arXiv Machine Learning
Jul 10
Persistent Multiscale Density-based Clustering
arXiv:2512. 16558v3 Announce Type: replace Abstract: Clustering is a cornerstone of modern data analysis.
Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
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arXiv Machine Learning
Jun 5
Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
arXiv:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations.
arXiv AI
Jun 29
Learning Topology-Aware Representations via Test-Time Adaptation for Anomaly Segmentation
arXiv:2606. 28268v1 Announce Type: cross Abstract: Test-time adaptation (TTA) has emerged as a promising paradigm for mitigating distribution shifts in deep models.
arXiv AI
Jul 23
A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv Machine Learning
Jul 7
Topological data analysis using persistent discrete homology
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 AI
Aug 3
Dimensionality reduction for homological stability and global structure preservation
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 Machine Learning
Jun 17
Non-negative Matrix Factorisation with Topological Regularisation
arXiv:2606. 17531v1 Announce Type: new Abstract: We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions.
arXiv Machine Learning
Jun 11
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
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 Machine Learning
Jul 30
Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams
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 AI
Aug 10
Density-aware Hierarchical Clustering Based on Element-Categorized Connection Subgraphs
arXiv:2608. 06990v1 Announce Type: cross Abstract: Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning.
arXiv Machine Learning
Jul 28
The K-SCAN Clustering Algorithm
arXiv:2607. 24537v1 Announce Type: new Abstract: In the Big Data era, the scalability of clustering algorithms constitutes a key challenge.
arXiv Machine Learning
Jul 31
TopoFormer: Topology Meets Attention for Graph Learning
arXiv:2607. 28259v1 Announce Type: new Abstract: We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences.