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.

支持向量机（SVM）是机器学习中分类和回归问题中最研究的范例之一。矩阵格式的真实世界数据往往在 SVM 中通过将矩阵转化为向量的方式输入，但转化过程中会破坏矩阵数据中的空间关联性，并导致高维度的输入数据引入了显著的计算复杂度。为了克服这些问题，提出了支持矩阵机（SMM），该方法通过使用核范数和弗罗贝尼乌斯范数的光谱弹性网方法来保留矩阵数据的结构信息。本文首次深入分析了 SMM 模型的发展，可供初学者和专家使用的全面摘要。我们讨论了各种 SMM 变体，如鲁棒、稀疏、类别不平衡和多类别分类模型。我们还分析了 SMM 模型的应用，并通过概述潜在的未来研究方向和可能性来总结本文，以促使学术界推动 SMM 算法的发展。