ECE Seminar Lecture Series
Graph Semi-Supervised Learning for Point Classification on Data Manifolds
Luana Ruiz, Associate Professor, Applied Mathematics and Statistics and the MINDS and DSAI Institutes, Johns Hopkins University
Wednesday, March 25, 2026
Noon–1 p.m.
601 Computer Studies Building
Abstract: Many modern classification problems involve data that live in high-dimensional spaces but exhibit strong low-dimensional structure. Motivated by the manifold hypothesis, this talk presents a graph-based semi-supervised learning framework that explicitly exploits this geometric structure to improve generalization. We model data as samples from an unknown low-dimensional manifold embedded in a high-dimensional ambient space. The manifold is first approximated in an unsupervised manner using a variational autoencoder, whose latent representations provide data-dependent coordinates. From these embeddings, we construct a geometric graph using Gaussian-weighted edges based on pairwise distances, turning the original classification problem into a semi-supervised node classification task on a graph, which we solve using a graph neural network.
The main contribution of this work is a theoretical analysis of the statistical generalization behavior of this data–manifold–graph pipeline. Under uniform sampling assumptions, we show that the generalization gap of the semi-supervised learning task decreases as the graph size grows, up to the optimization error of the GNN. We further show that a simple training strategy that periodically resamples slightly larger graphs during training leads to asymptotically vanishing generalization error.
We conclude with experimental results on image classification benchmarks, including MedMNIST, which support the theory and illustrate how leveraging learned geometric structure can improve both robustness and scalability in graph-based learning.
Bio: Luana Ruiz received the Ph.D. degree in electrical engineering from the University of Pennsylvania in 2022, and the M.Eng. and B.Eng. double degree in electrical engineering from the École Supérieure d'Electricité and the University of São Paulo in 2017. She is an Assistant Professor with the Department of Applied Mathematics and Statistics and the MINDS and DSAI Institutes at Johns Hopkins University, as well as the Electrical and Computer Engineering and Computer Science departments (by courtesy). Luana's work focuses on large-scale graph information processing and graph neural network architectures. She was awarded an Eiffel Excellence scholarship from the French Ministry for Europe and Foreign Affairs between 2013 and 2015; nominated an iREDEFINE fellow in 2019, a MIT EECS Rising Star in 2021, a Simons Research Fellow in 2022, and a METEOR fellow in 2023; and received best student paper awards at the 27th and 29th European Signal Processing Conferences.