Geometric Autoencoders -- What You See is What You Decode
This work addresses a specific issue in exploratory data analysis for researchers using autoencoders, offering a method to avoid misleading visualizations.
The paper tackled the problem of distorted latent representations in autoencoders used for data visualization, proposing a geometric regularizer that reduces embedding distortion and improves faithfulness of visualizations.
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 embedding's distortion, and second a new regularizer mitigating such distortion. Our ``Geometric Autoencoder'' 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.