{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T18:53:09Z","timestamp":1783968789241,"version":"3.55.0"},"reference-count":61,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Sichuan Province","award":["2022NSFSC0536"],"award-info":[{"award-number":["2022NSFSC0536"]}]},{"name":"Natural Science Foundation of Sichuan Province","award":["HCIC201902"],"award-info":[{"award-number":["HCIC201902"]}]},{"name":"Natural Science Foundation of Sichuan Province","award":["2020KYQD123"],"award-info":[{"award-number":["2020KYQD123"]}]},{"name":"Natural Science Foundation of Sichuan Province","award":["3122022PT02"],"award-info":[{"award-number":["3122022PT02"]}]},{"name":"Open Project Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis","award":["2022NSFSC0536"],"award-info":[{"award-number":["2022NSFSC0536"]}]},{"name":"Open Project Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis","award":["HCIC201902"],"award-info":[{"award-number":["HCIC201902"]}]},{"name":"Open Project Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis","award":["2020KYQD123"],"award-info":[{"award-number":["2020KYQD123"]}]},{"name":"Open Project Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis","award":["3122022PT02"],"award-info":[{"award-number":["3122022PT02"]}]},{"name":"Research Foundation for Civil Aviation University of China","award":["2022NSFSC0536"],"award-info":[{"award-number":["2022NSFSC0536"]}]},{"name":"Research Foundation for Civil Aviation University of China","award":["HCIC201902"],"award-info":[{"award-number":["HCIC201902"]}]},{"name":"Research Foundation for Civil Aviation University of China","award":["2020KYQD123"],"award-info":[{"award-number":["2020KYQD123"]}]},{"name":"Research Foundation for Civil Aviation University of China","award":["3122022PT02"],"award-info":[{"award-number":["3122022PT02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Density peak clustering is the latest classic density-based clustering algorithm, which can directly find the cluster center without iteration. The algorithm needs to determine a unique parameter, so the selection of parameters is particularly important. However, for multi-density data, when one parameter cannot satisfy all data, clustering often cannot achieve good results. Moreover, the subjective selection of cluster centers through decision diagrams is often not very convincing, and there are also certain errors. In view of the above problems, in order to achieve better clustering of multi-density data, this paper improves the density peak clustering algorithm. Aiming at the selection of parameter dc, the K-nearest neighbor idea is used to sort the neighbor distance of each data, draw a line graph of the K-nearest neighbor distance, and find the global bifurcation point to divide the data with different densities. Aiming at the selection of cluster centers, the local density and distance of each data point in each data division is found, a \u03b3 map is drawn, the average value of the \u03b3 height difference is calculated, and through two screenings the largest discontinuity point is found to automatically determine the cluster center and the number of cluster centers. The divided datasets are clustered by the DPC algorithm, and then the clustering results are perfected and integrated by using the cluster fusion rules. Finally, a variety of experiments are designed from various perspectives on various artificial simulated datasets and UCI real datasets, which demonstrate the superiority of the F-DPC algorithm in terms of clustering effect, clustering quality, and number of samples.<\/jats:p>","DOI":"10.3390\/s22228814","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T04:39:03Z","timestamp":1668573543000},"page":"8814","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Improved Density Peak Clustering Algorithm for Multi-Density Data"],"prefix":"10.3390","volume":"22","author":[{"given":"Lifeng","family":"Yin","sequence":"first","affiliation":[{"name":"School of Software, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Dalian Jiaotong University, Dalian 116028, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huayue","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science, China West Normal University, Nanchong 637002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wu","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China"},{"name":"Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"ref_1","first-page":"1869","article-title":"Overview of Clustering Algorithms","volume":"39","author":"Zhang","year":"2019","journal-title":"Comput. Appl."},{"key":"ref_2","first-page":"134","article-title":"Overview of Unsupervised Learning Algorithms in Artificial Intelligence","volume":"1","author":"Gan","year":"2019","journal-title":"Strait Technol. Ind."},{"key":"ref_3","first-page":"1","article-title":"A recognition method for visual image of sports video based on fuzzy clustering algorithm","volume":"20","author":"Sun","year":"2022","journal-title":"Int. J. Inf. Commun. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1504\/IJCC.2021.113997","article-title":"An efficient document clustering using hybridized harmony search K-means algorithm with multi-view point","volume":"10","author":"Devi","year":"2021","journal-title":"Int. J. Cloud Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10207-020-00506-7","article-title":"Using homomorphic encryption for privacy-preserving clustering of intrusion detection alerts","volume":"20","author":"Spathoulas","year":"2021","journal-title":"Int. J. Inf. Secur."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1111\/tgis.12552","article-title":"Extracting human emotions at different places based on facial expressions and spatial clustering analysis","volume":"23","author":"Kang","year":"2019","journal-title":"Trans. GIS"},{"key":"ref_7","first-page":"321","article-title":"Several Problems in Cluster Analysis Research","volume":"27","author":"Wang","year":"2012","journal-title":"Control. Decis."},{"key":"ref_8","unstructured":"Han, J., and Kamber, M. (2012). Concept and Technology of Data Mining, Machinery Industry Press."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wu, D., and Wu, C. (2022). Research on the time-dependent split delivery green vehicle routing problem for fresh agricultural products with multiple time windows. Agriculture, 12.","DOI":"10.3390\/agriculture12060793"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jpdc.2022.01.029","article-title":"SG-PBFT: A secure and highly efficient distributed blockchain PBFT consensus algorithm for intelligent Internet of vehicles","volume":"164","author":"Xu","year":"2022","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8742","DOI":"10.1016\/j.egyr.2021.11.138","article-title":"Optimal reactive power dispatch using an improved slime Mould algorithm","volume":"7","author":"Wei","year":"2021","journal-title":"Energy Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"108576","DOI":"10.1016\/j.ymssp.2021.108576","article-title":"Bearing fault diagnosis via generalized logarithm sparse regularization","volume":"167","author":"Zhang","year":"2022","journal-title":"Mech. Syst. Signal Processing"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"99900","DOI":"10.1109\/ACCESS.2020.2997912","article-title":"Hyperspectral remote sensing image classification with CNN based on quantum genetic-optimized sparse representation","volume":"8","author":"Chen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"106724","DOI":"10.1016\/j.asoc.2020.106724","article-title":"Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem","volume":"100","author":"Deng","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Huang, C., Zhou, X., Ran, X.J., Liu, Y., Deng, W.Q., and Deng, W. Co-evolutionary competitive swarm optimizer with three-phase for large-scale complex optimization problem. Inf. Sci., 2022.","DOI":"10.1016\/j.ins.2022.11.019"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1126\/science.1242072","article-title":"Clustering by fast search and find of density peaks","volume":"344","author":"Rodriguez","year":"2014","journal-title":"Science"},{"key":"ref_17","first-page":"726","article-title":"Analysis of Weibo Public Sentiment Based on Density Peak Optimization K-means Clustering Algorithm","volume":"50","author":"Ye","year":"2022","journal-title":"Comput. Digit. Eng."},{"key":"ref_18","first-page":"1019","article-title":"K-means text clustering algorithm based on density peak optimization","volume":"38","author":"Tian","year":"2017","journal-title":"Comput. Eng. Des."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"168282","DOI":"10.1109\/ACCESS.2020.3021903","article-title":"Density Peaks Clustering Algorithm Based on Weighted k-Nearest Neighbors and Geodesic Distance","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, F. (2021). Research on Adaptive Density Peak Clustering Algorithm, Xi\u2019an University of Technology.","DOI":"10.36227\/techrxiv.17597669"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ins.2020.01.032","article-title":"Adaptive weighted over-sampling for imbalanced datasets based on density peaks clustering with heuristic filtering","volume":"519","author":"Tao","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yin, L., Li, M., Chen, H., and Deng, W. (2022). An Improved Hierarchical Clustering Algorithm Based on the Idea of Population Reproduction and Fusion. Electronics, 11.","DOI":"10.3390\/electronics11172735"},{"key":"ref_23","first-page":"61","article-title":"Multi-density fast clustering algorithm using regional division","volume":"55","author":"Niu","year":"2019","journal-title":"Comput. Eng. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"74883","DOI":"10.1109\/ACCESS.2022.3190958","article-title":"A Density Peaks Clustering Algorithm With Sparse Search and K-d Tree","volume":"10","author":"Shan","year":"2022","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"113900","DOI":"10.1109\/ACCESS.2020.3003057","article-title":"Adaptive density peaks clustering based on k-nearest neighbor and gini coefficient","volume":"8","author":"Jiang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lv, Y., Liu, M., and Xiang, Y. (2020). Fast Searching Density Peak Clustering Algorithm Based on Shared Nearest Neighbor and Adaptive Clustering Center. Symmetry, 12.","DOI":"10.3390\/sym12122014"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/j.neucom.2020.03.125","article-title":"A density-peak-based clustering algorithm of automatically determining the number of clusters","volume":"458","author":"Tong","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5171","DOI":"10.1007\/s00500-018-3183-0","article-title":"A feasible density peaks clustering algorithm with a merging strategy","volume":"23","author":"Xu","year":"2018","journal-title":"Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1007\/s13042-020-01198-0","article-title":"GDPC: Generalized density peaks clustering algorithm based on order similarity","volume":"12","author":"Yang","year":"2020","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"109419","DOI":"10.1016\/j.asoc.2022.109419","article-title":"An adaptive differential evolution algorithm based on belief space and generalized opposition-based learning for resource allocation","volume":"127","author":"Deng","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"118834","DOI":"10.1016\/j.eswa.2022.118834","article-title":"Dynamic hybrid mechanism-based differential evolution algorithm and its application","volume":"213","author":"Song","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.ins.2022.08.115","article-title":"Multi-strategy particle swarm and ant colony hybrid optimization for airport taxiway planning problem","volume":"612","author":"Deng","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"105139","DOI":"10.1016\/j.engappai.2022.105139","article-title":"Parameter adaptation-based ant colony optimization with dynamic hybrid mechanism","volume":"114","author":"Zhou","year":"2022","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109422","DOI":"10.1016\/j.ymssp.2022.109422","article-title":"Data-driven simultaneous identification of the 6DOF dynamic model and wave load for a ship in waves","volume":"184","author":"Ren","year":"2023","journal-title":"Mech. Syst. Signal Processing"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2781","DOI":"10.1109\/JSTARS.2021.3059451","article-title":"A hyperspectral image classification method using multifeature vectors and optimized KELM","volume":"14","author":"Chen","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.isatra.2021.07.017","article-title":"A novel mathematical morphology spectrum entropy based on scale-adaptive techniques","volume":"126","author":"Yao","year":"2022","journal-title":"ISA Trans."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108731","DOI":"10.1016\/j.asoc.2022.108731","article-title":"Pyramid particle swarm optimization with novel strategies of competition and cooperation","volume":"121","author":"Li","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_38","unstructured":"Zhao, H.M., Liu, J., Chen, H.Y., Chen, J., Li, Y., Xu, J.J., and Deng, W. (2022). Intelligent diagnosis using continuous wavelet transform and gauss convolutional deep belief network. IEEE Trans. Reliab., 1\u201311."},{"key":"ref_39","first-page":"1800","article-title":"Research progress of density peak clustering algorithm","volume":"33","author":"Xu","year":"2022","journal-title":"J. Softw."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Li, T., Yue, S., and Sun, C. (2021, January 17\u201320). General density-peaks-clustering algorithm. Proceedings of the 2021 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Glasgow, UK.","DOI":"10.1109\/I2MTC50364.2021.9460001"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"14478","DOI":"10.1007\/s10489-022-03360-3","article-title":"Fast density peaks clustering algorithm in polar coordinate system","volume":"52","author":"Li","year":"2022","journal-title":"Appl. Intell."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.neucom.2018.06.087","article-title":"REDPC: A residual error-based density peak clustering algorithm","volume":"348","author":"Parmar","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"74612","DOI":"10.1109\/ACCESS.2019.2918772","article-title":"HCFS: A Density Peak Based Clustering Algorithm Employing A Hierarchical Strategy","volume":"7","author":"Zhuo","year":"2019","journal-title":"IEEE Access"},{"key":"ref_44","first-page":"273","article-title":"Overview of KNN Algorithm","volume":"10","author":"Dou","year":"2018","journal-title":"Commun. World"},{"key":"ref_45","first-page":"1","article-title":"Performance Comparison of New Adjusted Min-Max with Decimal Scaling and Statistical Column Normalization Methods for Artificial Neural Network Classification","volume":"2022","author":"Sinsomboonthong","year":"2022","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_46","first-page":"36","article-title":"Comparative analysis of KNN algorithm using various normalization techniques","volume":"9","author":"Pandey","year":"2017","journal-title":"Int. J. Comput. Netw. Inf. Secur."},{"key":"ref_47","unstructured":"Li, M. (2018). Improvement of K-Means Algorithm and Its Application in Text Clustering, Jiangnan University."},{"key":"ref_48","first-page":"277","article-title":"Research Status and Analysis of Density Peak Clustering Algorithms","volume":"29","author":"Ge","year":"2022","journal-title":"Guangxi Sci."},{"key":"ref_49","first-page":"111","article-title":"Density Peak Clustering Algorithm Based on K-Nearest Neighbors and Multi-Class Merging","volume":"57","author":"Xue","year":"2019","journal-title":"J. Jilin Univ."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Vinh, N.X., Julien, E., and James, B. (2009, January 14\u201318). Information theoretic measures for clusterings comparison: Is a correction for chance necessary?. Proceedings of the 26th annual international conference on machine learning, Montreal, QC, Canada.","DOI":"10.1145\/1553374.1553511"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01908075","article-title":"Comparing partitions","volume":"2","author":"Hubert","year":"1985","journal-title":"J. Classif."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1631\/FITEE.1500411","article-title":"Feature matching using quasi-conformal maps","volume":"18","author":"Wang","year":"2017","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Al Alam, P., Constantin, J., Constantin, I., and Lopez, C. (2022). Partitioning of Transportation Networks by Efficient Evolutionary Clustering and Density Peaks. Algorithms, 15.","DOI":"10.3390\/a15030076"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Cao, L., Zhang, X., Wang, T., Du, K., and Fu, C. (2020). An Adaptive Ellipse Distance Density Peak Fuzzy Clustering Algorithm Based on the Multi-target Traffic Radar. Sensors, 20.","DOI":"10.3390\/s20174920"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"e5641","DOI":"10.1002\/cpe.5641","article-title":"A privacy-preserving density peak clustering algorithm in cloud computing","volume":"32","author":"Sun","year":"2020","journal-title":"Concurr. Comput. Pr. Exper."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Wang, Z., Zhang, T., and Du, H. (2019, January 13\u201316). A Collaborative Filtering Recommendation Algorithm Based on Density Peak Clustering. Proceedings of the 2019 15th International Conference on Computational Intelligence and Security (CIS), Macao, China.","DOI":"10.1109\/CIS.2019.00018"},{"key":"ref_57","unstructured":"Liu, F., Xu, J., Xu, S., and Yung, M. (2019). Density Peak Clustering Algorithm Based on Differential Privacy Preserving. Science of Cyber Security. SciSec 2019. Lecture Notes in Computer Science, Springer."},{"key":"ref_58","first-page":"5503005.1-5","article-title":"Semisupervised hyperspectral band selection based on dual-constrained low-rank representation","volume":"19","author":"Yu","year":"2022","journal-title":"IEEE Geosci. Remote. S."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/TNB.2021.3109067","article-title":"Solving the family traveling salesperson problem in the adleman\u2013lipton model based on DNA computing","volume":"21","author":"Wu","year":"2021","journal-title":"IEEE Trans. NanoBioscience"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1960","DOI":"10.3934\/mbe.2023090","article-title":"Optimal search mapping among sensors in heterogeneous smart homes","volume":"20","author":"Yu","year":"2023","journal-title":"Math. Biosci. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"12287","DOI":"10.1109\/JSTARS.2021.3128932","article-title":"Unsupervised domain adaptation with dense-based compaction for hyperspectral imagery","volume":"14","author":"Yu","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8814\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:20Z","timestamp":1760145500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,15]]},"references-count":61,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22228814"],"URL":"https:\/\/doi.org\/10.3390\/s22228814","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,15]]}}}