Overview
Co-clustering algorithms aim to identify homogeneous sub-matrices within a dyadic data matrix, such as a document-word matrix. These algorithms can be formulated as a non-negative matrix tri-factorization problem, where X ≈ FSGT, subject to non-negativity constraints on all factor matrices and orthogonality constraints on the row-coefficient matrix F and the column-coefficient matrix G.
Most existing approaches are based on Euclidean distance or Kullback-Leibler divergence and do not include explicit parameters for controlling orthogonality. In this work, we introduce orthogonality parameters by adding two penalty terms to an α-divergence-based objective function. The proposed orthogonal parametric non-negative matrix tri-factorization method controls the orthogonality of the row and column spaces separately.
Finally, the proposed algorithms are compared with existing co-clustering methods on six real-world text datasets.
The official implementation is available in the NMTFcoclust GitHub repository.
Publication
Title: Orthogonal Parametric Non-negative Matrix Tri-Factorization with α-Divergence for Co-clustering
Authors: Saeid Hoseinipour, Mina Aminghafari, Adel Mohammadpour
Journal: Expert Systems with Applications
Year: 2023
Paper DOI: https://doi.org/10.1016/j.eswa.2023.120680
Software and Code
Repository: https://github.com/Saeidhoseinipour/NMTFcoclust
Associated paper DOI: https://doi.org/10.1016/j.eswa.2023.120680
Software archive: https://zenodo.org/records/21093166
Zenodo DOI: https://doi.org/10.5281/zenodo.21093166
Version: v1.0.0
Links
How to Cite
Hoseinipour, S., Aminghafari, M., Mohammadpour, A. Orthogonal Parametric Non-negative Matrix Tri-Factorization with α-Divergence for Co-clustering. Expert Systems with Applications, 2023. DOI: 10.1016/j.eswa.2023.120680 .
@article{Saeid_OPNMTF_2023,
title = {Orthogonal Parametric Non-negative Matrix Tri-Factorization with α-Divergence for Co-clustering},
author = {Hoseinipour, Saeid and Aminghafari, Mina and Mohammadpour, Adel},
journal = {Expert Systems with Applications},
volume = {231},
pages = {120680},
year = {2023},
doi = {10.1016/j.eswa.2023.120680}
url = {https://doi.org/10.1016/j.eswa.2023.120680}
}AI Summary
This work presents a co-clustering method that identifies homogeneous sub-blocks within dyadic data matrices, such as document-word matrices. The approach is formulated as a non-negative matrix tri-factorization problem (X ≈ FSGT) that imposes both non-negativity and orthogonality constraints. Unlike existing methods that rely on Euclidean distance or Kullback-Leibler divergence without controlling orthogonality, we introduce two penalty terms into an α-divergence-based objective, enabling separate control over the orthogonality of the row and column spaces. The proposed algorithm is validated against existing co-clustering methods on six real-world text datasets, with an official implementation available in the NMTFcoclust GitHub repository.