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.

翻译：大型矩阵的可视化涉及许多棘手的问题。这些问题的各种普遍解决办法涉及抽样、集群、投影或特征选择,以减少最初任务的规模和复杂性。这些方法的一个重要方面是,如何在将行和列缩小到适合较低维度空间之后,在高维空间各点之间保持相对距离。这个方面很重要,因为根据错误的视觉推理作出的结论可能有害。根据可视化得出不同点的相似或相似点可能会导致错误的结论。为了消除这种偏差并使非常大数据集的可视化成为可行,我们引入了两种新的算法,分别选择了一组长方形矩阵的行和列。这种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造和实际数据集的较传统的替代图作比较。