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...
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
The paper introduces a differentiability framework for zigzag persistent homology, enabling the use of zigzag persistence in learning pipelines. By linearly interpolating filtering values on a fixed complex and assigning real-valued times to persistence diagram endpoints, the authors transfer continuity from filtering values to diagram points, yielding smooth local lifts and almost everywhere differentials under mild regularity conditions. They prove local Lipschitz continuity outside an explicit measure‑zero exclusion set and demonstrate the framework’s practical effectiveness through experiments on sensor network coverage optimization and dynamic graph classification.
arXiv:2506. 15020v2 Announce Type: replace-cross Abstract: We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods.
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
The paper introduces a unified pipeline that classifies univariate time series by first converting them into graphs using one of five constructions from three families (visibility, transition, proximity). The resulting graph is turned into a dissimilarity matrix, from which a Vietoris–Rips filtration produces persistence diagrams that are vectorized via persistence landscapes and topological summary statistics. Experiments on twelve UCR benchmarks reveal that no single graph construction dominates, diffusion distance consistently outperforms shortest-path metrics, and persistence-based features remain robust to noise.
The paper presents TopoGPU, a GPU streaming pipeline that computes persistence diagrams of cubical complexes from 2D and 3D images. It processes image chunks with massively parallel GPU kernels, accumulates boundary relations in host memory, and performs boundary matrix reduction on the CPU. TopoGPU introduces a stratification‑aware discrete Morse matching, parallel topological sorting, and a parallel V‑path parity algorithm, achieving up to 198× speedup over Cubical Ripser and reducing persistent homology computation costs in a topology‑preserving deep network.
arXiv:2512.23348v3 Announce Type: replace-cross Abstract: We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construc...
arXiv:2607. 27126v1 Announce Type: new Abstract: Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity.
arXiv:2606. 28268v1 Announce Type: cross Abstract: Test-time adaptation (TTA) has emerged as a promising paradigm for mitigating distribution shifts in deep models.
Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity. Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple subsets of a point cloud and it serves as a distribution of topological features.
The paper introduces a topological method for detecting Hopf bifurcations directly from scalar time series. It combines delay-coordinate reconstruction with persistent homology, using the maximum persistence of one‑dimensional homology classes as a scalar descriptor of cyclic structure. Finite‑resolution persistence bounds are derived for the supercritical Hopf case, and a derivative‑based estimator localizes the critical parameter; the method is tested on the Hopf normal form, Lorenz system, and a reduced Belousov–Zhabotinsky model.