Kumari Anuradha, Akhtar Mushir, Shah Rupal, Tanveer M
Department of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, 453552, Madhya Pradesh, India.
Department of Electrical Engineering, Indian Institute of Technology Indore, Simrol, Indore, 453552, Madhya Pradesh, India.
Neural Netw. 2025 Jan;181:106767. doi: 10.1016/j.neunet.2024.106767. Epub 2024 Oct 9.
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. SMM 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 and conclude the article by outlining potential future research avenues and possibilities that may motivate researchers to advance the SMM algorithm.
支持向量机（SVM）是机器学习领域中针对分类和回归问题研究最多的范式之一。它依赖于矢量化输入数据。然而，现实世界中的很大一部分数据以矩阵形式存在，通过将矩阵重塑为向量作为SVM的输入。重塑过程破坏了矩阵数据中固有的空间相关性。此外，将矩阵转换为向量会导致输入数据具有高维度，这会带来显著的计算复杂性。为了克服在对矩阵输入数据进行分类时的这些问题，提出了支持矩阵机（SMM）。它是为处理矩阵输入数据而量身定制的新兴方法之一。SMM通过使用谱弹性网属性（它是核范数和弗罗贝尼乌斯范数的组合）来保留矩阵数据的结构信息。本文首次对SMM模型的发展进行了深入分析，可供新手和专家全面总结参考。我们讨论了众多SMM变体，如鲁棒、稀疏、类别不平衡和多类分类模型。我们还分析了SMM的应用，并通过概述潜在的未来研究途径和可能性来结束本文，这些可能会激励研究人员推进SMM算法。
