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Multidimensional data visualization applying a variety-oriented scatterplot selection technique


Multidimensional data visualization is one of the most active research topics in information visualization since various information in our daily life forms multidimensional datasets. Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluating scatterplots, such as scagnostics, have been applied to scatterplot selection. One of the open problems of this research topic is that various scatterplots cannot be selected if we simply apply one of the metrics. In other words, we may want to apply multiple metrics simultaneously in a balanced manner when we want to select a variety of scatterplots. This paper presents a new scatterplot selection technique that solves this problem. First, the technique calculates the scores of scatterplots with multiple metrics and then constructs a graph by connecting pairs of scatterplots that have similar scores. Next, it uses a graph coloring algorithm to assign different colors to scatterplots that have similar scores. We can extract a set of various scatterplots by selecting them that the specific same color is assigned. This paper introduces two case studies: the former study is with a retail transaction dataset while the latter study is with a design optimization dataset.

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  • Aupetit M, Sedlmair M (2016) Sepme: 2002 new visual separation measures. In: IEEE Pacific visualization symposium 2012:43–52

  • Claessen JHT, van Wijk JJ (2011) lexible linked axes for multivariate data visualization. IEEE Trans Visual Comput Graphics 17(12):2310–2316

    Article  Google Scholar 

  • Dang TN, Wilkinson L (2014) Scagexplorer: Exploring scatterplots by their scagnostics. In: IEEE Pacific visualization symposium 2014:73–80

  • Harrison L, Yang F, Franconeri S, Chang R (2014) Ranking visualizations of correlation using weber’s law. IEEE Trans Visual Comput Graphics 20(12):1943–1952

    Article  Google Scholar 

  • Itoh T, Kumar A, Klein A, Kim J (2017) High-dimensional data visualization by interactive construction of low-dimensional parallel coordinate plots. J Vis Lang Comput 43(1):1–13

    Article  Google Scholar 

  • Itoh T, Nakabayashi A, Hagita M (2021) Scatterplot selection applying a graph coloring algorithm. In: The 14th International symposium on visual information communication and interaction (VINCI)

  • Lee JH, McDonell KT, Zelenyuk A, Imre D, Muller K (2013) A structure-based distance metric for high-dimensional space exploration with multidimensional scaling. IEEE Trans Comput Graph 20(3):351–364

    Article  Google Scholar 

  • Liu S, Wang B, Bremer P-T, Pascucci V (2014) Distortion-guided structure-driven interactive exploration of high-dimensional data. Comput Graph Forum 33(3):101–110

    Article  Google Scholar 

  • Matute J, Telea AC, Linsen L (2017) Skeleton-based scagnostics. IEEE Trans Comput Graph 24(1):542–552

    Article  Google Scholar 

  • Nakabayashi A, Itoh T (2019) A technique for selection and drawing of scatterplots for multi-dimensional data visualization. In: 23rd international conference on information visualisation (IV2019), pp 62–67

  • Nohno K, Wu H-Y, Watanabe K, Takahashi S, Fujishiro I (2014) Spectral-based contractible parallel coordinates. In: 18th international conference on information visualisation, pp 7–12

  • Sasaki D, Obayashi S, Nakahashi K (2002) Navier-stokes optimization of supersonic wings with four objectives using evolutionary algorithm. J Aircr 39(4):621–629

    Article  Google Scholar 

  • Sedlmair M, Tatu A, Munzner T, Tory M (2012) A taxonomy of visual cluster separation factors. Comput Graph Forum 31(3):1335–1344

    Article  Google Scholar 

  • Shao L, Mahajan A, Schreck T, Lehmann DJ (2017) Interactive regression lens for exploring scatter plots. Comput Graph Forum 36(3):157–166

    Article  Google Scholar 

  • Sips M, Neubert B, Lewis JP, Hanrahan P (2009) Selecting good views of high-dimensional data using class consistency. Comput Graph Forum 28(3):831–838

    Article  Google Scholar 

  • Suematsu H, Zheng Y, Itoh T, Fujimaki R, Morinaga S, Kawahara Y (2013) Arrangement of low-dimenional parallel coordinate plots for high-dimensional data visualization. In: 17th international conference on information visualisation, pp 59–65

  • Wang Y, Wang Z, Liu T, Correll M, Cheng Z, Deussen O, Sedlmair M (2020) Improving the robustness of scagnostics. IEEE Trans Visual Comput Graphics 26(1):759–769

    Article  Google Scholar 

  • Watanabe A, Itoh T, Kanazaki M, Chiba K (2017) A scatterplots selection technique for multi-dimensional data visualization combining with parallel coordinate plots. In: 21st international conference on information visualisation (IV2017), pp 78–83

  • Wilkinson L, Anand A, Grossman R (2005) Graph-theoretic Scagnostics. In: IEEE symposium on information visualization, pp 157–164

  • Yuan X, Ren D, Wang Z, Guo C (2013) Dimension projection matrix/tree: interactive subspace visual exploration and analysis of high dimensional data. IEEE Trans Visual Comput Graphics 19(12):2625–2633

    Article  Google Scholar 

  • Zhang Z, McDonnel KT, Zadak E, Muller K (2015) Visual correlation analysis of numerical and categorical data on the correlation map. IEEE Trans Visual Comput Graphics 21(2):289–303

    Article  Google Scholar 

  • Zhang Z, McDonnell KT, Mueller K (2012) A network-based interface for the exploration of high-dimensional data spaces. In: IEEE Pacific visualization symposium 2012:17–24

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

    Article  Google Scholar 

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We appreciate ABEJA, Inc. for providing the retail transaction dataset. Also, we appreciate Prof. Shigeru Obayashi of Tohoku University, Japan, for providing the design optimization dataset.

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Correspondence to Takayuki Itoh.

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Itoh, T., Nakabayashi, A. & Hagita, M. Multidimensional data visualization applying a variety-oriented scatterplot selection technique. J Vis (2022).

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  • Multidimensional data visualization
  • Scatterplot selection
  • Graph coloring algorithm
  • Retail transaction data
  • Design optimization data