利用极排序和快速多维投影揭示可重排序矩阵中的带状和环状模式

IF 0.2 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
C. G. Silva
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引用次数: 2

摘要

分析人员可以使用基于矩阵的可视化(如热图)来揭示数据集的模式,并借助重新排序算法来正确地排列矩阵的行和列。其中一种算法是Polar Sort,这是一种以模式为中心的重排序方法,它使用多维投影技术(经典MDS)来显示可重排序矩阵中的带状和环状模式。尽管对于上述模式具有良好的重排序结果,但由于经典MDS的渐近时间复杂度(对于大小为n × n的输入矩阵)为O(n3), Polar排序不具有可扩展性。在本文中,我们提出了该算法的一个新版本,其中我们用FastMap替代了经典MDS, FastMap是一种渐近时间复杂度为O(n)的方法。新算法(使用Fastmap的Polar Sort,简称PSF)根据它们的二维投影排列行和列,并使用与Polar Sort方法相同的基于重心的排序。实验结果表明,在对合成矩阵进行重排序时,PSF在最小跨度损失函数、摩尔应力和循环相关性方面保持了Polar Sort的输出质量。此外,PSF的渐近时间复杂度为O(n log n),这一复杂度与我们的实验结果一致,表明PSF的执行时间比其他比较方法要短。我们还展示了一些例子,其中现实世界的矩阵通过PSF重新排序显示出类似于Band和Circumplex的模式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
REVEALING BAND AND CIRCUMPLEX PATTERNS IN REORDERABLE MATRICES USING POLAR SORT AND FAST MULTIDIMENSIONAL PROJECTIONS
Analysts may use matrix-based visualizations (such as heatmaps) to reveal patterns of a dataset with the help of reordering algorithms that permute matrix rows and columns properly. One of these algorithms is Polar Sort, a pattern-focused reordering method that uses a multidimensional projection technique – Classical MDS – to reveal Band and Circumplex patterns in reorderable matrices. Despite its good reordering results regarding the mentioned patterns, Polar sort is not scalable due to Classical MDS’ asymptotic time complexity (O(n3) for an input matrix with size n × n). In this paper, we propose a new version of this algorithm, in which we replace Classical MDS with FastMap, a method with asymptotic time complexity O(n). The new algorithm (Polar Sort with Fastmap, or PSF for short) permutes rows and columns according to their bidimensional projections and uses a barycenter-based ordering identical to Polar Sort’s approach. The results of an experiment indicate that PSF maintained the output quality of Polar Sort regarding minimal span loss function, Moore stress, and circular correlation when reordering synthetic matrices. Besides, PSF’s asymptotic time complexity is O(n log n). This complexity is coherent with our experiment results, which point out that PSF had lower execution time than other compared methods. We also show some examples in which real-world matrices reordered by PSF revealed patterns similar to Band and Circumplex.
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来源期刊
IADIS-International Journal on Computer Science and Information Systems
IADIS-International Journal on Computer Science and Information Systems COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-
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