Projections (or dimensionality reduction) methods $P$ aim to map high-dimensional data to typically 2D scatterplots for visual exploration. Inverse projection methods $P^{-1}$ aim to map this 2D space to the data space to support tasks such as data augmentation, classifier analysis, and data imputation. Current $P^{-1}$ methods suffer from a fundamental limitation -- they can only generate a fixed surface-like structure in data space, which poorly covers the richness of this space. We address this by a new method that can `sweep' the data space under user control. Our method works generically for any $P$ technique and dataset, is controlled by two intuitive user-set parameters, and is simple to implement. We demonstrate it by an extensive application involving image manipulation for style transfer.

翻译：投影（或降维）方法$P$旨在将高维数据映射到通常为二维的散点图以进行可视化探索。逆投影方法$P^{-1}$则旨在将此二维空间映射回数据空间，以支持数据增强、分类器分析和数据填补等任务。当前的$P^{-1}$方法存在一个根本性局限——它们只能在数据空间中生成固定的类曲面结构，难以覆盖该空间的丰富性。我们通过一种新方法解决了这一问题，该方法能够在用户控制下“扫掠”数据空间。我们的方法通用适用于任何$P$技术和数据集，由两个直观的用户设定参数控制，且易于实现。我们通过一项涉及风格迁移图像处理的广泛应用展示了其有效性。