用梯度优化生成更优的二维网格排序布局
Creating Sorted Grid Layouts with Gradient-based Optimization
- 首次引入梯度优化方法解决网格排序难题
- 在8×8网格上排列数超10^89，仍高效生成有序布局
- 适合需要高质量可视化排列的研究者和开发者
视觉上有序的网格布局能有效将高维向量映射到二维空间，使空间邻近性与相似性对齐。该方法适用于从数据点到图像等多样元素的排序，并可同时展示大量元素。然而，二维网格排序因组合爆炸而极具挑战：仅8×8网格就有超过1.3×10^89种排列方式，远超宇宙原子总数，暴力搜索不可行。尽管已有多种排序方法，但尚未探索梯度优化的潜力。本文首次提出基于梯度优化的网格排序新方法，设计一种新型损失函数，平衡生成“合法”排列矩阵与优化向量相似性布局之间的矛盾目标，借鉴评估排序质量的指标。虽学习方法计算复杂，但本方法在排序质量上显著优于现有技术。
原文摘要 · Abstract (English)
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of diverse elements ranging from data points to images, and enables the simultaneous visualization of a significant number of elements. However, sorting data on two-dimensional grids is a challenge due to its high complexity. Even for a small 8-by-8 grid with 64 elements, the number of possible arrangements exceeds $1.3 \cdot 10^{89}$ - more than the number of atoms in the universe - making brute-force solutions impractical. Although various methods have been proposed to address the challenge of determining sorted grid layouts, none have investigated the potential of gradient-based optimization. In this paper, we present a novel method for grid-based sorting that exploits gradient optimization for the first time. We introduce a novel loss function that balances two opposing goals: ensuring the generation of a "valid" permutation matrix, and optimizing the arrangement on the grid to reflect the similarity between vectors, inspired by metrics that assess the quality of sorted grids. While learning-based approaches are inherently computationally complex, our method shows promising results in generating sorted grid layouts with superior sorting quality compared to existing techniques.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。