7 papers
Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis
Alice Wachira, Xiang Liu, Zhe Su +3
Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural ne…
Unmasking Face Embeddings: Reading, Rendering and Naming with Foundation Models
Fizza Rubab, Yiying Tong, Arun Ross
Modern face recognition (FR) owes much of its success to deep neural networks that learn to extract compact identity embeddings from face images. These models are typically trained…
Weighted Hodge Laplacians on Manifolds with Boundary
Zhe Su, Yiying Tong, Guo-Wei Wei
The spectrum of the Hodge Laplacian on differential manifolds encodes rich topological and geometric information and thus provides a powerful tool for analyzing data on manifolds.…
Compatibility of Face Embeddings Across Deep Neural Networks
Fizza Rubab, Yiying Tong, Arun Ross
Automated face recognition has made rapid strides over the past decade due to the unprecedented rise of deep neural network (DNN) models that can be trained for domain-specific tas…
Manifold Topological Deep Learning for Biomedical Data
Xiang Liu, Zhe Su, Yongyi Shi +3
Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging a…
Topology-preserving Hodge Decomposition in the Eulerian Representation
Zhe Su, Yiying Tong, Guo-Wei Wei
The Hodge decomposition is a fundamental result in differential geometry and algebraic topology, particularly in the study of differential forms on a Riemannian manifold. Despite e…
Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning
Zhe Su, Yiying Tong, Guo-Wei Wei
Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology,…