JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (5): 55-64.doi: 10.6040/j.issn.1671-9352.8.2024.026

Previous Articles     Next Articles

Application of topology neighborhood bases in density clustering algorithm

ZHANG Xiaoyuan1,2, TIAN Yi1, REN Zihan1, DUAN Tianyu1, YANG Siyuan1, ZHANG Yuexuan1   

  1. 1. School of Statistics and Data Science, Hebei Finance University, Baoding 071051, Hebei, China;
    2. Baoding Key Laboratory of Financial Big Data Intelligent Computing and Application, Hebei Finance University, Baoding 071051, Hebei, China
  • Online:2026-05-20 Published:2026-05-15

Abstract: Closure, cluster point and neighborhood base in topology are applied to density-based clustering problems. Matrix computation method for density clustering algorithm is proposed, and an example is given to illustrate how to use matrix multiplication to cluster a data set with density clustering algorithm.

Key words: density clustering algorithm, closure, cluster point, neighborhood base, matrix multiplication

CLC Number: 

  • TP391
[1] 曹雨康. 基于拓扑学和机器学习的药物属性预测研究[D]. 武汉:武汉纺织大学,2022. CAO Yukang. Research on drug properties prediction based on topology and machine learning[D]. Wuhan: Wuhan Textile University, 2022.
[2] 傅秋婷. 基于拓扑数据分析技术的股票价格时间序列聚类研究[D]. 成都:西南财经大学,2022. FU Qiuting. Research on clustering of stock price time series based on topological data analysis[D]. Chengdu: Southwestern University of Finance and Economics, 2022.
[3] 张家琛. 基于拓扑数据分析方法的人体步态研究[D]. 天津:天津理工大学,2022. ZHANG Jiachen. Research on human gait based on topological data analysis[D]. Tianjin: Tianjin University of Technology, 2022.
[4] FIX E, HODGES J L. Discriminatory analysis, nonparametric discrimination: consistency properties[R]. Texas: USAF School of Aviation Medicine, 1951.
[5] COVER T M, HART P E. Nearest neighbor pattern classification[J]. IEEE Transactions on Information Theory, 1967, 13(1):21-27.
[6] MACQUEEN J. Some methods for classification and analysis of multivariate observations[J]. Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, 1967, 5(1):281-297.
[7] FORGY E W. Cluster analysis of multivariate data: efficiency versus interpretability of classifications[J]. Biometrics, 1965, 21(3):768-769.
[8] LLOYD S. Least square quantization in PCM[J]. IEEE Transactions on Information Theory, 1982, 28(2):129-137.
[9] JOHNSON S. Hierachical clustering schemes[J]. Psychometrika, 1967, 32(3):241-254.
[10] HARDING E F. The number of partitions of a set of n points in k dimensions induced by hyperplanes[J]. Proceedings of the Edinburgh Mathematical Society, 1967, 15(4):285-289.
[11] JARDINE N, SIBSON R. The construction of hierarchic and non-hierarchic classifications[J]. The Computer Journal, 1968, 11(2):117-184.
[12] HARTIGAN J A. Clustering algorithms[M]. Toronto: Wiley, 1975.
[13] ESTER M, KRIEGEL H P, SANDER J, et al. A density-based algorithm for discovering clusters in large spatial databases with noise[C] //Proceedings of the Second International Conference on Knowledge Discovery and Data Mining. Oregon: AAAI, 1996.
[14] 周志华. 机器学习[M]. 北京:清华大学出版社,2016. ZHOU Zhihua. Machine learning[M]. Beijing: Tsinghua University Press, 2016.
[15] ENGELKING R. General topology[M]. Berlin: Heldermann Verlag, 1989.
[16] HU Wanjun. Typed topology and its application to data sets[J]. Topology and Its Applications, 2024, 342:108760.
[17] MA Liwen. Important matrix computations in finite topological spaces[J]. Applied Mathematics and Computation, 2021, 395:125808.
[1] WANG Wu. Notes on the continuity of directed spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(4): 62-68.
[2] ZHANG Jiping, WU Weizhi, ZHOU Miaojuan, LI Jinjin. Distributed serial fuzzy relations and the meshing of fuzzy knowledge structures [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 116-124.
[3] BAI Yiman, HAI Jinke. The influence of subnormal subgroups on the n-solvability of groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(11): 32-36.
[4] ZHANG Jiping, WU Weizhi, ZHOU Miaojuan, LI Jinjin. Some properties of the fuzzy knowledge structures [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(1): 91-100.
[5] GAO Ya, WU Hong-bo. Closure elements and closure sets in topological systems and their related properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 30-36.
[6] GUI Yun-miao, HU Hong-chun, GONG Ben-gang. Research on information disclosure decision of bilateral platform in the blockchain era [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(3): 89-95.
[7] DENG Wei-na, ZHAO Xian-zhong. Linear operators preserving transitive closures of matrices over the binary Boolean semiring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 64-70.
[8] Jing ZHANG,Jian-min MA. F-C variable threshold concept lattices based on dependence spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 68-74.
[9] ZHENG Jing-zhu, YANG Hai-ning, SU Ye, QIN Jing. A blindly public verifiable outsourcing scheme for matrix multiplication [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 1-11.
[10] XU Hui, ZHAO Zhi-bing. Relative torsionless modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 75-80.
[11] MA Hai-cheng, LI Sheng-gang. The digraphs representation of finite topologies [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 100-104.
[12] LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71.
[13] GUO Lan-lan1,2, GENG Jie1, SHI Shuo1,3, YUAN Fei1, LEI Li1, DU Guang-sheng1*. Computing research of the water hammer pressure in the process of #br# the variable speed closure of valve based on UDF method [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 27-30.
[14] ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu. Products, sums, and quotients of M-closure spaces [J]. J4, 2010, 45(4): 74-76.
[15] YU Wen-jing, LI Sheng-gang*. Categorical properties of three kinds of special closure spaces [J]. J4, 2010, 45(10): 73-77.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!