensor decomposition packages, and reproduce the results obtained in the paper, the users will have to install and download external packages themselves. An exception to this is the implementation of the FOOBI algorithm, from Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures, for which we did not find a MATLAB implementation, and implemented ourselves. If you need assistance setting this up, you can send an e-mail to [email protected]. A README for the installation of other packages may also be added in the future.
The following are required packages:

• TensorLAB

• Low rank Symmetric Tensor Approximations code

• GPCA-PDA (GPCA only)

• GPCA-Voting (GPCA only)

Installation

To install you just need to add the folders MATLAB\ and MATLAB\helper_functions\ to the MATLAB path. Alternatively, you may run the file MATLAB\setup.m.

Reproducibility

• To reproduce the results in Subspace power method for symmetric tensor decomposition, run the file MATLAB\tests\run_SPM_paper.m.

Python

Required Packages

• numpy
• scipy

Optional Package

• numba: This package provides a just-in-time pre-compiler that can considerably speed up SPM performance. It is used only if the numba package is installed.

Installation

To install you just need to copy the python files, and from SPM.py, import the method subspace_power_method. Additional methods (such as generate_lowrank_tensor) are also available which can be useful for testing SPM.