arXiv:2503. 03156v4 Announce Type: replace-cross Abstract: We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware.
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: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:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
The article introduces a new non‑archimedean metric, the cophenetic metric, defined on persistent homology classes of all degrees. It demonstrates that zeroth persistent homology combined with this metric and various hierarchical clustering algorithms yields statistically verifiable, commensurate topological information on multiple datasets. The resulting clusters, evaluated by silhouette score and Rand index, perform well, and the metric enables visualization of inter‑relations among persistent homology classes across all degrees via rooted trees.
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.
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...
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.
arXiv:2608. 09997v1 Announce Type: new Abstract: Transformers have had a profound impact on the world of language processing and computer vision.
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
arXiv:2606. 14737v1 Announce Type: cross Abstract: Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings.
arXiv:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
arXiv:2608. 11269v1 Announce Type: cross Abstract: Omics datasets, particularly single-cell RNA sequencing data, are high-dimensional, sparse, noisy, and dominated by zero values, making faithful low-dimensional representation challenging.