Projection techniques are often used to visualize high-dimensional data, allowing users to better understand the overall structure of multi-dimensional spaces on a 2D screen. Although many such methods exist, comparably little work has been done on generalizable methods of inverse-projection -- the process of mapping the projected points, or more generally, the projection space back to the original high-dimensional space. In this paper we present NNInv, a deep learning technique with the ability to approximate the inverse of any projection or mapping. NNInv learns to reconstruct high-dimensional data from any arbitrary point on a 2D projection space, giving users the ability to interact with the learned high-dimensional representation in a visual analytics system. We provide an analysis of the parameter space of NNInv, and offer guidance in selecting these parameters. We extend validation of the effectiveness of NNInv through a series of quantitative and qualitative analyses. We then demonstrate the method's utility by applying it to three visualization tasks: interactive instance interpolation, classifier agreement, and gradient visualization.
翻译:投影技术常常被用来对高维数据进行可视化,使用户能够更好地了解二维屏幕上多维空间的整体结构。虽然存在许多这类方法,但在反射一般方法方面所做的工作却相当少,即对预测点进行绘图的过程,或更笼统地说,投影空间返回原始的高维空间。在本文中,我们介绍了NNNInv,这是一种深层次的学习技术,能够与任何投影或绘图相近。NNNInv学会从二维投影空间的任何任意点重建高维数据,使用户能够在视觉分析系统中与所学的高维代表进行互动。我们分析了NNNINv的参数空间,并为选择这些参数提供了指导。我们通过一系列定量和定性分析来扩大NNINv的有效性的验证。然后我们通过将它应用于三个可视化任务来证明该方法的效用:交互式实例内插、分类协议和梯度可视化。