# Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering

arXiv: https://arxiv.org/abs/2005.09229 · HTML: https://mlsanity.com/paper/2005.09229/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

## Built on by (most cited first, 3 of 3)

- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)
- [Initialization for Nonnegative Matrix Factorization: a Comprehensive Review](https://mlsanity.com/paper/2109.03874/) (2021)
- [Log-based Sparse Nonnegative Matrix Factorization for Data Representation](https://mlsanity.com/paper/2204.10647/) (2022)

## Abstract (arXiv)

In this paper, we propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step. In particular, projection matrices are sought under the guidance of building new data representations, such that the spatial information is retained and projections are enhanced by the goal of clustering, which helps construct optimal projection directions. Moreover, to exploit nonlinear structures of the data, manifold is constructed in the projected subspace, which is adaptively updated according to the projections and less afflicted with noise and outliers of the data and thus more representative in the projected space. Hence, seeking projections, building new data representations, and learning manifold are seamlessly integrated in a single model, which mutually enhance other and lead to a powerful data representation. Comprehensive experimental results verify the effectiveness of TS-NMF in comparison with several state-of-the-art algorithms, which suggests high potential of the proposed method for real world applications.