基于隐式神经场的归纳式图布局
Inductive Graph Layout with Implicit Neural Fields
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中文总结 AI 辅助
本文提出Fling模型，以固定参数的神经网络替代传统力导向算法优化节点坐标，在图布局任务中性能优于PivotMDS等方法，还可生成多种布局变体。
中文摘要 AI 辅助
图布局通常是包含N个自由坐标的表格，我们优化一个参数数量固定的函数，这赋予了绘制结果样本复杂度与可扩展的定义域。力导向算法仍是图绘制的标准工具，其中最精确的算法通过直接优化节点坐标最小化Kamada-Kawai公式中的应力，其时间和空间复杂度为O(N²)，开销极大。本文提出Fling（Field Layout via Implicit Neural Geometry，基于隐式神经几何的场布局），这是一个小型神经网络，将每个节点到一组地标点的距离映射为节点坐标，通过在布局能量上训练实现平面定位。完整的弹簧系统无需距离矩阵即可处理，每对节点的静止长度可通过地标界以常数时间获得；另有一个网络从精确锚点行学习 majorisation 求和，每步复杂度为O(|A|N)，其中|A|为锚点数量且|A|≪N。与通过消息传递读取图的神经绘制器不同，我们将绘制结果表示为节点特征的函数，未见过的节点仅需一次前向传播，且稀疏低秩的 majorisation 仍为转导式。由于未知量是权重而非坐标，能量仅需要小部分节点，以此拟合的场在从节点样本拟合图能量的任务中，性能优于PivotMDS、地标MDS以及在相同能量和特征上训练的核岭回归。此外，同一参数化可实现随机枢轴应力变体、美学优化变体（在同一字段上携带带有节点-边间距和交叉项的邻域嵌入能量），并通过对两种能量间的权重进行条件设置，一次运行即可生成完整的布局族。
英文摘要
A graph layout is normally a table of $N$ free coordinates. We optimise a function with a fixed number of parameters instead. This gives a drawing a sample complexity and an extensible domain. Force-directed algorithms remain the standard tools for graph drawing. The most accurate among them minimise stress in the Kamada-Kawai formulation by directly optimising the node coordinates, at a full objective cost of $O(N^2)$ in time and space. Here, we propose Fling (Field Layout via Implicit Neural Geometry), a small neural network mapping the distances of each node to a set of landmarks, positioning it in the plane by training on the layout energy. The full spring system then becomes tractable without its distance matrix, as rest lengths follow from a landmark bound in constant time per pair while a second network learns the majorisation sums from exact anchor rows, at $O(|\mathcal{A}|N)$ per step for $|\mathcal{A}|\ll N$ anchors. Unlike neural drawers that read the graph by message passing, we represent the drawing as a function of node features. An unseen node costs one forward pass, where sparse and low-rank majorisation remain transductive. As the unknowns are weights rather than coordinates, the energy only requires a small fraction of the nodes, and a field fitted that way outperforms PivotMDS, landmark MDS, and a kernel ridge trained on the same energy and features, when the task is fitting the energy of a graph from a sample of its nodes. In addition, the same parameterisation enables a stochastic pivot stress variant, an aesthetics-optimised variant carrying a neighbour-embedding energy with node-edge clearance and crossing terms on the same field, and conditioning on the weight between two energies gives a whole layout family from one run.
发表机构
- Wageningen Univeristy & Research（瓦赫宁根大学及研究中心）
机构由 AI 辅助整理，请以论文原文为准。
