Matrix reordering permutes the rows and columns of a matrix to reveal meaningful visual patterns, such as blocks that represent clusters. A comprehensive collection of matrices, along with a scoring method for measuring the quality of visual patterns in these matrices, contributes to building a benchmark. This benchmark is essential for selecting or designing suitable reordering algorithms for specific tasks. In this paper, we build a matrix reordering benchmark, ReorderBench, with the goal of evaluating and improving matrix reordering techniques. This is achieved by generating a large set of representative and diverse matrices and scoring these matrices with a convolution- and entropy-based method. Our benchmark contains 2,835,000 binary matrices and 5,670,000 continuous matrices, each featuring one of four visual patterns: block, off-diagonal block, star, or band. We demonstrate the usefulness of ReorderBench through three main applications in matrix reordering: 1) evaluating different reordering algorithms, 2) creating a unified scoring model to measure the visual patterns in any matrix, and 3) developing a deep learning model for matrix reordering.

翻译：矩阵重排序通过对矩阵的行和列进行置换，以揭示有意义的视觉模式，例如代表聚类的块状结构。构建一个全面的矩阵集合，并辅以衡量这些矩阵中视觉模式质量的评分方法，有助于建立一个基准测试。该基准对于为特定任务选择或设计合适的重排序算法至关重要。本文构建了一个矩阵重排序基准测试——ReorderBench，旨在评估和改进矩阵重排序技术。我们通过生成大量具有代表性和多样性的矩阵，并采用一种基于卷积和熵的方法对这些矩阵进行评分来实现这一目标。我们的基准包含2,835,000个二元矩阵和5,670,000个连续矩阵，每个矩阵呈现四种视觉模式之一：块状、非对角块状、星状或带状。我们通过矩阵重排序的三个主要应用来证明ReorderBench的实用性：1) 评估不同的重排序算法，2) 创建一个统一的评分模型以衡量任意矩阵中的视觉模式，以及3) 开发一个用于矩阵重排序的深度学习模型。