基于模糊隶属度的最优间隔分布矩阵分类器  

Optimal-margin Distribution Matrix Classifier Based on Fuzzy Membership

作　　者：江山 杨金瑞 武士裕 张里博 杨帆 JIANG Shan;YANG Jinrui;WU Shiyu;ZHANG Libo;YANG Fan(College of Computer and Information Science,Southwest University,Chongqing 400715,China;College of Artificial Intelligence,Southwest University,Chongqing 400715,China;Chongqing Education Information Technology and Equipment Center,Chongqing 400020,China)

机构地区：[1]西南大学计算机与信息科学学院,重庆400715 [2]西南大学人工智能学院,重庆400715 [3]重庆市教育信息技术与装备中心,重庆400020

出　　处：《西南大学学报(自然科学版)》2025年第4期230-238,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家重点研发计划项目(2021YFB 3101500);国家自然科学基金项目(62106205);大学生创新创业训练计划资助项目(S20241063028)。

摘　　要：提出了一种模糊最优间隔分布矩阵分类器(Fuzzy Optimal-margin Distribution Matrix Classifier,FODMC)。该模型通过整合模糊隶属度理论与间隔分布优化机制,实现了矩阵结构信息的有效提取与异常值的鲁棒处理。具体而言,FODMC采用基于间隔分布的损失函数来优化分类边界,结合核范数正则化策略保持矩阵的低秩特性,并利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现模型的高效训练。在多个基准数据集上的实验结果表明:与现有方法相比,FODMC在分类准确率、鲁棒性和泛化能力等方面均展现出显著优势,为矩阵数据分类问题提供了一种有效的解决方案。This study proposes an innovative Fuzzy Optimal-margin Distribution Matrix Classifier(FODMC).The model integrates fuzzy membership theory with margin distribution optimization mechanisms to achieve effective extraction of matrix structural information and robust handling of outliers.Specifically,FODMC employs a margin distribution-based loss function to optimize classification boundaries,incorporates a nuclear norm regularization strategy to maintain the low-rank characteristics of matrices,and utilizes the Alternating Direction Method of Multipliers(ADMM)for efficient model training.Experimental results on multiple benchmark datasets demonstrated that compared to existing methods,FODMC showed significant advantages in classification accuracy,robustness,and generalization capability,providing an effective solution for matrix data classification problems.

关 键 词：机器学习 支持矩阵机 支持向量机 间隔分布 模糊隶属度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]