论文标题
通过梯度下降的图形图，$（gd）^2 $
Graph Drawing via Gradient Descent, $(GD)^2$
论文作者
论文摘要
可读性标准（例如距离或邻居保存）通常用于优化图形的节点链接表示，以使基础数据理解。除了少数例外，图形绘制算法通常会优化一个这样的标准，通常以其他为代价。我们提出了一种布局方法，即通过梯度下降的图形图，$（gd）^2 $，可以处理多个可读性标准。 $（gd）^2 $可以优化可以通过平滑函数描述的任何标准。如果无法通过平滑函数捕获标准，则将标准的非平滑函数与另一个平滑函数结合使用，或使用自动分化工具进行优化。我们的方法是灵活的，可用于优化已经考虑到的几个标准（例如，获得理想的边缘长度，压力，邻里保存）以及其他尚未以这种方式明确优化的标准（例如，顶点分辨率，分辨率，角度分辨率，宽高比）。我们提供了具有实验数据和功能原型的$（gd）^2 $有效性的定量和定性证据：\ url {http://hdc.cs.arizona.edu/~mwli/~mwli/graph-drawing/}。
Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Graph Drawing via Gradient Descent, $(GD)^2$, that can handle multiple readability criteria. $(GD)^2$ can optimize any criterion that can be described by a smooth function. If the criterion cannot be captured by a smooth function, a non-smooth function for the criterion is combined with another smooth function, or auto-differentiation tools are used for the optimization. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., vertex resolution, angular resolution, aspect ratio). We provide quantitative and qualitative evidence of the effectiveness of $(GD)^2$ with experimental data and a functional prototype: \url{http://hdc.cs.arizona.edu/~mwli/graph-drawing/}.
