Ordering has been extensively studied in many visualization applications, such as axis and matrix reordering, for the simple reason that the order will greatly impact the perceived pattern of data. Many quality metrics concerning data pattern, perception, and aesthetics are proposed, and respective optimization algorithms are developed. However, the optimization problems related to ordering are often difficult to solve (e.g., TSP is NP-complete), and developing specialized optimization algorithms is costly. In this paper, we propose Versatile Ordering Network (VON), which automatically learns the strategy to order given a quality metric. VON uses the quality metric to evaluate its solutions, and leverages reinforcement learning with a greedy rollout baseline to improve itself. This keeps the metric transparent and allows VON to optimize over different metrics. Additionally, VON uses the attention mechanism to collect information across scales and reposition the data points with respect to the current context. This allows VONs to deal with data points following different distributions. We examine the effectiveness of VON under different usage scenarios and metrics. The results demonstrate that VON can produce comparable results to specialized solvers. The code is available at https://github.com/sysuvis/VON.

翻译：排序在众多可视化应用中（如坐标轴与矩阵重排）已得到广泛研究，其根本原因在于排序会显著影响数据呈现的模式。针对数据模式、感知效果与美学特征，研究者提出了多种质量度量指标，并开发了相应的优化算法。然而，与排序相关的优化问题往往难以求解（例如旅行商问题属于NP完全问题），且开发专用优化算法成本高昂。本文提出通用排序网络（VON），该网络能够根据给定的质量度量指标自动学习排序策略。VON利用质量度量评估自身生成的排序方案，并采用基于贪婪策略的强化学习方法进行自我优化。这种设计保持了度量指标的透明性，使VON能够适配不同度量标准进行优化。此外，VON通过注意力机制跨尺度收集信息，并根据当前上下文动态调整数据点的位置。这使得VON能够处理遵循不同分布的数据点。我们在多种使用场景和度量标准下验证了VON的有效性。实验结果表明，VON能够取得与专用求解器相媲美的排序效果。代码已开源：https://github.com/sysuvis/VON。