Geometry-Based Data Generation

by   Ofir Lindenbaum, et al.

Many generative models attempt to replicate the density of their input data. However, this approach is often undesirable, since data density is highly affected by sampling biases, noise, and artifacts. We propose a method called SUGAR (Synthesis Using Geometrically Aligned Random-walks) that uses a diffusion process to learn a manifold geometry from the data. Then, it generates new points evenly along the manifold by pulling randomly generated points into its intrinsic structure using a diffusion kernel. SUGAR equalizes the density along the manifold by selectively generating points in sparse areas of the manifold. We demonstrate how the approach corrects sampling biases and artifacts, while also revealing intrinsic patterns (e.g. progression) and relations in the data. The method is applicable for correcting missing data, finding hypothetical data points, and learning relationships between data features.


Manifold Alignment with Feature Correspondence

We propose a novel framework for combining datasets via alignment of the...

Generating High Fidelity Data from Low-density Regions using Diffusion Models

Our work focuses on addressing sample deficiency from low-density region...

Compressed Diffusion

Diffusion maps are a commonly used kernel-based method for manifold lear...

Diffusion Representations

Diffusion Maps framework is a kernel based method for manifold learning ...

Manifold-based Test Generation for Image Classifiers

Neural networks used for image classification tasks in critical applicat...

Coarse Graining of Data via Inhomogeneous Diffusion Condensation

Big data often has emergent structure that exists at multiple levels of ...

Intrinsic Isometric Manifold Learning with Application to Localization

Data living on manifolds commonly appear in many applications. We show t...

Code Repositories


Synthesis using Geometrically Aligned Random-walks

view repo

Please sign up or login with your details

Forgot password? Click here to reset