Dimensionality reduction techniques for order-3 tensors
Project description
tred
----
tred implements a range of order-3 tensor decompositions. Mathematically,
they rely on a novel tensor algebra introduced in [1]. Within this framework,
natural tensor analogues of SVD and PCA were recently formulated; these
decomposition techniques also have analytically proven optimality properties
that mirror those of their matrix counterparts.
The only top-level dependency, for an end user, is scikit-learn. We inherit from
their base classes, so tred's class API's should be natural to any past
scikit-learn users. tred's function API's also mirror scipy counterparts as much
as possible.
For the underlying tensor-product framework and tensor t-SVDM, see [1].
For the explicit rank truncation, and the TCAM algorithm, see [2].
Use
---
See examples folder for basic use.
tred is on PyPI, simply run
pip install --upgrade tred
To use the package.
tred is in active development. But, most of the existing implementations are
covered by unit tests, and we aim to keep the API relatively stable.
Users are highly encouraged to visit the GitHub site, and open issues.
Literature
----------
[1] Kilmer, M.E., Horesh, L., Avron, H. and Newman, E., 2021. Tensor-tensor
algebra for optimal representation and compression of multiway data. Proceedings
of the National Academy of Sciences, 118(28), p.e2015851118.
[2] Mor, U., Cohen, Y., Valdés-Mas, R., Kviatcovsky, D., Elinav, E. and Avron,
H., 2022. Dimensionality reduction of longitudinal’omics data using modern
tensor factorizations. PLoS Computational Biology, 18(7), p.e1010212.
NOTE: In literature, the authors use m, p, n as the dimensions of the tensors,
whereas throughout this package one will see we prefer n, p, t instead. We will
also use k = min(n, p), where from an `omics analysis perspective, typically
means k = n, as p >> n typically.
Development
-----------
For anyone who is interested in contributing to / modifying the package:
For development dependencies, invoke:
pip install -r requirements.txt
In the root to install all of the required packages for development.
To test any changes, invoke:
pytest .
In the root to run the tests in the test folder.
If opening pull requests, invoke:
black .
In the root to autoformat code.
Much of the implementation and code practice mirrors that of scikit-learn. We
adopt their utilities and general coding guidelines whenever we can.
For any interested contributors, please be very liberal in adding tests, both
for new and existing features.
Credit
------
Our implementation was inspired by analogues at
https://github.com/scikit-learn/scikit-learn
And also by
https://github.com/UriaMorP/mprod_package
Future
------
New experimental methods may be added to tred.
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