Papers Topological Data Analysis
“Topological Data Analysis” 태그가 달린 논문 498편 · 필터 해제
Lipschitz Bounds for Persistent Laplacian Eigenvalues under One-Simplex Insertions
Persistent Laplacians are matrix operators that track how the shape and structure of data transform across scales and are popularly adopted in biology, physics, and machine learning. Their eigenvalues are concise descrip…
Topological Data AnalysisThe Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series
Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time…
ClusteringMarketingTime SeriesTopological Data AnalysisTDACloud: Point Cloud Recognition Using Topological Data Analysis
Point cloud-based object/place recognition remains a problem of interest in applications such as autonomous driving, scene reconstruction, and localization. Extracting meaningful local descriptors from a query point clou…
Autonomous DrivingGPUTopological Data AnalysisTorsion in Persistent Homology and Neural Networks
We explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in…
SensitivityTopological Data AnalysisAn Incremental Framework for Topological Dialogue Semantics: Efficient Reasoning in Discrete Spaces
We present a tractable, incremental framework for topological dialogue semantics based on finite, discrete semantic spaces. Building on the intuition that utterances correspond to open sets and their combinatorial relati…
Topological Data AnalysisComparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging
In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates r…
Feature EngineeringMedical Image AnalysisTopological Data AnalysisTopological Machine Learning for Protein-Nucleic Acid Binding Affinity Changes Upon Mutation
Understanding how protein mutations affect protein-nucleic acid binding is critical for unraveling disease mechanisms and advancing therapies. Current experimental approaches are laborious, and computational methods rema…
Topological Data AnalysisTopological Deep Learning for Speech Data
Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networ…
Deep LearningPhoneme Recognitionspeech-recognitionSpeech Recognition+1Holes in Latent Space: Topological Signatures Under Adversarial Influence
Understanding how adversarial conditions affect language models requires techniques that capture both global structure and local detail within high-dimensional activation spaces. We propose persistent homology (PH), a to…
DiversityTopological Data AnalysisA Novel Shape-Aware Topological Representation for GPR Data with DNN Integration
Ground Penetrating Radar (GPR) is a widely used Non-Destructive Testing (NDT) technique for subsurface exploration, particularly in infrastructure inspection and maintenance. However, conventional interpretation methods …
GPRobject-detectionObject DetectionTopological Data AnalysisHow high is `high'? Rethinking the roles of dimensionality in topological data analysis and manifold learning
We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random function model of data, we clarify the roles p…
Topological Data AnalysisPersiST: Robust Identification of Spatially Variable Features in Spatial Omics Datasets via Topological Data Analysis
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating the analysis of a large number of spatially resolved variables. With spatial transcriptomics data sets typically containing d…
Topological Data AnalysisTopology across Scales on Heterogeneous Cell Data
Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent …
Topological Data AnalysisAdvanced Clustering Framework for Semiconductor Image Analytics Integrating Deep TDA with Self-Supervised and Transfer Learning Techniques
Semiconductor manufacturing generates vast amounts of image data, crucial for defect identification and yield optimization, yet often exceeds manual inspection capabilities. Traditional clustering techniques struggle wit…
ClusteringImage ClusteringSelf-Supervised LearningTopological Data Analysis+1Dynamical System Parameter Path Optimization using Persistent Homology
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied …
Topological Data AnalysisClassification of Firn Data via Topological Features
In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advantages, pitfalls, and trade-offs in topolog…
ClassificationRobust classificationTopological Data AnalysisTopological model selection: a case-study in tumour-induced angiogenesis
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-t…
Model SelectionTopological Data AnalysisPersistence-based Hough Transform for Line Detection
The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of l…
Line DetectionTopological Data AnalysisUse of Topological Data Analysis for the Detection of Phenomenological Bifurcations in Stochastic Epidemiological Models
We investigate predictions of stochastic compartmental models on the severity of disease outbreaks. The models we consider are the Susceptible-Infected-Susceptible (SIS) for bacterial infections, and the Susceptible -Inf…
Topological Data AnalysisFiltering through a topological lens: homology for point processes on the time-frequency plane
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pro…
Point ProcessesTopological Data Analysis