Topological Data Analysis
125 papers with code • 0 benchmarks • 3 datasets
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Latest papers
Linguistics from a topological viewpoint
Typological databases in linguistics are usually categorical-valued.
Topological Analysis of Mouse Brain Vasculature via 3D Light-sheet Microscopy Images
In this paper, we study the morphology of brain vasculature through a topological lens.
A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams
In this work we introduce a class of pseudodistances called Extended Topological Pseudodistances (ETD)s, which have tunable complexity, and can approximate Sliced and classical Wasserstein distances at the high-complexity extreme, while being computationally lighter and close to Persistence Statistics at the lower complexity extreme, and thus allow users to interpolate between the two metrics.
Differentiable Mapper For Topological Optimization Of Data Representation
ziyadoulhaj/mapper-optimization
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While highly generic and applicable, its use has been hampered so far by the manual tuning of its many parameters-among these, a crucial one is the so-called filter: it is a continuous function whose variations on the data set are the main ingredient for both building the Mapper representation and assessing the presence and sizes of its topological structures.
Flexible filtrations for multiparameter persistent homology detect digital images
Two important problems in the field of Topological Data Analysis are defining practical multifiltrations on objects and showing ability of TDA to detect the geometry.
Explaining the Power of Topological Data Analysis in Graph Machine Learning
However, claims regarding the power and usefulness of TDA have only been partially tested in application domains where TDA-based models are compared to other graph machine learning approaches, such as graph neural networks.
Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis
Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution.
Hierarchical Clustering in $Λ$CDM Cosmologies via Persistence Energy
In this research, we investigate the structural evolution of the cosmic web, employing advanced methodologies from Topological Data Analysis.
Train-Free Segmentation in MRI with Cubical Persistent Homology
antonfrancois/gliomasegmentation_tda
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We describe a new general method for segmentation in MRI scans using Topological Data Analysis (TDA), offering several advantages over traditional machine learning approaches.
LITE: A Stable Framework for Lattice-Integrated Embedding of Topological Descriptors
In this paper, we introduce a new family of descriptors for persistence diagrams.
