Skip to main content
SpringerLink
Log in

FuzzyRadar: visualization for understanding fuzzy clusters

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

Fuzzy clustering assigns a membership degree (MD) on a datum to a cluster, which reflects real-world clustering scenarios but increases the complexity of understanding fuzzy clusters. Many studies have demonstrated that multidimensional visualization techniques are beneficial to fuzzy clusters analysis. However, empirically, no single existing visualization technique can support most analytical tasks featured by fuzzy clustering. This work proposes a new visualization called FuzzyRadar for understanding fuzzy clusters. Its basic idea is to combine the advantages of radial coordinate visualization (Radviz), which specializes in data-oriented analytical tasks, and parallel coordinate plot (PCP), which performs well in cluster-oriented analytical tasks. First, we adopt a compact and compounded layout to integrate Radviz and PCP into one visualization view. Then, we introduce a strip-edge-bundling method to reduce the visual cluster caused by PCP polylines and a histogram embedding method to facilitate the recognition of MD distribution. We also provide a group of additional visual encodings and a set of lightweight interactions. Finally, we use a case study to demonstrate the usability of FuzzyRadar and conduct a controlled quantitative evaluation to compare the performance of FuzzyRadar, Radviz, PCP, and scatterplot matrix. Result shows that FuzzyRadar supports all the seven examined analytical tasks well and presents a significant capability improvement compared with Radviz and PCP.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Abonyi J, Babuska R (2004) Fuzzsam-visualization of fuzzy clustering results by modified Sammon mapping. In: Proceedings of the IEEE international conference on fuzzy systems. IEEE, pp 365–370

  • Albuquerque G, Eisemann M, Lehmann DJ, Theisel H, Magnor M (2010) Improving the visual analysis of high-dimensional datasets using quality measures. In: Proceedings of the IEEE symposium on visual analytics science and technology, pp 19–26

  • Artero AO, de Oliveira MCF (2014) Viz3D: effective exploratory visualization of large multidimensional data sets. In: Proceedings of the 17th Brazilian symposium on computer graphics and image processing, pp 340–347

  • Asuncion A, Newman D (2007) UCI machine learning repository. http://archive.ics.uci.edu/ml/datasets.html. Accessed 15 Apr 2019

  • Berthold MR, Hall LO (2003) Visualizing fuzzy points in parallel coordinates. IEEE Trans Fuzzy Syst 11(3):369–374

    Article  Google Scholar 

  • Bi C, Fu B, Chen J, Zhao Y, Yang L, Duan Y, Shi Y (2019) Machine learning based fast multi-layer liquefaction disaster assessment. In: World Wide Web: internet and web information systems, pp 1–16. https://doi.org/10.1007/s11280-018-0632-8

    Article  Google Scholar 

  • Cao N, Lin YR, Gotz D (2015) UnTangle map: visual analysis of probabilistic multi-label data. IEEE Trans Vis Comput Graph 22(2):1149–1163

    Article  Google Scholar 

  • Chen H, Zhang S, Chen W et al (2015) uncertainty-aware multidimensional ensemble data visualization and exploration. IEEE Trans Vis Comput Graph 21(9):1072–1086

    Article  Google Scholar 

  • Chen W, Xia J, Wang X, Chen J, Wang Y, Chang L (2018a) RelationLines: visual reasoning of egocentric relations from heterogeneous urban data. ACM Trans Intell Syst Technol 10(1):1–22

    Google Scholar 

  • Chen W, Huang Z, Wu F, Zhu M, Guan H, Maciejewski R (2018b) VAUD: a visual analysis approach for exploring spatio-temporal urban data. IEEE Trans Vis Comput Graph 24(9):2636–2648

    Article  Google Scholar 

  • De Oliveira JV, Pedrycz W (2007) Advances in fuzzy clustering and its applications. Wiley, London

    Book  Google Scholar 

  • Dimara E, Bezerianos A, Dragicevic P (2018) Conceptual and methodological issues in evaluating multidimensional visualizations for decision support. IEEE Trans Vis Comput Graph 24(1):749–759

    Article  Google Scholar 

  • Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well separated cluster. J Cybern 3(3):32–57

    Article  MathSciNet  MATH  Google Scholar 

  • Epp CD, Bull S (2015) Uncertainty representation in visualizations of learning analytics for learners: current approaches and opportunities. IEEE Trans Learn Technol 8(3):242–260

    Article  Google Scholar 

  • Etemadpour R, Motta R, Jg DSP (2015) Perception-based evaluation of projection methods for multidimensional data visualization. IEEE Trans Vis Comput Graph 21(1):81–94

    Article  Google Scholar 

  • Feil B, Balasko B, Abonyi J (2007) Visualization of fuzzy clusters by fuzzy sammon mapping projection: application to the analysis of phase space trajectories. Soft Comput 11(5):479–488

    Article  Google Scholar 

  • Ferreira N, Fisher D, Konig AC (2014) Sample-oriented task-driven visualizations: allowing users to make better, more confident decisions. In: Proceedings of the Sigchi conference. ACM, pp 571–580

  • Holten D, Van Wijk JJ (2010) Evaluation of cluster identification performance for different PCP variants. Comput Graph Forum 29(3):793–802

    Article  Google Scholar 

  • Hoppner F, Klawonn F (2006) Visualising clusters in high-dimensional data sets by intersecting spheres. In: Proceedings of the international symposium on evolving fuzzy systems. IEEE, pp 106–111

  • Inselberg A, Dimsdale B (1987) Parallel coordinates for visualizing multi-dimensional geometry. In: Proceedings of the international conference on computer graphics, pp 25–44

  • Klawonn F, Chekhtman V, Janz E (2003) Visual inspection of fuzzy clustering results. In: Proceedings of advances in soft computing. CRC, pp 65–76

  • Kuntal BK, Ghosh TS, Mande SS (2014) Igloo-Plot: a tool for visualization of multidimensional datasets. Genomics 103(1):11–20

    Article  Google Scholar 

  • Leban G, Zupan B, Vidmar G, Bratko I (2006) Vizrank: data visualization guided by machine learning. Data Min Knowl Discov 13(2):119–136

    Article  MathSciNet  Google Scholar 

  • Lin YR, Cao N, Gotz D, Lu L (2015) Untangle: visual mining for data with uncertain multi-labels via triangle map. In: Proceedings of the IEEE international conference on data mining. IEEE, pp 340–349

  • Liu M, Shi J, Li Z, Li C, Zhu J, Liu S (2017) Towards better analysis of deep convolutional neural networks. IEEE Trans Visual Comput Graph 23(1):91–100

    Article  Google Scholar 

  • Long TV (2014) iSPLOM: interactive with scatterplot matrix for exploring multidimensional data. In: Proceedings of the international conference on knowledge and systems engineering, pp 175–186

  • Ma Y, Tung AKH, Wang W, Gao X, Pan Z, Chen W (2019) ScatterNet: a deep subjective similarity model for visual analysis of scatterplots. IEEE Trans Vis Comput Graph. https://doi.org/10.1109/tvcg.2018.2875702

    Article  Google Scholar 

  • Manuel R, Laura R, Francisco D, Alberto S (2016) A comparative study between Radviz and star coordinates. IEEE Trans Vis Comput Graph 22(1):619–628

    Article  Google Scholar 

  • Marghescu D (2007) User evaluation of multidimensional data visualization techniques for financial benchmarking. In: Proceedings of the European conference on information management and evaluation. AMCIS, p 509

  • Novakova L, Stepankova O (2009) Radviz and identification of clusters in multidimensional data. In: Proceeding of the 17th international conference on information visualization, pp 104–109

  • Palmas G, Bachynskyi M, Oulasvirta A (2014) An edge-bundling layout for interactive parallel coordinates. In: Proceedings of IEEE Pacific visualization symposium. IEEE, pp 57–64

  • Peng W, Ward MO, Rundensteiner EA (2004) Clutter reduction in multidimensional data visualization using dimension reordering. In: Proceedings of the IEEE symposium on information visualization. IEEE, pp 89–96

  • Rueda L, Zhang Y (2006) Geometric visualization of clusters obtained from fuzzy clustering algorithms. Pattern Recogn 39(8):1415–1429

    Article  MATH  Google Scholar 

  • Ruspini EH (1969) A new approach to clustering. Inf Control 15(15):22–32

    Article  MATH  Google Scholar 

  • Rzeźniczak T (2013) Evaluation of multidimensional visualization techniques for medical patterns representation. J Theor Appl Comput Sci 7(4):75–85

    Google Scholar 

  • Sanyal J, Zhang S, Bhattacharya G (2009) A user study to compare four uncertainty visualization methods for 1D and 2D datasets. IEEE Trans Vis Comput Graph 15(6):1209–1218

    Article  Google Scholar 

  • Sedlmair M, Munzner T, Tory M (2013) Empirical guidance on scatterplot and dimension reduction technique choices. IEEE Trans Vis Comput Graph 19(12):2634–2643

    Article  Google Scholar 

  • Sharko J, Grinstein G (2009) Visualizing fuzzy clusters using RadViz. In: Proceedings of the 13th international conference on information visualisation. IEEE, pp 307–316

  • Shi R, Yang M, Zhao Y, Zhou F, Huang W, Zhang S (2016) A matrix-based visualization system for network traffic forensics. IEEE Syst J 10(4):1350–1360

    Article  Google Scholar 

  • Shi Y, Bryan C, Bhamidipati S, Zhao Y, Zhang Y, Ma K-L (2018) MeetingVis: visual narratives to assist in recalling meeting context and content. IEEE Trans Vis Comput Graph 24(6):1918–1929

    Article  Google Scholar 

  • Wu Y, Yuan G-X, Ma K-L (2012) Visualizing flow of uncertainty through analytical processes. IEEE Trans Vis Comput Graph 18(12):2526–2535

    Article  Google Scholar 

  • Wu Y, Cao N, Gotz D, Tan Y-P, Keim DA (2016) A survey on visual analytics of social media data. IEEE Trans Multimed 18(11):2135–2148

    Article  Google Scholar 

  • Xia J, Ye F, Chen W, Wang Y, Chen W, Ma Y, Tung AKH (2018a) LDSScanner: exploratory analysis of low-dimensional structures in high-dimensional datasets. IEEE Trans Vis Comput Graph 24(1):236–245

    Article  Google Scholar 

  • Xia J, Gao L, Kong K, Zhao Y, Chen Y, Kui X, Liang Y (2018b) Exploring linear projections for revealing clusters, outliers, and trends in subsets of multi-dimensional datasets. J Vis Lang Comput 48:52–60

    Article  Google Scholar 

  • Xie C, Chen W, Huang X, Hu Y, Barlowe S, Yang J (2014) VAET: a visual analytics approach for E-Transactions time-series. IEEE Trans Vis Comput Graph 20(12):1743–1752

    Article  Google Scholar 

  • Yang J, Peng W, Ward M, Rundensteiner E (2003) Interactive hierarchical dimension ordering, spacing and filtering for exploration of high dimensional datasets. In: Proceedings of IEEE symposium on information visualization. IEEE, pp 105–112

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  • Zhao Y, She Y, Chen W, Lu Y, Xia J, Chen W, Liu J, Zhou F (2018) EOD edge sampling for visualizing dynamic network via massive sequence view. IEEE Access 6(1):53006–53018

    Article  Google Scholar 

  • Zhao Y, Luo F, Chen M, Wang Y, Xia J, Zhou F, Wang Y, Chen Y, Chen W (2019) evaluating multi-dimensional visualizations for understanding fuzzy clusters. IEEE Trans Vis Comput Graph 25(1):12–21

    Article  Google Scholar 

  • Zhou F, Li J, Huang W (2016) Dimension reconstruction for visual exploration of subspace clusters in high-dimensional data. In: Proceedings of the IEEE Pacific visualization symposium. IEEE, pp 128–135

  • Zhou Z, Ye Z, Liu Y, Liu F, Tao Y, Su W (2017a) Visual analytics for spatial clusters of air-quality data. IEEE Comput Graph Appl 37(5):98–105

    Article  Google Scholar 

  • Zhou F, Chen M, Wang Z (2017b) A Radviz-based visualization for understanding fuzzy clustering results. In: Proceedings of the international symposium on visual information communication and interaction, pp 9–15

  • Zhou F, Lin X, Liu C, Zhao Y, Xu P, Ren L, Xue T, Ren L (2019a) A survey of visualization for smart manufacturing. J Vis 22(1):1–19

    Article  Google Scholar 

  • Zhou Z, Meng L, Tang C, Zhao Y, Guo Z, Miaoxin H, Chen W (2019b) Visual abstraction of the large scale geospatial origin-destination movement Data. IEEE Trans Vis Comput Graph 25(1):43–53. https://doi.org/10.1109/TVCG.2018.2864503

    Article  Google Scholar 

  • Zuk T, Carpendale S (2006) Theoretical analysis of uncertainty visualizations. In: Proceedings of the international society for optical engineering, vol 6060, pp 606007–606014

Download references

Acknowledgements

This work is supported by the National Key Research and Development Program of China No. 2018YFB0904503, the National Science and Technology Fundamental Resources Investigation Program of China No. 2018FY10090002, the National Natural Science Foundation of China Nos. 61672538 and 61872388, and the Open Research Fund of Beijing Key Laboratory of Big Data Technology for Food Safety (Beijing Technology and Business University) No. BKBD-2018KF08.

Author information

Authors and Affiliations

  1. School of Computer Science and Engineer, Central South University, Changsha, China

    Fangfang Zhou, Yitao Wu, Minghui Chen, Zengsheng Zhong, Rongchen Zhu & Ying Zhao

  2. School of Automation, Central South University, Changsha, China

    Bing Bai

  3. Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing Technology and Business University, Beijing, China

    Yi Chen

Authors
  1. Fangfang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bing Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yitao Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zengsheng Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Rongchen Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ying Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Zhao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 7523 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, F., Bai, B., Wu, Y. et al. FuzzyRadar: visualization for understanding fuzzy clusters. J Vis 22, 913–926 (2019). https://doi.org/10.1007/s12650-019-00577-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-019-00577-2

Keywords

Search

Navigation