A three-way clustering method based on an improved DBSCAN algorithm

Clustering is a fundamental research field and plays an important role in data analysis. To better address the relationship between an element and a cluster, a Three-Way clustering method based on an Improved DBSCAN (3W-DBSCAN) algorithm is proposed in this paper. 3W-DBSCAN represents a cluster by a pair of nested sets called lower bound and upper bound respectively. The two bounds classify objects into three status: belong-to, not belong-to and ambiguity. Objects in lower bound certainly belong to the cluster. Objects in upper bound while not in the lower bound are ambiguous because they are in a boundary region and might belong to one or more clusters. Objects beyond the upper bound certainly do not belong to the same cluster. This clustering representation can well explain the clustering result and consist with human cognitive thinking. By improving similarity calculation, improved DBSCAN is presented to obtain initial clustering results, then three-way decision strategies are used to acquire the positive and boundary regions of a cluster. Three benchmarks Accuracy (Acc), F-measure (F1), NMI and ten datasets including three synthetic datasets, three UCI datasets and four shape datasets are used in experiments to evaluate the effectiveness of 3W-DBSCAN. Experimental results suggest that 3W-DBSCAN has a good performance and is effective in clustering.

[1]  Rong Zheng,et al.  RECOME: a New Density-Based Clustering Algorithm Using Relative KNN Kernel Density , 2016, Inf. Sci..

[2]  Nouman Azam,et al.  Web-Based Medical Decision Support Systems for Three-Way Medical Decision Making With Game-Theoretic Rough Sets , 2015, IEEE Transactions on Fuzzy Systems.

[3]  Alessandro Laio,et al.  Clustering by fast search and find of density peaks , 2014, Science.

[4]  Lin Yang,et al.  A method of incomplete data three-way clustering based on density peaks , 2018, ICCAD 2018.

[5]  Pasi Fränti,et al.  K-means properties on six clustering benchmark datasets , 2018, Applied Intelligence.

[6]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[7]  Pawan Lingras,et al.  Interval Set Clustering of Web Users with Rough K-Means , 2004, Journal of Intelligent Information Systems.

[8]  Bao Qing Hu,et al.  Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets , 2016, Knowl. Based Syst..

[9]  Yong Deng,et al.  Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis , 2019, Int. J. Comput. Commun. Control.

[10]  Kai Ming Ting,et al.  Grouping points by shared subspaces for effective subspace clustering , 2018, Pattern Recognit..

[11]  Enrico Scalas,et al.  Accuracy and robustness of clustering algorithms for small-size applications in bioinformatics , 2008, 0807.3838.

[12]  Richard Weber,et al.  Credit scoring using three-way decisions with probabilistic rough sets , 2020, Inf. Sci..

[13]  Vipin Kumar,et al.  Finding Clusters of Different Sizes, Shapes, and Densities in Noisy, High Dimensional Data , 2003, SDM.

[14]  Yong Deng,et al.  A cluster-growing dimension of complex networks: From the view of node closeness centrality , 2019, Physica A: Statistical Mechanics and its Applications.

[15]  Kai Ming Ting,et al.  Density-ratio based clustering for discovering clusters with varying densities , 2016, Pattern Recognit..

[16]  Keqin Li,et al.  DPC-LG: Density peaks clustering based on logistic distribution and gravitation , 2019, Physica A: Statistical Mechanics and its Applications.

[17]  Zeshui Xu,et al.  Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators , 2017, Inf. Sci..

[18]  Qinghua Hu,et al.  Generalized Latent Multi-View Subspace Clustering , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Thierry Denoeux,et al.  ECM: An evidential version of the fuzzy c , 2008, Pattern Recognit..

[20]  Yiyu Yao,et al.  CE3: A three-way clustering method based on mathematical morphology , 2018, Knowl. Based Syst..

[21]  Chunfeng Lian,et al.  Joint Tumor Segmentation in PET-CT Images Using Co-Clustering and Fusion Based on Belief Functions , 2019, IEEE Transactions on Image Processing.

[22]  Yiyu Yao,et al.  Actionable strategies in three-way decisions , 2017, Knowl. Based Syst..

[23]  Lixin Tian,et al.  Analysis of percolation behaviors of clustered networks with partial support-dependence relations , 2014 .

[24]  Ahmet Özmen,et al.  Distance and density based clustering algorithm using Gaussian kernel , 2017, Expert Syst. Appl..

[25]  Keqin Li,et al.  GDPC: Gravitation-based Density Peaks Clustering algorithm , 2018, Physica A: Statistical Mechanics and its Applications.

[26]  Zhi-Hua Zhou,et al.  Overcoming Key Weaknesses of Distance-based Neighbourhood Methods using a Data Dependent Dissimilarity Measure , 2016, KDD.

[27]  Yan Zhang,et al.  Game theoretic approach to shadowed sets: A three-way tradeoff perspective , 2020, Inf. Sci..

[28]  Kai Ming Ting,et al.  A Distance Scaling Method to Improve Density-Based Clustering , 2018, PAKDD.

[29]  Nouman Azam,et al.  A three-way approach for learning rules in automatic knowledge-based topic models , 2017, Int. J. Approx. Reason..

[30]  H. Stanley,et al.  Robustness of a partially interdependent network formed of clustered networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Siu-Ming Yiu,et al.  Predicting and understanding comprehensive drug-drug interactions via semi-nonnegative matrix factorization , 2018, BMC Systems Biology.

[32]  Xin Lu,et al.  Spatial clustering with Density-Ordered tree , 2016 .

[33]  Wei Yu,et al.  Exploring temporal community structure and constant evolutionary pattern hiding in dynamic networks , 2018, Neurocomputing.

[34]  Nouman Azam,et al.  A three-way clustering approach for handling missing data using GTRS , 2018, Int. J. Approx. Reason..

[35]  Kemal Alic,et al.  Network and Traffic Design Aspects in Network-Coding-Enabled Wireless Networks , 2019, Int. J. Comput. Commun. Control.

[36]  Hai Liu,et al.  A robust multi-view clustering method for community detection combining link and content information , 2019, Physica A: Statistical Mechanics and its Applications.

[37]  Xiaonan Li,et al.  Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set , 2018, Int. J. Approx. Reason..

[38]  Witold Pedrycz,et al.  Rough–Fuzzy Collaborative Clustering , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[39]  Guoyin Wang,et al.  An active three-way clustering method via low-rank matrices for multi-view data , 2020, Inf. Sci..

[40]  Yong Deng,et al.  A new method to measure the divergence in evidential sensor data fusion , 2019, Int. J. Distributed Sens. Networks.

[41]  Meisam Akbarzadeh,et al.  Detecting critical links of urban networks using cluster detection methods , 2019, Physica A: Statistical Mechanics and its Applications.

[42]  Kao-Shing Hwang,et al.  An adaptive decision-making method with fuzzy Bayesian reinforcement learning for robot soccer , 2018, Inf. Sci..

[43]  Guoyin Wang,et al.  A tree-based incremental overlapping clustering method using the three-way decision theory , 2016, Knowl. Based Syst..

[44]  Yiyu Yao,et al.  Detecting and refining overlapping regions in complex networks with three-way decisions , 2016, Inf. Sci..

[45]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[46]  Yong Deng,et al.  Generalized Ordered Propositions Fusion Based on Belief Entropy , 2018, Int. J. Comput. Commun. Control.

[47]  Thierry Denoeux,et al.  RECM: Relational evidential c-means algorithm , 2009, Pattern Recognit. Lett..

[48]  Yiyu Yao,et al.  Three-way decision and granular computing , 2018, Int. J. Approx. Reason..

[49]  Weixin Xie,et al.  Robust clustering by detecting density peaks and assigning points based on fuzzy weighted K-nearest neighbors , 2016, Inf. Sci..

[50]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

[51]  S. Mahdavifar,et al.  Integrable-chaos crossover in the spin-1∕2 XXZ chain with cluster interaction , 2019, Physica A: Statistical Mechanics and its Applications.

[52]  Hans-Peter Kriegel,et al.  OPTICS: ordering points to identify the clustering structure , 1999, SIGMOD '99.

[53]  Kai Ming Ting,et al.  Local contrast as an effective means to robust clustering against varying densities , 2017, Machine Learning.

[54]  Kao-Shing Hwang,et al.  Decoupled Visual Servoing With Fuzzy Q-Learning , 2018, IEEE Transactions on Industrial Informatics.

[55]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.