An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

Chazal, Frédéric; Michel, Bertrand

doi:10.3389/frai.2021.667963

Cited by 284 publications

(160 citation statements)

References 105 publications

(245 reference statements)

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“…One way of visualising the homological calculation is via the so-called persistence di- Fasy et al 2014;Chazal, B. Fasy, et al 2018;Chazal and Michel 2021) were investigated for this, including subsampling, bootstrapping together with a more robust filtration distance function and the bottleneck distance, which measures the distance between two persistence diagrams D 1 and D 2 . For sake of completeness, the bottleneck distance is defined as PH can tell us even more.…”

Section: Finding Holes In Niche Hypervolumesmentioning

confidence: 99%

‘Holey’ niche! Finding holes in niche hypervolumes using persistence homology

Conceição

Morimoto

2022

Preprint

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Hutchinsons niche hypervolume concept has enabled significant progress in our understanding of species ecological needs and distributions across environmental gradients. Nevertheless, the properties of Hutchinsons n-dimensional hypervolumes can be challenging to calculate and several methods have been proposed to extract meaningful measurements of hypervolumes properties (e.g., volume). One key property of hypervolumes are holes, which provide important information about the ecological occupancy of species. However, to date, current methods rely on volume estimates and set operations to identify holes in hypervolumes. Yet, this approach can be problematic because in high-dimensions, the volume of region enclosing a hole tends to zero. Here, we propose the use of the topological concept of persistence homology (PH) to identify holes in hypervolumes and in ecological datasets more generally. PH allows for the estimates of topological properties in n-dimensional niche hypervolumes and is independent of the volume estimates of the hypervolume. We demonstrate the application of PH to canonical datasets and to the identification of holes in the hypervolumes of five vertebrate species with diverse niches, highlighting the potential benefits of this approach to gain further insights into animal ecology. Overall, our approach enables the study of an yet unexplored property of Hutchinsons hypervolumes (i.e., holes), and thus, have important implications to our understanding of animal ecology.

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Section: Finding Holes In Niche Hypervolumesmentioning

confidence: 99%

‘Holey’ niche! Finding holes in niche hypervolumes using persistence homology

Conceição

Morimoto

2022

Preprint

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“…It allows to find shape-like structures in the data and has proven to be a powerful exploratory approach for noisy and multi-dimensional data sets. For a detailed introduction, the reader is invited to consult [26]. [27] highlights that TDA is usually concerned with analyzing complex data with a complicated geometric or topological structure.…”

Section: Topological Data Analysismentioning

confidence: 99%

Topology-Based Clusterwise Regression for User Segmentation and Demand Forecasting

Rivera-Castro

Pletnev

Pilyugina

et al. 2019

2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA)

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“…It allows to find shape-like structures in the data and has proven to be a powerful exploratory approach for noisy and multidimensional data sets. For a detailed introduction, the reader is invited to consult [CM17]. [TS19] highlight that TDA is usually concerned with analyzing complex data with a complicated geometric or topological structure.…”

Section: Topological Data Analysismentioning

confidence: 99%

Topological Data Analysis of Time Series Data for B2B Customer Relationship Management

Rivera-Castro,

Pilyugina,

Pletnev

et al. 2019

Preprint

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Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited to the field of financial time series primarily and as a method for feature generation in machine learning applications. In this work, TDA is presented as a technique to gain additional understanding of the customers' loyalty for businessto-business customer relationship management. Increasing loyalty and strengthening relationships with key accounts remain an active topic of discussion both for researchers and managers. Using two public and two proprietary data sets of commercial data, this research shows that the technique enables analysts to better understand their customer base and identify prospective opportunities. In addition, the approach can be used as a clustering method to increase the accuracy of a predictive model for loyalty scoring. This work thus seeks to introduce TDA as a viable tool for data analysis to the quantitate marketing practitioner.

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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

Cited by 284 publications

References 105 publications

‘Holey’ niche! Finding holes in niche hypervolumes using persistence homology

‘Holey’ niche! Finding holes in niche hypervolumes using persistence homology

Topology-Based Clusterwise Regression for User Segmentation and Demand Forecasting

Topological Data Analysis of Time Series Data for B2B Customer Relationship Management

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