A one‐dimensional homologically persistent skeleton of an unstructured point cloud in any metric space

Kurlin, Vitaliy

doi:10.1111/cgf.12713

Cited by 34 publications

(16 citation statements)

References 12 publications

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“…As the TDA step is not restricted to a 2-D scalar field on a grid, it is also possible to apply to higher-dimensional or multivariate fields. A similar TDA-based approach has successfully been applied to data skeletonization (Kurlin, 2015) and segmentation (Kurlin, 2016) problems. Hence, we believe that this method can be extended to be applied in a variety of other climate science problems where defining suitable thresholds remains a challenge.…”

Section: Limitations Of Our Methodsmentioning

confidence: 99%

Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets

et al. 2019

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Abstract. Identifying weather patterns that frequently lead to extreme weather events is a crucial first step in understanding how they may vary under different climate change scenarios. Here, we propose an automated method for recognizing atmospheric rivers (ARs) in climate data using topological data analysis and machine learning. The method provides useful information about topological features (shape characteristics) and statistics of ARs. We illustrate this method by applying it to outputs of version 5.1 of the Community Atmosphere Model version 5.1 (CAM5.1) and the reanalysis product of the second Modern-Era Retrospective Analysis for Research and Applications (MERRA-2). An advantage of the proposed method is that it is threshold-free – there is no need to determine any threshold criteria for the detection method – when the spatial resolution of the climate model changes. Hence, this method may be useful in evaluating model biases in calculating AR statistics. Further, the method can be applied to different climate scenarios without tuning since it does not rely on threshold conditions. We show that the method is suitable for rapidly analyzing large amounts of climate model and reanalysis output data.

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Section: Limitations Of Our Methodsmentioning

confidence: 99%

Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets

et al. 2019

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“…Graph representations are commonly used to illustrate the underlying structure of data, but nodes are aggregations of points rather than individual elements. Under this umbrella, data skeletonization is an important shape descriptor from a disconnected point cloud [22,23,24]. The selection of a proper skeleton is defined by the representation which shows the most persistent features.…”

Section: Exploration Of Data Through Network Structuresmentioning

confidence: 99%

Spanning Trees as Approximation of Data Structures

Alcaide

Aerts

2021

IEEE Trans. Visual. Comput. Graphics

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The connections in a graph generate a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this work, we present STAD (Simplified Topological Abstraction of Data), a parameter-free dimensionality reduction method that projects high-dimensional data into a graph. STAD generates an abstract representation of high-dimensional data by giving each data point a location in a graph which preserves the approximate distances in the original high-dimensional space. The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edges are added until the correlation between the distances from the graph and the original dataset is maximized. Additionally, STAD supports the inclusion of additional functions to focus the exploration and allow the analysis of data from new perspectives, emphasizing traits in data which otherwise would remain hidden. We demonstrate the effectiveness of our method by applying it to two real-world datasets: traffic density in Barcelona and temporal measurements of air quality in Castile and León in Spain.

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“…The extension to a graph with hanging vertices and branches is in Kurlin (2015a). Gaps in 1D persistence are studied for more general filtrations in Kurlin (2015b). Here are further open problems.…”

Section: Conclusion and Experiments On Synthetic And Real Datamentioning

confidence: 99%

A fast persistence-based segmentation of noisy 2D clouds with provable guarantees

Kurlin

2016

Pattern Recognition Letters

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A one‐dimensional homologically persistent skeleton of an unstructured point cloud in any metric space

Cited by 34 publications

References 12 publications

Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets

Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets

Spanning Trees as Approximation of Data Structures

A fast persistence-based segmentation of noisy 2D clouds with provable guarantees

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