Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
126 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Grid-based Method for Removing Overlaps of Dimensionality Reduction Scatterplot Layouts (1903.06262v8)

Published 8 Mar 2019 in cs.CV

Abstract: Dimensionality Reduction (DR) scatterplot layouts have become a ubiquitous visualization tool for analyzing multidimensional datasets. Despite their popularity, such scatterplots suffer from occlusion, especially when informative glyphs are used to represent data instances, potentially obfuscating critical information for the analysis under execution. Different strategies have been devised to address this issue, either producing overlap-free layouts that lack the powerful capabilities of contemporary DR techniques in uncovering interesting data patterns or eliminating overlaps as a post-processing strategy. Despite the good results of post-processing techniques, most of the best methods typically expand or distort the scatterplot area, thus reducing glyphs' size (sometimes) to unreadable dimensions, defeating the purpose of removing overlaps. This paper presents Distance Grid (DGrid), a novel post-processing strategy to remove overlaps from DR layouts that faithfully preserves the original layout's characteristics and bounds the minimum glyph sizes. We show that DGrid surpasses the state-of-the-art in overlap removal (through an extensive comparative evaluation considering multiple different metrics) while also being one of the fastest techniques, especially for large datasets. A user study with 51 participants also shows that DGrid is consistently ranked among the top techniques for preserving the original scatterplots' visual characteristics and the aesthetics of the final results.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (63)
  1. Neurocomputing: Foundations of Research. MIT Press, Cambridge, MA, USA, 1988.
  2. J. L. Bentley. Multidimensional binary search trees used for associative searching. Commun. ACM, 18(9):509–517, Sept. 1975.
  3. E. Bertini and G. Santucci. Give chance a chance: Modeling density to enhance scatter plot quality through random data sampling. Information Visualization, 5:110 – 95, 2006.
  4. R. Brath. 3d infovis is here to stay: Deal with it. In 2014 IEEE VIS International Workshop on 3DVis (3DVis), pp. 25–31, 2014. doi: 10 . 1109/3DVis . 2014 . 7160096
  5. Rank products: a simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments. FEBS Letters, 573(1-3):83–92, 2004. doi: 10 . 1016/j . febslet . 2004 . 07 . 055
  6. R. A. Brown. Building a balanced k𝑘kitalic_k-d tree in o⁢(k⁢n⁢log⁡n)𝑜𝑘𝑛𝑛o(kn\log n)italic_o ( italic_k italic_n roman_log italic_n ) time. Journal of Computer Graphics Techniques (JCGT), 4(1):50–68, March 2015.
  7. Dicon: Interactive visual analysis of multidimensional clusters. IEEE Transactions on Visualization and Computer Graphics, 17(12):2581–2590, 2011. doi: 10 . 1109/TVCG . 2011 . 188
  8. Scatterplot matrix techniques for large n. Journal of the American Statistical Association, 82(398):424–436, 1987. doi: 10 . 1080/01621459 . 1987 . 10478445
  9. Node overlap removal algorithms: an extended comparative study. Journal of Graph Algorithms and Applications, 24(4):683–706, 2020. doi: 10 . 7155/jgaa . 00532
  10. A recursive subdivision technique for sampling multi-class scatterplots. IEEE Transactions on Visualization and Computer Graphics, 26(1):729–738, 2020. doi: 10 . 1109/TVCG . 2019 . 2934541
  11. Hagrid: using hilbert and gosper curves to gridify scatterplots. Journal of Visualization, 25(6):1291–1307, 2022.
  12. D. Dua and C. Graff. UCI machine learning repository, 2017.
  13. Nmap: A novel neighborhood preservation space-filling algorithm. IEEE Transactions on Visualization and Computer Graphics, 20(12):2063–2071, 2014. doi: 10 . 1109/TVCG . 2014 . 2346276
  14. Fast node overlap removal. In P. Healy and N. S. Nikolov, eds., Graph Drawing, pp. 153–164. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006.
  15. Visual analysis of image collections. Vis. Comput., 25(10):923–937, 2009. doi: 10 . 1007/s00371-009-0368-7
  16. N. Elmqvist. Balloonprobe: Reducing occlusion in 3d using interactive space distortion. In Proceedings of the ACM Symposium on Virtual Reality Software and Technology, VRST ’05, p. 134–137. Association for Computing Machinery, New York, NY, USA, 2005. doi: 10 . 1145/1101616 . 1101643
  17. Improved grid map layout by point set matching. In 2013 IEEE Pacific Visualization Symposium (PacificVis), pp. 25–32, 2013. doi: 10 . 1109/PacificVis . 2013 . 6596124
  18. Toward a quantitative survey of dimension reduction techniques. IEEE Transactions on Visualization and Computer Graphics, 27(3):2153–2173, 2021. doi: 10 . 1109/TVCG . 2019 . 2944182
  19. Isomatch: Creating informative grid layouts. Comput. Graph. Forum, 34(2):155–166, May 2015.
  20. The influence of contour on similarity perception of star glyphs. IEEE Transactions on Visualization and Computer Graphics, 20(12):2251–2260, 2014. doi: 10 . 1109/TVCG . 2014 . 2346426
  21. E. Gansner and Y. Hu. Efficient, proximity-preserving node overlap removal. J. Graph Algorithms Appl., 14:53–74, 2010.
  22. Minimum-Displacement Overlap Removal for Geo-referenced Data Visualization. Computer Graphics Forum, 2017. doi: 10 . 1111/cgf . 13199
  23. Mixed integer optimization for layout arrangement. In 2013 XXVI Conference on Graphics, Patterns and Images, pp. 115–122, 2013. doi: 10 . 1109/SIBGRAPI . 2013 . 25
  24. Similarity preserving snippet-based visualization of web search results. IEEE Transactions on Visualization and Computer Graphics, 20(3):457–470, 2014. doi: 10 . 1109/TVCG . 2013 . 242
  25. A layout adjustment problem for disjoint rectangles preserving orthogonal order. In Graph Drawing, 1998.
  26. World Happiness Report 2019. New York: Sustainable Development Solutions Network, 2019.
  27. G. F. Jenks. The data model concept in statistical mapping. International Yearbook of Cartography, 7:186–190, 1967.
  28. Glyphboard: Visual exploration of high-dimensional data combining glyphs with dimensionality reduction. IEEE Transactions on Visualization and Computer Graphics, 26(4):1661–1671, 2020. doi: 10 . 1109/TVCG . 2020 . 2969060
  29. J. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1):1–27, 1964.
  30. A model of symbol size discrimination in scatterplots. In Proceedings of the 28th International Conference on Human Factors in Computing Systems, 2010.
  31. Evaluation of symbol contrast in scatterplots. In 2009 IEEE Pacific Visualization Symposium, 2009.
  32. A unified approach to interpreting model predictions. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, eds., Advances in Neural Information Processing Systems 30, pp. 4765–4774. Curran Associates, Inc., 2017.
  33. Evaluation of approaches proposed to avoid overlap of markers in visualizations based on multidimensional projection techniques. Information Visualization, 18(4):426–438, 2019. doi: 10 . 1177/1473871619845093
  34. Visual analysis of dimensionality reduction quality for parameterized projections. Computers & Graphics, 41:26–42, 2014. doi: 10 . 1016/j . cag . 2014 . 01 . 006
  35. A. Mayorga and M. Gleicher. Splatterplots: Overcoming overdraw in scatter plots. IEEE Transactions on Visualization and Computer Graphics, 19(9):1526–1538, 2013. doi: 10 . 1109/TVCG . 2013 . 65
  36. Umap: Uniform manifold approximation and projection for dimension reduction, 2020.
  37. G. McNeill and S. A. Hale. Generating tile maps. Computer Graphics Forum, 36(3):435–445, 2017. doi: 10 . 1111/cgf . 13200
  38. W. Meulemans. Efficient optimal overlap removal: Algorithms and experiments. Computer Graphics Forum, 38(3):713–723, 2019. doi: 10 . 1111/cgf . 13722
  39. Small multiples with gaps. IEEE Transactions on Visualization and Computer Graphics, 23(1):381–390, Jan 2017.
  40. Towards perceptual optimization of the visual design of scatterplots. IEEE Transactions on Visualization and Computer Graphics, 23(6):1588–1599, 2017. doi: 10 . 1109/TVCG . 2017 . 2674978
  41. Towards perceptual optimization of the visual design of scatterplots. IEEE Transactions on Visualization and Computer Graphics, 2017.
  42. Layout adjustment and the mental map. J. Vis. Lang. Comput., 6:183–210, 1995.
  43. Layout adjustment and the mental map. Journal of Visual Languages & Computing, 6(2):183–210, 1995. doi: 10 . 1006/jvlc . 1995 . 1010
  44. Node overlap removal by growing a tree. In Y. Hu and M. Nöllenburg, eds., Graph Drawing and Network Visualization, pp. 33–43. Springer International Publishing, Cham, 2016.
  45. L. G. Nonato and M. Aupetit. Multidimensional projection for visual analytics: Linking techniques with distortions, tasks, and layout enrichment. IEEE Transactions on Visualization and Computer Graphics, 25(8):2650–2673, 2019. doi: 10 . 1109/TVCG . 2018 . 2846735
  46. Hexboard: Conveying pairwise similarity in an incremental visualization space. In 2009 13th International Conference Information Visualisation, pp. 32–37, 2009. doi: 10 . 1109/IV . 2009 . 12
  47. Incremental board: A grid-based space for visualizing dynamic data sets. In Proceedings of the 2009 ACM Symposium on Applied Computing, p. 1757–1764. Association for Computing Machinery, New York, NY, USA, 2009. doi: 10 . 1145/1529282 . 1529679
  48. Kernelized sorting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32:1809–1821, 2010.
  49. E. Raisz. The rectangular statistical cartogram. Geographical Review, 24:292–296, 1934.
  50. Testing the degree of overlap for the expected value of random intervals. International Journal of Approximate Reasoning, 119:1–19, 2020. doi: 10 . 1016/j . ijar . 2019 . 12 . 012
  51. Projections as visual aids for classification system design. Information Visualization, 17(4):282–305, 2018. doi: 10 . 1177/1473871617713337
  52. A. Sarikaya and M. Gleicher. Scatterplots: Tasks, data, and designs. IEEE Transactions on Visualization and Computer Graphics, 24(1):402–412, 2018. doi: 10 . 1109/TVCG . 2017 . 2744184
  53. Empirical guidance on scatterplot and dimension reduction technique choices. IEEE Transactions on Visualization and Computer Graphics, 19(12):2634–2643, 2013. doi: 10 . 1109/TVCG . 2013 . 153
  54. Rolled‐out wordles: A heuristic method for overlap removal of 2d data representatives. Computer Graphics Forum, 31, 2012.
  55. G. Strong and M. Gong. Data organization and visualization using self-sorting map. In Proceedings of Graphics Interface 2011, GI ’11, p. 199–206, 2011.
  56. Spatialization design: Comparing points and landscapes. IEEE Transactions on Visualization and Computer Graphics, 13(6):1262–1269, 2007. doi: 10 . 1109/TVCG . 2007 . 70596
  57. L. van der Maaten and G. Hinton. Visualizing High-Dimensional Data Using t-SNE. Journal of Machine Learning Research, 9:2579–2605, Nov. 2008.
  58. M. van Kreveld and B. Speckmann. On rectangular cartograms. In S. Albers and T. Radzik, eds., Algorithms – ESA 2004, pp. 724–735. Springer Berlin Heidelberg, Berlin, Heidelberg, 2004.
  59. J. Venna and S. Kaski. Neighborhood preservation in nonlinear projection methods: An experimental study. In G. Dorffner, H. Bischof, and K. Hornik, eds., Artificial Neural Networks — ICANN 2001, pp. 485–491. Springer Berlin Heidelberg, Berlin, Heidelberg, 2001.
  60. J. Wood and J. Dykes. Spatially ordered treemaps. IEEE Transactions on Visualization and Computer Graphics, 14(6):1348–1355, 2008. doi: 10 . 1109/TVCG . 2008 . 165
  61. Visualisation of origins, destinations and flows with od maps. The Cartographic Journal, 47:117 – 129, 2010.
  62. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. ArXiv, abs/1708.07747, 2017.
  63. Evaluation of sampling methods for scatterplots. IEEE Transactions on Visualization and Computer Graphics, 27(02):1720–1730, feb 2021. doi: 10 . 1109/TVCG . 2020 . 3030432
Citations (6)

Summary

We haven't generated a summary for this paper yet.