# Support matrix machine: A review

arXiv: https://arxiv.org/abs/2310.19717 · HTML: https://mlsanity.com/paper/2310.19717/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 174 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 3 of 3)

- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)
- [The Matrix Hilbert Space and Its Application to Matrix Learning](https://mlsanity.com/paper/1706.08110/) (2017)
- [Geometric feature performance under downsampling for EEG classification tasks](https://mlsanity.com/paper/2102.07669/) (2021)

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

- [Enhancing Multiview Synergy: Robust Learning by Exploiting the Wave Loss Function with Consensus and Complementarity Principles](https://mlsanity.com/paper/2408.06819/) (2024)
- [GL-TSVM: A robust and smooth twin support vector machine with guardian loss function](https://mlsanity.com/paper/2408.16336/) (2024)
- [Heaviside Low-Rank Support Matrix Machine](https://mlsanity.com/paper/2603.00491/) (2026)

## Abstract (arXiv)

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm.