Topological Data Analysis
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Related Articles from SNS
Prototype Selection Using Topological Data Analysis
arXiv:2511.04873v2 Announce Type: replace-cross Abstract: Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data. This paper introduces two different persistence-based prototype selector variants, Topological Prototype Selector (TPS) and Boundary-Conscious Topological Prototype...
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. However, existing paired topological divergences (e.g., RTD) are limited by heuristic asymmetry and, more critically, unbounded scores that depend on sample size, hindering reliable cross-scenario benchmarking. To address these challenges, we develop a unified topological toolkit serving two complementary needs: fine-grained structural...
Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties
arXiv:2606.02048v1 Announce Type: cross Abstract: We propose a novel computational toolbox that integrates Topological Data Analysis (TDA), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP), applied to time-lapse super-resolution STED microscopy images of sodium caseinate gelation induced by glucono-delta-lactone (GDL) at 30 {\deg}C and 40 {\deg}C and two GDL concentrations (1.8% and 3.5% w/v). TDA tracked topological loops, closed ring-like...
Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties
arXiv:2606.02048v1 Announce Type: new Abstract: We propose a novel computational toolbox that integrates Topological Data Analysis (TDA), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP), applied to time-lapse super-resolution STED microscopy images of sodium caseinate gelation induced by glucono-delta-lactone (GDL) at 30 {\deg}C and 40 {\deg}C and two GDL concentrations (1.8% and 3.5% w/v). TDA tracked topological loops, closed ring-like...
Graph Mamba Survival Analysis Based on Topology-Aware ordering
arXiv:2606.02602v1 Announce Type: new Abstract: In computational pathology, Whole Slide Images (WSIs) survival analysis is crucial for patient prognosis assessment, but it faces multiple technical challenges. Although the Transformer captures long-range dependencies through its self-attention mechanism, its $O(N^2)$ time complexity causes a severe computational bottleneck in large-scale WSIs graph structures. The Mamba model breaks through the Transformer's computational bottleneck with...
$p$-adic Bi-Filtrations for Topological Machine Learning on Genomic Sequences
arXiv:2606.06117v1 Announce Type: cross Abstract: We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a $p$-adic distance on $k$-mer prefixes, which captures hierarchical positional structure, and a compositional $L_1$ distance on $k$-mer frequencies, which captures local sequence content. The two distances jointly...
Hosting Capacity Assessment and Enhancement for Edge Data Centers in Active Distribution Networks
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Cycle-Space Informed Detection of Autoencoded Blind False Data Injection Attacks on Power Systems
Announce Type: replace Abstract: The rapid growth of AI-driven data centers and large-scale energy storage systems is increasing the reliance of power system operation on real-time measurement data and automated decision-making. However, many existing detection methods rely on statistical or data-driven analysis of measurements and can fail when attackers exploit the same data structure to craft stealthy perturbations. To illustrate this limitation, we demonstrate a blind False Data...
SFILES 2.0: An extended text-based flowsheet representation
arXiv:2208.00778v2 Announce Type: replace Abstract: SFILES are a text-based notation for chemical process flowsheets. They were originally proposed by d'Anterroches (Process flow sheet generation & design through a group contribution approach) who was inspired by the text-based SMILES notation for molecules. The text-based format has several advantages compared to flowsheet images regarding the storage format, computational accessibility, and eventually for data analysis and processing.
UModel: An Agent-Ready Observability Data Modeling Method at Scale
arXiv:2606.04799v1 Announce Type: new Abstract: When networked system failures occur, automatically performing Root Cause Analysis (RCA) using observability data is critical for ensuring networked system reliability. Recently, LLM-based agents have shown promise for automating this diagnosis process through advanced reasoning and autonomous exploration.