Geometric Autoencoders - What You See is What You Decode
Philipp Nazari,u00a0Sebastian Damrich,u00a0Fred A Hamprecht
Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks can achieve low reconstruction error even when the latent representation is distorted. To avoid such misleading visualizations, we propose first a differential geometric perspective on the decoder, leading to insightful diagnostics for an embeddingu2019s distortion, and second a new regularizer mitigating such distortion. Our u201cGeometric Autoencoderu201d avoids stretching the embedding spuriously, so that the visualization captures the data structure more faithfully. It also flags areas where little distortion could not be achieved, thus guarding against misinterpretation.
