legendre-decomposition-python

An implementation of Legendre Decomposition in Python.

Description

An implementation of the Legendre Decomposition[1] in Python(>=3.6), which is non-negative tensor decomposition method using information geometric formulation of the log-linear model which we can solve as a convex optimization problem.

This is not an official implementation and the author's implementation in C++ is available here [2].

Usage

import numpy as np
from ld import LegendreDecomposition

# generate third-order tensor.
P = np.random.rand(8, 5, 3)

# create an instance of Legendre Decomposition.
ld = LegendreDecomposition(solver='ng', max_iter=5)

# compute and get reconstructed tensors using scikit-learn like API.
reconst_tensor = ld.fit_transform(P)

LegendreDecomposition offers some options including the following:

• core_size : integer, default: 2

  • The parameter for a decomposition basis.

• solver : ng | gd, default: ng

  • Type of solver.
    • ng: natural gradient method.
    • gd: gradient descent method.

• tol : float, default: 1e-4

  • Tolerance of the stopping condition.

• max_iter : integer, default: 10

  • Maximum number of iterations before timing out.

• learning_rate : float, default: 0.1

  • The learning rate used in gradient descent method.

• random_state : int, RandomState instance, default=None

  • Used to randomize selection of a decomposition basis, when shuffle is set to True. Pass an int for reproducible results across multiple function calls. See :term:Glossary <random_state>.

• shuffle : boolean, default: False

  • If true, randomize selection of a decomposition basis.

• verbose : integer, default: 0

  • The verbosity level.

As of now, it doesn't support order of input tensor more than 4, means it supports second or third order.

Licence

MIT

References

[1] M. Sugiyama, H. Nakahara, K. Tsuda. Legendre Decomposition for Tensors. Advances in Neural Information Processing Systems 31(NeurIPS2018), pages 8825-8835, 2018.

[2] Legendre Decomposition implementaion in C++.