Abstract

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An important aspect of these methods is how to preserve relative distances between points in the higher-dimensional space after reducing rows and columns to fit in a lower dimensional space. This aspect is important because conclusions based on faulty visual reasoning can be harmful. Judging dissimilar points as similar or similar points as dissimilar on the basis of a visualization can lead to false conclusions. To ameliorate this bias and to make visualizations of very large datasets feasible, we introduce two new algorithms that, respectively, select a subset of rows and columns of a rectangular matrix. This selection is designed to preserve relative distances as closely as possible. We compare our matrix sketch to more traditional alternatives on a variety of artificial and real datasets. Supplementary materials for this article are available online.

摘要

可视化非常大的矩阵涉及许多棘手的问题。这些问题的各种流行解决方案涉及采样、聚类、投影或特征选择，以减少原始任务的大小和复杂性。这些方法的一个重要方面是如何在减少行和列以适应较低维空间后保持较高维空间中点之间的相对距离。这方面很重要，因为基于错误的视觉推理得出的结论可能是有害的。在可视化的基础上将不同点判断为相似或将相似点判断为不同可能会导致错误的结论。为了改善这种偏差并使非常大的数据集的可视化变得可行，我们引入了两种新算法，它们分别选择矩形矩阵的行和列的子集。此选择旨在尽可能保持相对距离。我们将我们的矩阵草图与各种人工和真实数据集上的更传统的替代方案进行比较。本文的补充材料可在线获取。