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Sample selection improves the efficiency and effectiveness of machine learning models by providing informative and representative samples. Typically, samples can be modeled as a sample graph, where nodes are samples and edges represent their similarities. Most existing methods are based on local information, such as the training difficulty of samples, thereby overlooking global information, such as connectivity patterns. This oversight can result in suboptimal selection because global information is crucial for ensuring that the selected samples well represent the structural properties of the graph. To address this issue, we employ structural entropy to quantify global information and losslessly decompose it from the whole graph to individual nodes using the Shapley value. Based on the decomposition, we present $\textbf{S}$tructural-$\textbf{E}$ntropy-based sample $\textbf{S}$election ($\textbf{SES}$), a method that integrates both global and local information to select informative and representative samples. SES begins by constructing a $k$NN-graph among samples based on their similarities. It then measures sample importance by combining structural entropy (global metric) with training difficulty (local metric). Finally, SES applies importance-biased blue noise sampling to select a set of diverse and representative samples. Comprehensive experiments on three learning scenarios -- supervised learning, active learning, and continual learning -- clearly demonstrate the effectiveness of our method., Comment: Published as a conference paper at ICLR 2025

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., Comment: Submitted to IEEE TVCG