Topological Autoencoders

About

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt · 2019

Related benchmarks

Task	Dataset	Result
Classification	warpPIE 10P	Accuracy73	30
Cell Type Classification	ssREAD (evaluation)	Accuracy95.24	20
Dimensionality Reduction	Spheres synthetic (test)	L. C.62.2	10
Representation Learning	MNIST non-uniform	k-NN Accuracy87.7	10
Representation Learning	dSprites	k-NN Accuracy55.8	10
Dimensionality Reduction	SPHERES	Trustworthiness Score0.658	10
Representation Learning	MNIST Uniform (test)	k-NN Accuracy82.9	10
Manifold Representation Learning	Swiss Roll, dSprites, and MNIST combined average across datasets	k-NN Recall3.8	10
Representation Learning	MNIST	Scaling Equivariance Error—	9
Classification	PROT579	Accuracy88.3	8