# Deep Learning Inverse Projections

*Projections* are the method of choice for mapping high-dimensional data to 2D or 3D scatterplots which can be next easily visualized. In several applications, it is necessary however to do the *inverse* operation: Given a (2D or 3D) point in the space of such a scatterplot, which high-dimensional point corresponds to it?

## Method

We propose a method to compute such inverse projections using deep learning. The technique is very simple to implement, generic (handles any direct projection method), and fast. It works as follows

- given a direct projection technique, one constructs several 2D projections of one or more datasets
- we train a neural network to learn the mapping from high dimensions to 2D from the above data
- we then use the network to infer the high-dimensional position of any 2D point

## Applications

The image below shows how inverse projections can be used. Given a 2D projection of a labeled dataset (left column), we can construct a *dense map* showing the high-dimensional sample label that corresponds to every 2D pixel. This effectively partitions the 2D image space into *decision zones* corresponding to a classifier trained on the labeled data. Columns 2-5 show such dense maps constructed by iLAMP, RBF (clusters), RBF (fixed control points), and our method. Our method constructs cleaner decision zones and runs much faster than RBF and iLAMP.

## References

Deep Learning Inverse Multidimensional Projections M. Espadoto, F. C. M. Rodrigues, N. S. T. Hirata, R. Hirata Jr, A. Telea. Proc. EuroVA, 2019

UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data M. Espadoto, G. Appleby, A. Suh, D. Cashman, M. Li, C. Scheidegger, E. Anderson, R. Chang, A. Telea. IEEE TVCG, 2021

Self-Supervised Dimensionality Reduction with Neural Networks and Pseudo-labeling M. Espadoto, N. Hirata, A. Telea. Proc. IVAPP

Improving Self-Supervised Dimensionality Reduction: Exploring Hyperparameters and Pseudo-labeling Strategies A. Oliveira, M. Espadoto, R. Hirata, N. Hirata, A. Telea. Springer CCIS 1691, 135-161