# Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public

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## Abstract

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## 1. Introduction

#### 1.1. History

_{1}, x

_{2}, …, x

_{k}, researchers can display k dimensions by a k × k scatterplot matrix. Therefore, a scatterplot can display not only 2D data but data with more dimensions. A concept similar to the scatterplot matrix is used in macroeconomics. Figure 1 shows a four-quadrant diagram in part of an IS-LM model. In the diagram, if the value in quadrant I moves from IS

_{0}to IS

_{1}, it will cause the values in quadrants IV, III, and II to move sequentially because quadrant I and IV share the same X-axis, quadrants IV and III share the same Y-axis, and quadrants III and II share the same X-axis as well. This method cleverly displays the relationship between the four changing variables. Although the above methods are helpful in some cases, they also have disadvantages: (a) The classic scatterplot usually cannot display negative values. (b) The severe limitation of a ternary plot when it comes to summing to a constant makes it not useful in many situations. (c) The bubbles in a bubble chart may overlap, or there may be too many to read. (d) A scatterplot matrix makes it complicated to see high-dimensional data patterns that can only be understood when considering three or more data dimensions simultaneously [11]. (e) A four-quadrant diagram is only suitable with 4D data and is relatively unintuitive.

#### 1.2. Research Aim

## 2. Developing the New Method

- For a specific row, the changes with time in a specific district are clearly visible. For example, the COVID-19-cases growth rate in district A changed from severe to slightly increasing; however, the death-case rate remained above the whole country’s average without significant change;
- For a specific column, the situations of all cities in a specific month are clearly visible. For example, the COVID-19-case growth rates were increasing severely, and the death-cases growth rates were above the whole country’s average in cities X and Y in January. The situation in city Z was not that serious in the same month;
- The situation in a specific space and time is shown for a particular bin. For example, in January, district A showed severe increases in COVID-19-case growth rates and a higher death-case growth rate than the averages of the whole country;
- Two sets of variables displayed by triangles and bin color can be combined to produce additional meaning. Therefore, the cumulative number and frequency of occurrences of that additional meaning at a particular time or place can be calculated. For example, suppose COVID-19 cases increase more than 1% and death-cases are higher than the nationwide average at the same time. In that case, it means the epidemic situation is “very severe” (i.e., “”). District A has had a “very severe” situation for 6 months, and two-thirds of the cities had a “very severe” situation in January;
- Because the spatial variables have category-related relationships in this case, readers can observe that the situation in the same city is similar. Among the three cities, the situations in cities X and Y are more similar but not similar in city Z. That is, the pattern of virus infections is not uniform across the country and is particularly severe in specific cities.

## 3. Case Study Example

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Bertini, E.; Tatu, A.; Keim, D. Quality metrics in high-dimensional data visualization: An overview and systematization. IEEE Trans. Vis. Comput. Graph.
**2011**, 17, 2203–2212. [Google Scholar] [CrossRef] [PubMed] - Card, S.K.; Mackinlay, J.D.; Schneiderman, B. Readings in Information Visualization: Using Vision to Think; Morgan Kaufmann: Burlington, MA, USA, 1999. [Google Scholar]
- Chernoff, H. The use of faces to represent points in k-dimensional space graphically. J. Am. Stat. Assoc.
**1973**, 68, 361–368. [Google Scholar] [CrossRef] - Kosara, R. A Critique of Chernoff Faces. 2007. Available online: https://eagereyes.org/criticism/chernoff-faces (accessed on 25 December 2023).
- Maphugger. The Trouble with Chernoff. 2013. Available online: https://maphugger.com/post/44499755749/the-trouble-with-chernoff (accessed on 25 December 2023).
- Becker, R.A.; Chambers, J.M. S: An Interactive Environment for Data Analysis and Graphics; Wadsworth: Belmont, CA, USA, 1984. [Google Scholar]
- Stata (n.d.) Graph Matrix. Available online: https://www.stata.com/manuals/g-2graphmatrix.pdf (accessed on 25 December 2023).
- Cleveland, W.S.; McGill, R. The many faces of a scatterplot. J. Am. Stat. Assoc.
**1984**, 79, 807–822. [Google Scholar] [CrossRef] - Friendly, M.; Denis, D. The early origins and development of the scatterplot. J. Hist. Behav. Sci.
**2005**, 41, 103–130. [Google Scholar] [CrossRef] [PubMed] - Chambers, J.M.; Clevland, W.S.; Kleiner, B.; Turkey, P.A. Graphical Methods for Data Analysis; Wadsworth Statistical/Probability Series; Wadsworth International Group: Fairview, TN, USA, 1983. [Google Scholar]
- Ware, C. Static and moving patterns. In Information Visualization: Perception for Design; Ware, C., Ed.; Morgan Kaufmann: Burlington, MA, USA, 2013; pp. 183–243. [Google Scholar]
- Inselberg, A.; Dimsdale, B. Parallel Coordinates: A Tool for Visualizing Multi-Dimensional Geometry. In Proceedings of the First IEEE Conference on Visualization, San Francisco, CA, USA, 23–26 October 1990; IEEE Computer Society Press: Washington, DC, USA, 1990; pp. 361–378. [Google Scholar]
- Holten, D.; van Wijk, J.J. Evaluation of cluster identification performance for different PCP variants. Comput. Graph. Forum
**2010**, 29, 793–802. [Google Scholar] [CrossRef] - Li, J.; Martens, J.B.; van Wijk, J.J. Judging correlation from scatterplots and parallel coordinate plots. Inf. Vis.
**2010**, 9, 13–29. [Google Scholar] [CrossRef] - Dimara, E.; Bezerianos, A.; Dragicevic, P. Conceptual and methodological issues in evaluating multidimensional visualizations for decision support. IEEE Trans. Vis. Comput. Graph.
**2017**, 24, 749–759. [Google Scholar] [CrossRef] [PubMed] - Partl, C.; Plaschzug, P.; Ladenhauf, D.; Fernitz, G. (n.d.) Star Plots: A Literature Survey. Available online: https://courses.isds.tugraz.at/ivis/surveys/ss2010/g4-survey-starplots.pdf (accessed on 25 December 2023).
- Sanftmann, H.; Weiskopf, D. 3D scatterplot navigation. IEEE Trans. Vis. Comput. Graph.
**2012**, 18, 1969–1978. [Google Scholar] [CrossRef] [PubMed] - Coimbra, D.B.; Martins, R.M.; Neves, T.T.; Telea, A.C.; Paulovich, F.V. Explaining three-dimensional dimensionality reduction plots. Inf. Vis.
**2016**, 15, 154–172. [Google Scholar] [CrossRef] - Friendly, M.; Denis, D.J. Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. 2001. Available online: http://www.datavis.ca/milestones/ (accessed on 25 December 2023).
- Peña-Araya, V.; Pietriga, E.; Bezerianos, A. A Comparison of Visualizations for Identifying Correlation over Space and Time. IEEE Trans. Vis. Comput. Graph.
**2020**, 26, 375–385. [Google Scholar] [CrossRef] [PubMed] - Lin, H.L.; Chen, J.C. Statistics: Methods and Application; Yeh Yeh Book Gallery: Taipei, Taiwan, 2006. [Google Scholar]
- Lu, C.T.; Boedihardjo, A.P.; Shekhar, S. Analysis of spatial data with map cubes: Highway traffic data. In Geographic Data Mining and Knowledge Discovery, 2nd ed.; Miller, H.J., Han, J.W., Eds.; Routledge: Abingdon, UK, 2009; pp. 69–97. [Google Scholar]
- Chang, K.C.; Tsai, Y.M. GIS data exploration and the application in traffic data. Public Gov. Q.
**2019**, 7, 42–47. [Google Scholar] - Ruffing, K. Indicators to measure decoupling of environmental pressure from economic growth. Sustain. Indic. Sci. Assess.
**2007**, 67, 211. [Google Scholar] - Vehmas, J.; Kaivo-oja, J.; Luukkanen, J. Global Trends of Linking Environmental Stress and Economic Growth; Finland Futures Research Centre 6: Turku, Finland, 2003. [Google Scholar]
- Wu, B.W. The Analysis of Material and Consumption and the Decoupling in Different Countries. Master’s Thesis, Department of Geography, National Taiwan Normal University, Taipei, Taiwan, 2018. Available online: https://hdl.handle.net/11296/y7pass (accessed on 15 December 2023).
- Dallison, R.J.; Patil, S.D.; Williams, A.P. Impacts of climate change on future water availability for hydropower and public water supply in Wales, UK. J. Hydrol. Reg. Stud.
**2021**, 36, 100866. [Google Scholar] [CrossRef]

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
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Dist. A, City X | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | △ | △ | △ | △ |

Dist. B, City X | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | △ | △ | △ | △ |

Dist. C, City X | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | △ | △ | △ | △ |

Dist. D, City Y | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | ▽ | ▽ | ▽ | ▽ |

Dist. E, City Y | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | ▽ | ▽ | ▽ | ▽ |

Dist. F, City Y | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | ▽ | ▽ | ▽ | ▽ |

Dist. G, City Z | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | △ | △ | △ | △ | △ | △ |

Dist. H, City Z | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | △ | △ | △ | △ | △ | △ |

Dist. I, City Z | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | △ | △ | △ | ▲ | ▲ | ▲ |

83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 00 | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

United States | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▼ | △ | ▲ | ▲ | ▲ | ▲ |

Germany | ▽ | ▽ | △ | ▲ | ▲ | ▲ | ▼ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | ▽ | ▽ | ▲ | ▽ | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | △ | ▲ | ▽ | ▲ | ▲ |

United Kingdom | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | △ | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ |

Norway | ▽ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | ▲ | ▽ | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | △ | ▲ | ▽ |

Netherlands | ▽ | ▽ | ▽ | ▲ | ▲ | ▲ | ▽ | ▲ | △ | ▲ | ▽ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▽ | ▲ | ▲ |

Japan | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▽ | ▽ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | ▽ | ▽ | ▽ | ▲ | ▲ | △ | ▲ | ▲ | ▽ | ▽ |

South Korea | △ | ▲ | △ | ▲ | ▲ | ▲ | ▲ | △ | ▲ | △ | ▲ | △ | ▲ | △ | ▽ | ▽ | ▲ | △ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | △ | ▲ | ▲ |

Taiwan | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | ▲ | ▲ | △ | △ | ▽ | ▲ | △ | ▽ | △ | △ | ▲ | ▲ | △ | ▲ | ▲ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ |

Brazil | ▲ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | ▲ | ▲ | △ | ▽ | ▽ | ▲ | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | ▽ | ▽ | ▽ |

India | ▲ | ▽ | ▲ | △ | ▲ | △ | ▽ | ▲ | ▽ | ▲ | ▽ | ▲ | ▲ | ▲ | △ | ▽ | ▲ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | △ | ▽ | △ | ▲ |

China | ▲ | ▲ | ▲ | ▽ | ▽ | ▲ | ▲ | △ | △ | △ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | △ | △ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ |

Thailand | △ | △ | ▽ | ▲ | ▲ | ▲ | △ | ▲ | ▲ | △ | ▲ | ▲ | ▲ | △ | ▽ | ▽ | ▲ | ▽ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | △ | ▲ | ▽ |

Philippines | ▽ | ▽ | ▽ | ▽ | ▲ | ▲ | △ | ▲ | ▼ | ▲ | △ | △ | ▲ | ▲ | ▽ | ▽ | ▲ | ▽ | ▽ | ▲ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | ▲ | ▲ | ▲ |

Saudi Arabia | ▽ | ▽ | ▽ | ▽ | ▽ | ▽ | △ | ▲ | ▲ | △ | ▽ | ▽ | △ | ▲ | △ | ▽ | ▲ | ▲ | ▽ | △ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▽ | ▲ | ▲ | ▲ | ▽ | ▽ |

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**MDPI and ACS Style**

Li, C.-E.; Wu, B.-W.; Kuo, N.-W.; Yuan, M.-H.
Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public. *Foundations* **2024**, *4*, 80-90.
https://doi.org/10.3390/foundations4010007

**AMA Style**

Li C-E, Wu B-W, Kuo N-W, Yuan M-H.
Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public. *Foundations*. 2024; 4(1):80-90.
https://doi.org/10.3390/foundations4010007

**Chicago/Turabian Style**

Li, Chong-En, Bing-Wen Wu, Nae-Wen Kuo, and Mei-Hua Yuan.
2024. "Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public" *Foundations* 4, no. 1: 80-90.
https://doi.org/10.3390/foundations4010007