GBSVM（Granular-ball Support Vector Machine，粒球支持向量机）是一项重要尝试，它使用粒球的由粗到细的粒度作为输入，而不是单一数据点来构建分类器。它是首个输入不包含任何点的分类器。然而，现有模型存在一些错误，且其对偶模型尚未被推导出来。因此，当前算法无法被实现或应用。为了解决这些问题，本文修复了现有GBSVM原始模型的错误，并推导了其对偶模型。此外，设计了粒子群优化算法来求解对偶模型。同时，还精心设计了序列最小优化算法来求解对偶模型。该求解方法比基于粒子群优化的版本更快且更稳定。在UCI基准数据集上的实验结果表明，GBSVM具有良好的鲁棒性和效率。所有代码已在开源库中发布。
英文摘要：
GBSVM (Granular-ball Support Vector Machine) is a significant attempt to construct a classifier using the coarse-to-fine granularity of a granular-ball as input, rather than a single data point. It is the first classifier whose input contains no points. However, the existing model has some errors, and its dual model has not been derived. As a result, the current algorithm cannot be implemented or applied. To address these problems, this paper has fixed the errors of the original model of the existing GBSVM, and derived its dual model. Furthermore, a particle swarm optimization algorithm is designed to solve the dual model. The sequential minimal optimization algorithm is also carefully designed to solve the dual model. The solution is faster and more stable than the particle swarm optimization based version. The experimental results on the UCI benchmark datasets demonstrate that GBSVM has good robustness and efficiency. All codes have been released in the open source library at http://www.cquptshuyinxia.com/GBSVM.html or https://github.com/syxiaa/GBSVM.
Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method
Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, and Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications（重庆邮电大学计算智能重庆市重点实验室、网络空间大数据智能安全教育部重点实验室、大数据智能计算重点实验室）；College of Computer and Information Science, the National Center for Applied Mathematics in Chongqing, Chongqing Normal University（重庆师范大学计算机与信息科学学院、重庆国家应用数学中心）
Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, and the Key Laboratory of Big Data Intelligent Computing, College of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆计算智能重点实验室、网络大数据智能安全重点实验室、教育部、大数据智能计算实验室、计算机科学与技术学院、重庆邮电大学）；National Center for Applied Mathematics, Chongqing Normal University（应用数学国家中心、重庆师范大学）
MDL-GBG: A Non-parametric and Interpretable Granular-Ball Generation Method for Clustering
Department of Mathematics and Computer Science, Gannan Normal University（赣南师范大学数学与计算机科学学院）；Key Laboratory of Data Science and Artificial Intelligence of Jiangxi Education Institutes, Gannan Normal University（江西省教育研究院数据科学与人工智能重点实验室）；Department of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程学院）
Granular-Balls based Fuzzy Twin Support Vector Machine for Classification
School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；School of Information Science and Technology, Nantong University（南通大学信息科学与技术学院）；Department of Computer Science and Technology, Tongji University（同济大学计算机科学与技术系）
A Boundary-Aware Non-parametric Granular-Ball Classifier Based on Minimum Description Length
Department of Mathematics and Computer Science, Gannan Normal University（数学与计算机科学学院，赣南师范大学）；Key Laboratory of Data Science and Artificial Intelligence of Jiangxi Education Institutes, Gannan Normal University（江西省数据科学与人工智能重点实验室，赣南师范大学）；Department of Computer Science and Technology, Tongji University（计算机科学与技术学院，同济大学）；Department of Electrical and Computer Engineering, University of Alberta（电气与计算机工程学院，阿尔伯塔大学）
Open Continual Feature Selection via Granular-Ball Knowledge Transfer
School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics（西南财经大学计算机与人工智能学院）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；School of Computing and Artificial Intelligence, Southwest Jiaotong University（西南交通大学计算机与人工智能学院）
Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification
School of Computer Science and Technology, Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, Sichuan-Chongqing Co-construction Key Laboratory of Digital Economy Intelligence and Key Laboratory of Big Data Intelligent Computing（计算机科学与技术学院，重庆 computational intelligence 重点实验室，网络安全大数据智能安全重点实验室，教育部，四川-重庆共建数字经济智能重点实验室和大数据智能计算重点实验室）；School of Computer Science and Technology, School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications（计算机科学与技术学院，网络安全与信息法学院，重庆邮电大学）；Chongqing Key Laboratory of Brain-Inspired Cognitive Computing and Educational Rehabilitation for Children with Special Needs, Chongqing Normal University（脑启发认知计算与特殊儿童教育康复重庆重点实验室，重庆师范大学）
Sichuan University（四川大学）；Engineering Research Center of Machine Learning and Industry Intelligence, Ministry of Education（教育部机器学习与产业智能工程研究中心）；Beijing Academy of Agriculture and Forestry Sciences（北京市农林科学院）；Stevens Institute of Technology（史蒂文斯理工学院）
GAdaBoost: An Efficient and Robust AdaBoost Algorithm Based on Granular-Ball Structure
School of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院）；Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications（重庆邮电大学计算智能重点实验室）；Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education（教育部空天大数据智能安全重点实验室）；College of Computer and Information Science, Chongqing Normal University（重庆师范大学计算机与信息科学学院）
Robust Smart Contract Vulnerability Detection via Contrastive Learning-Enhanced Granular-ball Training
Chongqing Key Laboratory of Computational Intelligence（重庆计算智能重点实验室）；Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education（教育部网络空间大数据智能安全重点实验室）；Key Laboratory of Big Data Intelligent Computing（大数据智能计算重点实验室）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；School of Cyber Science and Engineering, Huazhong University of Science and Technology（华中科技大学网络空间安全学院）；School of Computer Science and Artificial Intelligence, Zhengzhou University（郑州大学计算机与人工智能学院）；College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）
Efficient Quantum Approximate $k$NN Algorithm via Granular-Ball Computing
School of Artificial Intelligence, Chongqing University of Posts and Telecommunications（重庆邮电大学人工智能学院）；School of Electronic Science and Engineering, Chongqing University of Posts and Telecommunications（重庆邮电大学电子科学与工程学院）；Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications（重庆邮电大学大数据智能计算重点实验室）；School of Computing, University of Otago（奥塔哥大学计算机学院）
Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training
Chongqing University of Posts and Telecommunications（重庆邮电大学）；Chongqing Normal University（重庆师范大学）；National Center for Applied Mathematics in Chongqing（重庆国家应用数学中心）
Fuzzy Granule Density-Based Outlier Detection with Multi-Scale Granular Balls
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）；National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University（深圳大学大数据系统计算技术国家工程实验室）；School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机科学学院）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Department of Electrical and Computer Engineering, King Abdulaziz University（阿卜杜勒阿齐兹大学电气与计算机工程系）；Department of Computer Engineering, Istinye University（伊斯提尼耶大学计算机工程系）
Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering
Department of Mathematics and Computer Science, Gannan Normal University（赣南师范大学数学与计算机科学学院）；Key Laboratory of Data Science and Artificial Intelligence of Jiangxi Education Institutes, Gannan Normal University（江西省教育研究院数据科学与人工智能重点实验室）
Generation of Granular-Balls for Clustering Based on the Principle of Justifiable Granularity
Dalian University of Technology（大连理工大学）；University of Alberta（阿尔伯塔大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Istinye University（伊斯提尼耶大学）
EvoSampling: A Granular Ball-based Evolutionary Hybrid Sampling with Knowledge Transfer for Imbalanced Learning
School of Computer Science and Technology, Dalian University of Technology（大连理工大学计算机科学与技术学院）；Key Laboratory of Social Computing and Cognitive Intelligence (Dalian University of Technology), Ministry of Education（社会计算与认知智能重点实验室（大连理工大学））；School of Engineering and Computer Science, Victoria University of Wellington（惠灵顿维多利亚大学工程与计算机科学学院）；Department of Computer Science, Hong Kong Baptist University（香港浸会大学计算机科学系）
Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization
Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, Sichuan-Chongqing Co-construction Key Laboratory of Digital Economy Intelligence and Key Laboratory of Big Data Intelligent Computing, College of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院，计算智能重庆市重点实验室，网络空间大数据智能安全教育部重点实验室，川渝共建数字经济智能重点实验室，大数据智能计算重点实验室）；Chongqing Ant Consumer Finance Co,. Ltd , Ant Group（蚂蚁集团，重庆蚂蚁消费金融有限公司）
A New Perspective on Privacy Protection in Federated Learning with Granular-Ball Computing
Southwestern University of Finance and Economics（西南财经大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；Southwest Jiaotong University（西南交通大学）
GBSK: Skeleton Clustering via Granular-ball Computing and Multi-Sampling for Large-Scale Data
College of Computer Science and Technology, Huaqiao University（华侨大学计算机科学与技术学院）；Fujian Provincial Key Laboratory of Computer Vision and Machine Learning, Huaqiao University（华侨大学计算机视觉与机器学习省级重点实验室）；Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education（教育部网络空间大数据安全重点实验室）；Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications（重庆邮电大学计算智能市级重点实验室）；Chongqing Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications（重庆邮电大学大数据智能计算市级重点实验室）；College of Computer and Information Science, Chongqing Normal University（重庆师范大学计算机与信息科学学院）；College of Big Data and Intelligent Engine（大数据与智能工程学院）
LGBQPC: Local Granular-Ball Quality Peaks Clustering
Institute of Systems Engineering, School of Economics and Management, Dalian University of Technology（大连理工大学系统工程学院经济管理学院）；Department of Measurement and Control Systems, Silesian University of Technology（桑特大学测量与控制系统系）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；Institute of Systems Engineering, Macau University of Science and Technology（澳门科学技术大学系统工程研究所）；Research Center of Performance and Productivity Analysis, Istinye University（Istinye大学绩效与生产力分析研究中心）
