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Found 17 papers, 4 papers with code
TTK is Getting MPI-Ready
We provide a taxonomy for the distributed-memory topological algorithms supported by TTK, depending on their communication needs and provide examples of hybrid MPI+thread parallelizations.
Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)
Our novel neural network approach can be interpreted as a non-linear generalization of previous linear attempts [79] at merge tree encoding.
Wasserstein Dictionaries of Persistence Diagrams
This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams.
Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study
Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.
Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)
We show the utility of our contributions by extending to merge trees two typical PCA applications.
Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark
This fast pre-computation for the dimensions $0$ and $(d - 1)$ enables an aggressive specialization of [4] to the 3D case, which results in a drastic reduction of the number of input simplices for the computation of $D_1(f)$, the intermediate layer of the sandwich.
Wasserstein Distances, Geodesics and Barycenters of Merge Trees
We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance between merge trees, which is purposely designed to enable efficient computations of geodesics and barycenters.
0-dimensional Homology Preserving Dimensionality Reduction with TopoMap
This note presents TopoMap, a novel dimensionality reduction technique which provides topological guarantees during the mapping process.
TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data
With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example.
Statistical Parameter Selection for Clustering Persistence Diagrams
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data.
Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings
Different metrics, based on optimal transport, for comparing time-varying persistence diagrams in this specific applicative case are introduced.
Progressive Wasserstein Barycenters of Persistence Diagrams
This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data.
Lifted Wasserstein Matcher for Fast and Robust Topology Tracking
First, we revisit the seminal assignment algorithm by Kuhn and Munkres which we specifically adapt to the problem of matching persistence diagrams in an efficient way.
Persistence Atlas for Critical Point Variability in Ensembles
We show how to leverage spectral embedding to represent the ensemble members as points in a low-dimensional Euclidean space, where distances between points measure the dissimilarities between critical point layouts and where statistical tasks, such as clustering, can be easily carried out.
Topological Data Analysis Made Easy with the Topology ToolKit
This tutorial presents topological methods for the analysis and visualization of scientific data from a user's perspective, with the Topology ToolKit (TTK), a recently released open-source library for topological data analysis.
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization.
Topologically Controlled Lossy Compression
However, in many scenarios it is desirable to control in a similar way the preservation of higher-level notions, such as topological features , in order to provide guarantees on the outcome of post-hoc data analyses.
