Class
Article
College
College of Science
Department
Mathematics and Statistics Department
Faculty Mentor
Kevin Moon
Presentation Type
Poster Presentation
Abstract
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task use kernel methods for manifold learning. However, these methods typically only provide an embedding of fixed input data and cannot extend to new data points. Autoencoders have also recently become popular for representation learning. But while they naturally compute feature extractors that are both extendable to new data and invertible (i.e., reconstructing original features from latent representation), they have limited capabilities to follow global intrinsic geometry compared to kernel-based manifold learning. We present a new method for integrating both approaches by incorporating a geometric regularization term in the bottleneck of the autoencoder. Our regularization, based on the diffusion potential distances from the recently-proposed PHATE visualization method, encourages the learned latentrepresentation to follow intrinsic data geometry, similar to manifold learning algorithms, while still enabling faithful extension to new dataand reconstruction of data in the original feature space from latent coordinates. We compare our approach with leading kernel methods and autoencoder models for manifold learning to provide qualitative and quantitative evidence of our advantages in preserving intrinsicstructure, out of sample extension, and reconstruction. Our method is easily implemented for big-data applications, whereas other methods are limited in this regard. Presentation Time: Wednesday, 9-10 a.m.
Location
Logan, UT
Start Date
4-11-2021 12:00 AM
Included in
Extendable and Invertible Manifold Learning With Geometry Regularized Autoencoders
Logan, UT
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task use kernel methods for manifold learning. However, these methods typically only provide an embedding of fixed input data and cannot extend to new data points. Autoencoders have also recently become popular for representation learning. But while they naturally compute feature extractors that are both extendable to new data and invertible (i.e., reconstructing original features from latent representation), they have limited capabilities to follow global intrinsic geometry compared to kernel-based manifold learning. We present a new method for integrating both approaches by incorporating a geometric regularization term in the bottleneck of the autoencoder. Our regularization, based on the diffusion potential distances from the recently-proposed PHATE visualization method, encourages the learned latentrepresentation to follow intrinsic data geometry, similar to manifold learning algorithms, while still enabling faithful extension to new dataand reconstruction of data in the original feature space from latent coordinates. We compare our approach with leading kernel methods and autoencoder models for manifold learning to provide qualitative and quantitative evidence of our advantages in preserving intrinsicstructure, out of sample extension, and reconstruction. Our method is easily implemented for big-data applications, whereas other methods are limited in this regard. Presentation Time: Wednesday, 9-10 a.m.