Abstract
Heatmaps are a popular data visualization technique that allows to visualize a matrix or table in its entirety. An important step in the creation of insightful heatmaps is the determination of a good order for the rows and the columns, that is, the use of appropriate matrix reordering or seriation techniques. Unfortunately, by using artificial data with known patterns, it can be shown that existing matrix ordering techniques often fail to identify good orderings in data in the presence of noise. In this paper, we propose a novel technique that addresses this weakness. Its key idea is to make an underlying base matrix ordering technique more robust to noise by embedding it into an iterated loop with image processing techniques. Experiments show that this iterative technique improves the quality of the matrix ordering found by all base ordering methods evaluated, both for artificial and real-world data, while still offering high levels of computational performance as well.
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References
Bollen, T., Leurquin, G., Nijssen, S.: ConvoMap: Using Convolution to Order Boolean Data. In: Duivesteijn, W., Siebes, A., Ukkonen, A. (eds.) IDA 2018. LNCS, vol. 11191, pp. 62–74. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01768-2_6
Behrisch, M., Bach, B., Henry Riche, N., Schreck, T., Fekete, J.-D.: Matrix Reordering Methods for Table and Network Visualization. Comput. Graph. Forum 35, (2016). https://doi.org/10.1111/cgf.12935
Garriga, G., Junttila, E., Mannila, H.: Banded structure in binary matrices. Knowl. Inf. Syst. 28, 197–226 (2008)
Hubert, L.J.: Some applications of graph theory and related nonmetric techniques to problems of approximate seriation: The case of symmetric proximity measures. Br. J. Math. Stat. Psychol. 27, 133–153 (1974)
Mitchell-Jones, A. J., et al.: The atlas of European mammals, vol. 3. Academic Press, London (1999)
Sezgin, M., Sankur, B.: Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13(1), 146–165 (2004)
Makinen, E., Siirtola, H.: The barycenter heuristic and the reorderable matrix. Informatica (Slovenia) 29(3), 357–364 (2005)
Hahsler, M., Buchta, C., Hornik, K.: Seriation: Infrastructure for Ordering Objects Using Seriation. R package version 1.2-9 (2020)
Faskowitz, J., Yan, X., Zuo, X.N., et al.: Weighted stochastic block models of the human connectome across the life span. Sci Rep 8, 12997 (2018)
Adamic, L.A. Glance, N. The political Blogosphere and the 2004 U.S. election: divided they blog. In: Proceedings of the 3rd international workshop on Link discovery, LinkKDD 2005, New York, pp. 36–43. ACM (2005)
Yin, H., Benson, A.R., Leskovec, J., Gleich, D.F. Local higher-order graph clustering. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2017)
Banerjee, A., Chandrasekhar, A.G., Duflo, E., Jackson, M.O.: The Diffusion of Microfinance (2013). https://doi.org/10.7910/DVN/U3BIHX,HarvardDataverse,V9
Ding, C.H., He, X., Zha, H., Gu, M., Simon, H.D. A min-max cut algorithm for graph partitioning and data clustering. In: Proceedings IEEE International Conference on Data Mining (ICDM), 2001, pp. 107–114. IEEE (2001)
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Van Vracem, G., Nijssen, S. (2021). Iterated Matrix Reordering. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (eds) Machine Learning and Knowledge Discovery in Databases. Research Track. ECML PKDD 2021. Lecture Notes in Computer Science(), vol 12977. Springer, Cham. https://doi.org/10.1007/978-3-030-86523-8_45
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DOI: https://doi.org/10.1007/978-3-030-86523-8_45
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