# Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering

arXiv: https://arxiv.org/abs/1608.04290 · HTML: https://mlsanity.com/paper/1608.04290/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2016.

## Built on by (most cited first, 28 of 28)

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- [Maximum-Volume Nonnegative Matrix Factorization](https://mlsanity.com/paper/2602.04795/) (2026)
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- [A Tractable Two-Step Linear Mixing Model Solved with Second-Order Optimization for Spectral Unmixing under Variability](https://mlsanity.com/paper/2502.17212/) (2025)
- [Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition](https://mlsanity.com/paper/2511.04291/) (2025)

## Abstract (arXiv)

This paper considers volume minimization (VolMin)-based structured matrix factorization (SMF). VolMin is a factorization criterion that decomposes a given data matrix into a basis matrix times a structured coefficient matrix via finding the minimum-volume simplex that encloses all the columns of the data matrix. Recent work showed that VolMin guarantees the identifiability of the factor matrices under mild conditions that are realistic in a wide variety of applications. This paper focuses on both theoretical and practical aspects of VolMin. On the theory side, exact equivalence of two independently developed sufficient conditions for VolMin identifiability is proven here, thereby providing a more comprehensive understanding of this aspect of VolMin. On the algorithm side, computational complexity and sensitivity to outliers are two key challenges associated with real-world applications of VolMin. These are addressed here via a new VolMin algorithm that handles volume regularization in a computationally simple way, and automatically detects and iteratively downweights outliers, simultaneously. Simulations and real-data experiments using a remotely sensed hyperspectral image and the Reuters document corpus are employed to showcase the effectiveness of the proposed algorithm.