Title:	USING FAST MULTIDIMENSIONAL PROJECTIONS TO REVEAL BAND AND CIRCUMPLEX PATTERNS IN REORDERABLE MATRICES
Author(s):	Celmar Guimarães da Silva
ISBN:	978-989-8704-32-0
Editors:	Yingcai Xiao, Ajith Abraham and Guo Chao Peng
Year:	2021
Edition:	Single
Keywords:	Reorderable Matrices, Patterns, Multidimensional Projection
Type:	Full
First Page:	3
Last Page:	10
Language:	English
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Paper Abstract:	Matrix reordering techniques are essential to reveal patterns in tabular visualizations (such as heatmaps). Polar Sort is a state-of-the-art, pattern-focused reordering method that uses a multidimensional projection technique - Classical MDS - to reveal Band and Circumplex patterns in reorderable matrices. However, Polar Sort is not scalable due to Classical MDS' asymptotic time complexity (O(n³)). In this paper, we explore the use of a fast multidimensional projection technique - FastMap (O(n)) - as an alternative to Classical MDS inside Polar Sort. The new reordering algorithm - PSF - reorders rows and columns of a matrix according to bidimensional projections projected by FastMap (instead of Classical MDS), and uses a barycenter-based ordering identical to Polar Sort's approach. The results of an experiment with synthetic matrices point out that PSF maintained the output quality of its predecessor (according to minimal span loss function, Moore stress, and circular correlation) and had lower execution time than other compared methods. We present the results of these experiments and also some examples of real-world matrices that show patterns similar to Band and Circumplex when reordered by PSF.
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