Showing posts from August, 2022

Paper Breakdown: Parallel Transport Unfolding (Max Budninskiy et. al.)

Parallel Transport Unfolding: A Connection-based Manifold Learning Approach (Max Budninskiy, Gloria Yin, Leman Feng, Yiying Tong, and Mathieu Desbrun) is a recent manifold learning paper from the Applied Geometry Lab at Caltech. The paper presents the Parallel Transport Unfolding (PTU) algorithm, which is an extension to the well-known ISOMAP manifold learning algorithm. ISOMAP estimates the pairwise geodesic distances (distance along the manifold) between all of the input points in the high-dimensional ambient space, and produces an embedding in a low-dimensional space that best preserves these distances. Utilizing tools from the field of differential geometry, PTU improves the estimation of these geodesic distances, in turn improving the resulting embedding of the manifold. Additionally, PTU no longer requires that the source data be geodesically convex, which is an important requirement of the ISOMAP algorithm. In this blog post, I'll be summarizing the contents of the