EnAInem

EnAInem (pronounced /ɪˈneɪnəm/), is a Python class that implements state-of-the-art algorithms for decomposing nonnegative multiway array and multi-view data into rank-1 nonnegative tensors.

Motivation

In machine learning, multi-view data refers to datasets comprising multiple distinct attribute sets ("views") for the same set of observations. When these views share the same attributes but are observed in different contexts, the data can be represented as a tensor. EnAInem enables tensor decomposition using Non-Negative Tensor Factorization (NTF) and allows the integration of heterogeneous multi-view data into a shared latent space through the Integrated Sources Model (ISM).

Installation

EnAInem is distributed as a standalone Python file, which can be downloaded and installed at your convenience.

Dependencies

EnAInem has been tested with Python 3.11.9 and relies on the following libraries:

• NumPy 2.0.2 (Numerical computing)
• SciPy 1.13.1 (Scientific and technical computing)
• Matplotlib 3.9.4 (Visualizations)
• pandas 2.2.3 (Data manipulation and analysis)
• scikit-learn 1.6.0 (Machine learning)
• IPython 8.31.0 (Notebook interface)

All dependencies are listed in the requirements.txt file. To install them, run:

pip install -r requirements.txt to have them all installed in your python environment.

While EnAInem may work with other versions of these libraries or in older Python environments, these configurations have not been tested.

Usage

The API strictly follows scikit-learn standards:

1. Create an instance of EnAInem class.
2. EnAInem's fit_transform public method returns the decomposition in the form of a dictionary. The input type (multiway array or list of views) automatically routes fit_transform to either algorithm, NTF or ISM. See docstrings of the class and method for more details.

from enainem import EnAInem
enainem = EnAInem(n_components=n_components)
res = enainem.fit_transform(X)
B = res["B"]
relative_error = round(res["relative_error"], 4)
print(f"relative_error = {relative_error}")

Examples

Two simple examples (Python scripts) are provided:

• simple_ntf:
  • Generates a tensor X_gen from random basis vectors B_gen.
  • Adds random noise to X_gen with an intensity defined by the noise_coeff parameter.
  • Estimates the basis vectors B using the fit_transform method from EnAInem.
  • When the create_subplots parameter is set to True, visualizations show the association between the estimated base B and the original B_gen.
• simple_ism:
  • Generates a random non-negative matrix X_1.
  • Creates X_2 by swapping the columns of X_1 and adding noise.
  • Adds noise to X_1.
  • Applies fit_transform to the list of views {X_1, X_2} to recognize that both
    convey the same information (up to noise), with the columns of X_2 permuted.
  • When the create_subplots parameter is set to True, heatmaps visualize how the columns of X_1 and X_2 load onto ISM components, highlighting the effective permutation.

References and Credits

If you use EnAInem for array or multi-view processing, please cite the following papers:

• Cichocki, A., & Phan, A. (2009). Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations. IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 92-A, 708-721. https://doi.org/10.1587/transfun.E92.A.708
• Fogel, P., Geissler, C., Augé, F., Boldina, G., & Luta, G. (2024). Integrated sources model: A new space-learning model for heterogeneous multi-view data reduction, visualization, and clustering. Artificial Intelligence in Health. https://doi.org/10.36922/aih.3427

License

This project is licensed under the MIT License.

Authors

• Paul Fogel (paul.fogel@forvismazars.com)
• George Luta

Acknowledgements

scikit-learn

• EnAInem extends the BaseEstimator class of scikit-learn's base module, leveraging its parameter validation mechanisms.
• It also utilizes coordinate descent functions (_update_coordinate_descent and _update_cdnmf_fast), from the _nmf module implementing the fast HALS algorithm.

ForvisMazars

EnAInem is distributed through the R&D Forvis Mazars GitHub repository..