# Deep Approximately Orthogonal Nonnegative Matrix Factorization for Clustering

arXiv: https://arxiv.org/abs/1711.07437 · HTML: https://mlsanity.com/paper/1711.07437/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2017.

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

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [A Unified Framework for Optimization-Based Graph Coarsening](https://mlsanity.com/paper/2210.00437/) (2022)
- [Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization](https://mlsanity.com/paper/2104.12289/) (2021)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods mostly use the only nonnegativity while ignoring task-specific features of data. In this paper, we propose a novel deep approximately orthogonal nonnegative matrix factorization method where both nonnegativity and orthogonality are imposed with the aim to perform a hierarchical clustering by using different level of abstractions of data. Experiment on two face image datasets showed that the proposed method achieved better clustering performance than other deep matrix factorization methods and state-of-the-art single layer NMF variants.