Topological Autoencoders

06/03/2019
by   Michael Moor, et al.
0

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 can 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, while exhibiting favourable latent representations on synthetic manifold data sets. Moreover, on real-world data sets, introducing our topological loss leads to more meaningful latent representations while preserving low reconstruction errors.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

07/13/2017

Deep Learning with Topological Signatures

Inferring topological and geometrical information from data can offer an...
10/17/2019

Mapper Based Classifier

Topological data analysis aims to extract topological quantities from da...
06/21/2019

Connectivity-Optimized Representation Learning via Persistent Homology

We study the problem of learning representations with controllable conne...
06/27/2018

TopoReg: A Topological Regularizer for Classifiers

Regularization plays a crucial role in supervised learning. A successful...
03/03/2022

Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction

Reconstructing 3D objects from 2D images is both challenging for our bra...
04/20/2021

Robust Feature Disentanglement in Imaging Data via Joint Invariant Variational Autoencoders: from Cards to Atoms

Recent advances in imaging from celestial objects in astronomy visualize...
07/07/2016

Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies

The existence of characteristic structure, or shape, in complex data set...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.