Visual dimension analysis based on dimension subdivision

A Correction to this article was published on 09 April 2021

This article has been updated


Visualization of multidimensional data has always been a research hotspot. Dimensional analysis is an efficient way to solve multidimensional problems. The current dimensional analysis methods mostly consider that all dimension correlations are at the same granularity, but actually the correlation between dimensions may be multi-scale. Multi-scale dimensions can also reflect the multi-scale data association mode, which is of certain value for analyzing the hidden information of multidimensional data. In this paper, we propose a method of dimension subdivision to resolve the multi-scale correlations between dimensions. To explore the multi-scale complex relationship between dimensions, we subdivide the original dimensions into finer sub-dimensions and build a graph-based data structure of the correlations to partition strongly relevant and irrelevant dimensions. We also proposed D-div, a visual dimension analysis system to support our method. In D-div, we provide visualization and interaction techniques to explore subdivided dimensions. Via case studies with two datasets, we demonstrate the effectiveness of our method of dimension subdivision.

Graphic abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Change history


  1. Adrian M, Michael G (2013) Splatterplots: overcoming overdraw in scatter plots. IEEE Trans Vis Comput Graph 19(9):1526–1538

    Article  Google Scholar 

  2. Becker RA, Cleveland WS (1987) Brushing scatterplots. Technometrics 29(2):127–142

    MathSciNet  Article  Google Scholar 

  3. Cheng S, Mueller K (2016) The data context map: fusing data and attributes into a unified display. IEEE Trans Vis Comput Graph 22(1):121–130

    Article  Google Scholar 

  4. Cheng S, Xu W, Mueller K (2019) Colormapnd: a data-driven approach and tool for mapping multivariate data to color. IEEE Trans Vis Comput Graph 25(2):1361–1377

    Article  Google Scholar 

  5. Cheng S, Mueller K (2015) Improving the fidelity of contextual data layouts using a generalized barycentric coordinates framework. In: 2015 IEEE Pacific visualization symposium (PacificVis), pp 295–302

  6. Elmqvist N, Dragicevic P, Fekete JD (2008) Rolling the dice: multidimensional visual exploration using scatterplot matrix navigation. IEEE Trans Vis Comput Graph 14(6):1539–1548

    Article  Google Scholar 

  7. Ester M, Kriegel H. P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: International conference on knowledge discovery and data mining

  8. Hoffman P, Grinstein G, Marx K, Grosse I, Stanley E (1997) DNA visual and analytic data mining. In: Proceedings. Visualization ’97 (Cat. No. 97CB36155), pp 437–441

  9. Inselberg A, Dimsdale B (1990) Parallel coordinates: a tool for visualizing multi-dimensional geometry. In: Visualization, 1990. Visualization ’90., Proceedings of the first IEEE conference on, pp 361–378

  10. Itoh T, Kumar A, Klein K, Kim J (2017) High-dimensional data visualization by interactive construction of low-dimensional parallel coordinate plots. J Vis Lang Comput

  11. Iyer GR, Duttaduwarah S, Sharma A (2018) Datascope: interactive visual exploratory dashboards for large multidimensional data. In: IEEE workshop on visual analytics in healthcare, pp 17–23

  12. Jolliffe I (2002) Principal component analysis springerd verlag

  13. Kobourov SG (2012) Spring embedders and force directed graph drawing algorithms

  14. Kohonen T (1990) The self-organizing map. Proc IEEE 1(1–3):1–6

    MATH  Google Scholar 

  15. Kolhe S, Deshkar P (2017) Dimension reduction methodology using group feature selection. In: 2017 International conference on innovative mechanisms for industry applications (ICIMIA), pp 789–791

  16. Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. ACM SIGKDD Explor Newsl 6(1):90–105

    Article  Google Scholar 

  17. Sharko J, Grinstein G, Marx KA (2008) Vectorized radviz and its application to multiple cluster datasets. IEEE Trans Vis Comput Graphics 14(6):1427–1444

    Article  Google Scholar 

  18. Tatu A, Albuquerque G, Eisemann M, Bak P, Theisel H, Magnor M, Keim D (2011) Automated analytical methods to support visual exploration of high-dimensional data. IEEE Trans Vis Comput Graphics 17(5):584–597

    Article  Google Scholar 

  19. Tatu A, Bertini E, Schreck T, Keim D, Bremm S, Landesberger TV (2012) Clustnails: visual analysis of subspace clusters. Tsinghua Sci Technol 17(4):419–428

    Article  Google Scholar 

  20. Turkay C, Kaya E, Balcisoy S, Hauser H (2016) Designing progressive and interactive analytics processes for high-dimensional data analysis. IEEE Trans Vis Comput Graphics (99): 1–1

  21. Wong PC, Bergeron RD (1997) Multivariate visualization using metric scaling. In: Visualization ’97., Proceedings, pp 111–ff

  22. Xiaoru Y, Donghao R, Zuchao W, Cong G (2013) Dimension projection matrix/tree: interactive subspace visual exploration and analysis of high dimensional data. IEEE Trans Vis Comput Graphics 19(12):2625–2633

    Article  Google Scholar 

  23. Zhang Z, Zhang J, Chan T, Ying LU, Yuan X, Tianlong GU (2017) Interactive dimension reordering in radviz with correlation matrix. Pattern Recognit Artif Intell 30(7):637–645

    Google Scholar 

  24. Zhang T, Yang B (2016) Big data dimension reduction using PCA. In: 2016 IEEE international conference on smart cloud (SmartCloud), pp 152–157

  25. Zheng Y, Suematsu H, Itoh T, Fujimaki R, Morinaga S, Kawahara Y (2015) Scatterplot layout for high-dimensional data visualization. J Vis 18(1):111–119

    Article  Google Scholar 

  26. Zhou F, Huang W, Li J, Huang Y, Shi Y, Zhao Y (2015) Extending dimensions in radviz based on mean shift. In: 2015 IEEE Pacific visualization symposium (PacificVis), pp 111–115

Download references

Author information



Corresponding author

Correspondence to Yi Zhang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y., Yu, C., Wang, R. et al. Visual dimension analysis based on dimension subdivision. J Vis 24, 117–131 (2021).

Download citation


  • Multidimensional data
  • Dimensional analysis
  • Correlation analysis
  • Multidimensional visualization