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#Persistence Diagrams

Showing: 29 courses
Applied Algebraic Topology Network

Yulia Gel - Topological Clustering of Multilayer Networks

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Explore topological clustering of multilayer networks, focusing on higher-order interactions and local neighborhood shapes. Learn applications in climate-insurance and COVID-19 data analysis.
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22 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

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Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.
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11 Lesons
24 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

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Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.
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10 Lesons
27 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Ulrich Bauer - Persistence Diagrams as Diagrams

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Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.
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19 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Nonlinear Dynamics, High Dimensional Data, and Persistent Homology

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Explore nonlinear dynamics, high-dimensional data analysis, and persistent homology with Konstantin Mischaikow. Learn about algebraic topology applications, persistence diagrams, and recent advancements in data science.
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18 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Canonical Framework for Summarizing Persistence Diagrams

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Explore a canonical framework for summarizing persistence diagrams in topological data analysis, including theoretical foundations, applications, and future developments.
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18 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Liz Munch - Featurization of Persistence Diagrams Using Template Functions for ML Tasks

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Explore topological data analysis and persistence diagrams for machine learning, focusing on featurization techniques using template functions to map complex data into Euclidean space.
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24 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?

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Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.
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21 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistence in Functional Topology

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Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
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15 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Massimo Ferri - Selection of Points in Persistence Diagrams

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Explore point selection in persistence diagrams, including Kurlin's criterion and the Ziqqurat method, for noise reduction and improved data analysis in topological data analysis.
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9 Lesons
40 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Comparing Neural Networks via Generalized Persistence

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Exploring generalized persistence to compare neural network architectures, analyzing data representations at each layer and providing insights into network behavior and performance.
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19 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers

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Explore how generalized persistence diagrams encode bigraded Betti numbers in 2-parameter persistence modules, with implications for RIVET software and interval decomposable modules.
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1 Lesons
39 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Studying the Space of Persistence Diagrams Using Optimal Partial Transport II

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Exploring persistence diagrams through optimal transport theory, bridging topological data analysis with measure spaces to characterize convergence and prove new results in random settings.
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1 Lesons
30 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Studying the Space of Persistence Diagrams Using Optimal Partial Transport - Part I

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Exploring persistence diagrams through optimal partial transport, bridging topological data analysis with measure theory. Novel approach enables new insights into convergence, continuity, and random settings in TDA.
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1 Lesons
26 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

On the Metric Distortion of Embedding Persistence Diagrams into RKHS

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Explores embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces, analyzing metric properties and stability guarantees for machine learning applications in Topological Data Analysis.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Edit Distance and Persistence Diagrams Over Lattices

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Functorial pipeline for persistent homology: from filtered simplicial complexes to persistence diagrams. Addresses multiparameter persistent homology and functoriality of persistence diagrams.
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1 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Julien Tierny - Principal Geodesic Analysis of Merge Trees and Persistence Diagrams

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Computational framework for Principal Geodesic Analysis of merge trees, adapting PCA to Wasserstein metric space. Efficient algorithm for data reduction and dimensionality reduction in topological data analysis.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Data Analysis with Merge Trees

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Explore merge trees as topological summaries in data analysis, including their advantages over persistence diagrams, computational challenges, and applications in functional data and medical imaging.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

Algebraic Perspectives of Persistence

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Explore algebraic approaches to persistent homology, focusing on the stability of persistence diagrams and their relation to input data changes in topological data analysis.
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1 Lesons
1 hour 27 minutes
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Free-Video
Applied Algebraic Topology Network

Morse-Based Fibering of the Rank Invariant

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Explore multi-parameter persistence in data analysis using discrete Morse theory to compute rank invariants, partition parameter space, and deduce persistence diagrams for equivalent classes of lines.
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14 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Modeling and Replicating Persistence Diagrams

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Explore modeling and replicating persistence diagrams for statistical inference in topological data analysis. Learn about RST approach, parametric modeling, and improvements for clustered data.
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14 Lesons
41 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Pawel Dlotko - A Few Simple Stories on Topology in Action

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Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.
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20 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Michael Lesnick - Algebraic Stability of Zigzag Persistence Modules

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Explore algebraic stability in zigzag persistence modules, covering key concepts, theorems, and applications in topological data analysis and computational topology.
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24 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Tamal Dey - A Framework for Topological Summarization

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Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.
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17 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Žiga Virk - Information Encoded in Persistence Diagrams

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Explore topological data analysis through persistence diagrams, uncovering spatial properties like homology, geodesics, and proximity in various mathematical contexts.
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13 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances

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Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
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1 Lesons
28 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

RipsNet- Fast and Robust Estimation of Persistent Homology for Point Clouds

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Estimating persistence diagrams of point clouds using neural networks for faster, more robust topological analysis. Overcomes computational complexity and sensitivity to outliers in practical applications.
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1 Lesons
54 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

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Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
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1 Lesons
46 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Spectral Relaxations of the Persistent Rank Invariant - Applied Algebraic Topology Network

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Spectral relaxations of persistent rank invariant: A framework for continuous relaxations, offering stability and differentiability while preserving key properties and enabling efficient GPU-parallelized computation.
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1 Lesons
53 minutes
On-Demand
Free-Video