旋转粒支持向量机分类器算法

Rotated granular support vector machine classifier algorithm

摘要

针对传统支持向量机在低维度非线性可分和大规模数据集上的计算复杂性问题,本文提出旋转粒支持向量机算法。该算法基于粒计算理论,通过旋转特征点构建旋转粒子,在多平面坐标系粒化构建旋转粒向量,并定义粒的大小、度量和运算规则。实验结果表明旋转粒支持向量机能够在较低的计算资源需求下应对分布复杂的数据,本文提出的旋转粒支持向量机算法效率高且分类效果好。

Abstract

To address the computational complexity challenges of traditional support vector machine on low-dimensional nonlinearly separable and large-scale datasets, a rotated granular support vector machine algorithm is proposed. Based on granular computing theory, rotated granular particles by rotating feature points and forms rotated granular vectors in a multi-plane coordinate system is constructed. Additionally, the size, measurement, and operational rules of the granules are defined. It is demonstrated that the rotated granular support vector machine can effectively handle complexly distributed data with lower computational resource requirements, is efficient and achieves good classification performance.

关键词

支持向量机 / 粒计算 / 粒支持向量机 / 模糊集 / 损失函数

Key words

support vector machine / granular computing / granular support vector machine / fuzzy sets / loss function

参考文献

[1] LIN T Y . Granular computing on binary relations I: data mining and neighborhood systems[J]. Rough Sets in Knowledge Discovery, 1998, 1(1): 107-121.

[2] ZADEH L A . Fuzzy sets[J]. Information and Control, 1965, 8(3): 338-353.

[3] WANG Y , ISHIBUCHI H , PEDRYCZ W , et al. Convolutional fuzzy neural networks with random weights for image classification[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024, 8(5): 3279-3293.

[4] HU Xingchen , QIN Jindong , SHEN Yinghua , et al. An efficient federated multiview fuzzy c—means clustering method[J]. IEEE Transactions on Fuzzy Systems, 2024, 32(4): 1886-1899.

[5] YAĞˇCI M . Educational data mining: prediction of students′ academic performance using machine learning algorithms[J]. Smart Learning Environments, 2022, 9(1): 11.

[6] LI X , ZHOU J , PEDRYCZ W . Linking granular computing, big data and decision making: a case study in urban path planning[J]. Soft Computing, 2020, 24(10): 7435-7450.

[7] GAO Can , ZHOU Jie , MIAO Duoqian , et al. Granular—conditional—entropy—based attribute reduction for partially labeled data with proxy labels[J]. Information Sciences, 2021, 580: 111-128.

[8] QIAN Jin , WANG Taotao , LU Yuehua , et al. A multi—granularity hesitant fuzzy linguistic decision making VIKOR method based on entropy weight and information transformation[J]. Journal of Intelligent & Fuzzy Systems, 2024, 46(3): 6505-6516.

[9] FU Xingyu , CHEN Yingyue , YAN Jingru , et al. BGRF: a broad granular random forest algorithm[J]. Journal of Intelligent & Fuzzy Systems, 2023, 44(5): 8103-8117.

[10] LI Wei , MA Xiaoyu , CHEN Yumin , et al. Random fuzzy granular decision tree[J]. Mathematical Problems in Engineering, 2021, 2021(1): 5578682.

[11] HE Linjie , CHEN Yumin , WU Keshou . Fuzzy granular deep convolutional network with residual structures[J]. Knowledge—Based Systems, 2022, 258: 109941.

[12] 陈玉明, 郑光宇, 焦娜 . 基于粒神经网络的多标签学习[J]. 山东大学学报(理学版), 2024, 59(5): 1-11.

[13] CHEN Yuming , ZHENG Guangyu , JIAO Na . Multi—label learning based on granular neural networks[J]. Journal of Shandong University(Natural Science), 2024, 59(5): 1-11.

[14] SULEYMANOV U , KALEJAHI B K , AMRAHOV E , et al. Text classification for Azerbaijani language using machine learning[J]. Computer Systems Science & Engineering, 2020, 35(6): 467-475.

[15] 张仰森, 彭媛媛, 段宇翔, 等 . 基于评论异常度的新浪微博谣言识别方法[J]. 自动化学报, 2020, 46(8): 1689-1702.

[16] ZHANG Yangsen , PENG Yuanyuan , DUAN Yuxiang , et al. The method of Sina Weibo rumor detecting based on comment abnormality[J]. Acta Automatica Sinica, 2020, 46(8): 1689-1702.

[17] LI Yifan , LI Junbao , PAN Weifeng . Hyperspectral image recognition using SVM combined deep learning[J]. Journal of Internet Technology, 2019, 20(3): 851-859.

[18] RASHID M , RAMASAMY S , RAGHAVA G P S . A simple approach for predicting protein—protein interactions[J]. Current Protein and Peptide Science, 2010, 11(7): 589-600.

[19] ALI A , ABDRAZAK S , OTHMAN S H , et al. Financial fraud detection based on machine learning: a systematic literature review[J]. Applied Sciences, 2022, 12(19): 9637.

[20] HOFMANN T , SCHÖLKOPF B , SMOLA A J . Kernel methods in machine learning[J]. The Annals of Statistics, 2008, 36(3): 1171-1220.

[21] 肖开研, 廉洁 . 基于多核支持向量机的句子分类算法[J]. 华东师范大学学报(自然科学版), 2023(6): 85-94.

[22] XIAO Kaiyan , LIAN Jie . Sentence classification algorithm based on multi—kernel support vector machine[J]. Journal of East China Normal University(Natural Science), 2023(6): 85-94.

[23] 曹国刚, 李梦雪, 陈颖, 等 . 改进支持向量机分类方法及其在原发性肝癌筛查中的应用[J]. 应用科学学报, 2021, 39(3): 481-494.

[24] CAO Guogang , LI Mengxue , CHEN Ying , et al. Classification method of improved support vector machine and its application in early detection of primary liver cancer[J]. Journal of Applied Sciences, 2021, 39(3): 481-494.

[25] 李苍柏, 肖克炎, 李楠, 等 . 支持向量机,随机森林和人工神经网络机器学习算法在地球化学异常信息提取中的对比研究[J]. 地球学报, 2020, 41(2): 309-319.

[26] LI Cangbai , XIAO Keyan , LI Nan , et al. A comparative study of support vector machine, random forest and artificial neural network machine learning algorithms in geochemical anomaly information extraction[J]. Acta Geoscientica Sinica, 2020, 41(2): 309-319.

[27] CHENG Shitong , SU Xinyu , CHEN Baiyang , et al. GBMOD: a granular—ball mean—shift outlier detector[J]. Pattern Recognition, 2025, 159: 111115.

[28] XIE Qin , ZHANG Qinghua , XIA Shuyin , et al. GBG++: a fast and stable granular ball generation method for classification[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024, 8(2): 2022-2036.

[29] 肖振国, 陈林书, 孙少杰, 等 . 基于代数粒的聚类方法[J]. 计算机工程与科学, 2024, 46(1): 150-158.

[30] XIAO Zhenguo , CHEN Linshu , SUN Shaojie , et al. A clustering method based on algebraic granularity[J]. Computer Engineering & Science, 2024, 46(1): 150-158.

[31] 徐伟华, 黄旭东, 蔡可 . 基于粒计算的多源信息融合方法综述[J]. 数据采集与处理, 2023, 38(2): 245-261.

[32] XU Weihua , HUANG Xudong , CAI Ke . Review of multi—source information fusion methods based on granular computing[J]. Journal of Data Acquisition and Processing, 2023, 38(2): 245-261.

[33] CHEN Qiangqiang , HE Linjie , DIAO Yanan , et al. A novel neighborhood granular mean shift clustering algorithm[J]. Mathematics, 2023, 11(1): 207.

[34] JIANG Hailiang , CHEN Yumin , KONG Liru , et al. An LVQ clustering algorithm based on neighborhood granules[J]. Journal of Intelligent & Fuzzy Systems, 2022, 43(5): 6109-6122.

[35] CHEN Yumin , ZHU Shunzhi , LI Wei , et al. Fuzzy granular convolutional classifiers[J]. Fuzzy Sets and Systems, 2022, 426: 145-162.

[36] LI Wei , WEI Zhongnan , CHEN Yumin , et al. Fuzzy granular hyperplane classifiers[J]. IEEE Access, 2020, 8: 112066-112077.

[37] 郑晨颖, 陈颖悦, 侯贤宇, 等 . 一种邻域粒的模糊C均值聚类算法[J]. 山东大学学报(理学版), 2024, 59(5): 35-44.

[38] ZHENG Chenying , CHEN Yingyue , HOU Xianyu , et al. A neighbourhood granular fuzzy C—means clustering algorithm[J]. Journal of Shandong University(Natural Science), 2024, 59(5): 35-44.

[39] 吴海, 牛娇娇, 铁文彦, 等 . 基于粒概念网络的概念格构造方法[J]. 山东大学学报(理学版), 2025, 60(12): 21-31.

[40] WU Hai , NIU Jiaojiao , TIE Wenyan , et al. Concept lattice construction method based on granular concept network[J]. Journal of Shandong University(Natural Science), 2025, 60(12): 21-31.

[41] HE Linjie , CHEN Yumin , ZHONG Caiming , et al. Granular elastic net work regression with stochastic gradient descent[J]. Mathematics, 2022, 10(15): 2628.

[42] JIANG Hailiang , CHEN Yumin , JIANG Hongbo , et al. A granular sigmoid extreme learning machine and its application in a weather forecast[J]. Applied Soft Computing, 2023, 147: 110799.

基金资助

厦门市自然科学基金资助项目(3502Z202473069)

福建省自然科学基金资助项目(2024J011192)