arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
By Guangyu Meng, Pengfei Gu, Xueyang Li, Yiyu Shi, Erin Wolf Chambers, Danny Z. Chen
arXiv:2609.37177v1 Announce Type: cross
Abstract: Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segme...
By Alexander H. Berger, Marco Fontana, Daniel Rueckert, Johannes C. Paetzold, Laurin Lux, Ulrich Bauer
Topological signal processing (TSP) traditionally uses oriented boundary operators to process signals on simplicial complexes, which is suitable for flow signals or when topological invariants are important. This paper introduces an unoriented TSP (UTSP) framework that replaces oriented boundaries with unoriented incidence matrices, demonstrating that these matrices retain graph-like spectral properties across simplicial levels. By removing orientation, the authors develop an interaction-order decomposition—an analogue to Hodge decomposition—to quantify how higher-order signals are explained by aggregating lower-order signals, and use this decomposition to create order-aware regularizers that outperform oriented baselines in real-world experiments, especially when signal energy is unevenly distributed across orders.
By Andrea Cavallo, Varun Sarathchandran, Geert Leus, Elvin Isufi
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
By Arghya Pratihar, Kushal Bose, Swagatam Das
Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collapse, or have position-dependent geometry. We introdu...
The paper proposes using concepts from low‑dimensional topology—specifically Morse theory and cobordism—to enhance graph diffusion models, introducing the MG‑Diff pipeline. It provides theoretical guarantees that the Morse‑theoretic guidance remains stable under small perturbations when a positive decision‑gap exists. The authors demonstrate the approach on spatio‑temporal graph forecasting and graph regeneration, suggesting broader potential for topology in machine learning.
By Jennifer Rozenblit, Chenguang Yang, Yuxin Liu, Yuzhou Chen, Yulia Gel