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Generation of Granular-Balls for Clustering Based on the Principle of Justifiable Granularity

Zihang Jia, Zhen Zhang, Witold Pedrycz

TL;DR

This paper tackles the challenge of robust clustering by improving the generation of Granular-Balls (GBs) through a principled quality measure based on the Principle of Justifiable Granularity (POJG). By defining GB quality via the product of coverage and specificity, and employing a binary-tree pruning strategy plus anomaly detection, the method produces GBs that better reflect the data distribution. Empirical results on synthetic and public datasets show higher clustering accuracy and NMI for GB-based clustering, with competitive computing overhead and improved reliability over prior threshold/greedy approaches. The proposed framework offers a principled, scalable path to using GBs for clustering tasks in large-scale data analysis, with potential extensions to parameter learning and alternative metrics.

Abstract

Efficient and robust data clustering remains a challenging task in the field of data analysis. Recent efforts have explored the integration of granular-ball (GB) computing with clustering algorithms to address this challenge, yielding promising results. However, existing methods for generating GBs often rely on single indicators to measure GB quality and employ threshold-based or greedy strategies, potentially leading to GBs that do not accurately capture the underlying data distribution. To address these limitations, this article introduces a novel GB generation method. The originality of this method lies in leveraging the principle of justifiable granularity to measure the quality of a GB for clustering tasks. To be precise, we define the coverage and specificity of a GB and introduce a comprehensive measure for assessing GB quality. Utilizing this quality measure, the method incorporates a binary tree pruning-based strategy and an anomaly detection method to determine the best combination of sub-GBs for each GB and identify abnormal GBs, respectively. Compared to previous GB generation methods, the new method maximizes the overall quality of generated GBs while ensuring alignment with the data distribution, thereby enhancing the rationality of the generated GBs. Experimental results obtained from both synthetic and publicly available datasets underscore the effectiveness of the proposed GB generation method, showcasing improvements in clustering accuracy and normalized mutual information.

Generation of Granular-Balls for Clustering Based on the Principle of Justifiable Granularity

TL;DR

This paper tackles the challenge of robust clustering by improving the generation of Granular-Balls (GBs) through a principled quality measure based on the Principle of Justifiable Granularity (POJG). By defining GB quality via the product of coverage and specificity, and employing a binary-tree pruning strategy plus anomaly detection, the method produces GBs that better reflect the data distribution. Empirical results on synthetic and public datasets show higher clustering accuracy and NMI for GB-based clustering, with competitive computing overhead and improved reliability over prior threshold/greedy approaches. The proposed framework offers a principled, scalable path to using GBs for clustering tasks in large-scale data analysis, with potential extensions to parameter learning and alternative metrics.

Abstract

Efficient and robust data clustering remains a challenging task in the field of data analysis. Recent efforts have explored the integration of granular-ball (GB) computing with clustering algorithms to address this challenge, yielding promising results. However, existing methods for generating GBs often rely on single indicators to measure GB quality and employ threshold-based or greedy strategies, potentially leading to GBs that do not accurately capture the underlying data distribution. To address these limitations, this article introduces a novel GB generation method. The originality of this method lies in leveraging the principle of justifiable granularity to measure the quality of a GB for clustering tasks. To be precise, we define the coverage and specificity of a GB and introduce a comprehensive measure for assessing GB quality. Utilizing this quality measure, the method incorporates a binary tree pruning-based strategy and an anomaly detection method to determine the best combination of sub-GBs for each GB and identify abnormal GBs, respectively. Compared to previous GB generation methods, the new method maximizes the overall quality of generated GBs while ensuring alignment with the data distribution, thereby enhancing the rationality of the generated GBs. Experimental results obtained from both synthetic and publicly available datasets underscore the effectiveness of the proposed GB generation method, showcasing improvements in clustering accuracy and normalized mutual information.
Paper Structure (16 sections, 15 equations, 7 figures, 5 tables)

This paper contains 16 sections, 15 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Granular-Ball Computing for Clustering
  4. Cheng et al.'s GB Generation Method
  5. Xie et al.'s GB Generation Method
  6. Principle of Justifiable Granularity
  7. The Proposed Method
  8. Measuring the Quality of GBs
  9. Binary tree pruning-based strategy to generate GBs
  10. Detecting Abnormal Granular-Balls
  11. Algorithm and Its Time Complexity Analysis
  12. Numerical Experiments
  13. Clustering on Synthetic Datasets
  14. Clustering on Publicly Available Datasets
  15. Parameter Analysis
  16. ...and 1 more sections

Figures (7)

  • Figure 1: Representing instances through GBs. (a) A synthetic dataset; (b) The GBs used to represent the synthetic dataset.
  • Figure 2: The framework of the proposed method.
  • Figure 3: The GBs with average radius generated from the six synthetic datasets. (a)-(f) Our method. (g)-(l) Cheng et al.'s method ChengDongDong2023. (m)-(r) Xie et al.'s method XieJiang2023.
  • Figure 4: The clustering results of GBSC on the six synthetic datasets. (a)-(f) Our method. (g)-(l) Cheng et al.'s method ChengDongDong2023. (m)-(r) Xie et al.'s method XieJiang2023.
  • Figure 5: Comparison of three generation methods of GBs on synthetic datasets. (a) The number of generated GBs. (b) The computing overhead (in seconds) of GBSC.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Definition 1
  • Remark 1
  • Definition 2
  • Example 1
  • Definition 3
  • Remark 2
  • Definition 4
  • Remark 3
  • Definition 5