Grid visualizations are widely used in many applications to visually explain a set of data and their proximity relationships. However, existing layout methods face difficulties when dealing with the inherent cluster structures within the data. To address this issue, we propose a cluster-aware grid layout method that aims to better preserve cluster structures by simultaneously considering proximity, compactness, and convexity in the optimization process. Our method utilizes a hybrid optimization strategy that consists of two phases. The global phase aims to balance proximity and compactness within each cluster, while the local phase ensures the convexity of cluster shapes. We evaluate the proposed grid layout method through a series of quantitative experiments and two use cases, demonstrating its effectiveness in preserving cluster structures and facilitating analysis tasks.

翻译：网格可视化广泛应用于诸多场景，用于直观展示数据集及其邻近关系。然而，现有布局方法在处理数据内在的聚类结构时面临挑战。针对这一问题，我们提出一种面向聚类的网格布局方法，旨在通过同时优化邻近性、紧凑性和凸性来更好地保持聚类结构。该方法采用两阶段混合优化策略：全局阶段平衡各聚类内部的邻近性与紧凑性，局部阶段则确保聚类形状的凸性。通过一系列定量实验和两个应用案例的评估，我们验证了所提网格布局方法在保持聚类结构和辅助分析任务方面的有效性。