🤖 AI Summary
Existing grid-based visualization layout methods struggle to preserve the inherent cluster structure of data. This paper proposes a cluster-aware grid layout method that, for the first time, jointly models cluster proximity, compactness, and convexity within grid layouts. We introduce a two-stage hybrid optimization framework: a global stage employs nonlinear programming to achieve intra-cluster balance, while a local stage enforces shape constraints to guarantee cluster convexity. The method incorporates a cluster identification preprocessing step and a quantitative structural fidelity metric. Evaluations on multiple datasets show an average 32% improvement in convexity scores; two real-world case studies demonstrate its effectiveness in supporting cluster-oriented visual analysis tasks. Our core contribution lies in the explicit modeling of cluster geometric integrity—ensuring high-fidelity preservation of topological and spatial cluster structure within constrained grid layouts.
📝 Abstract
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.
