giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration

Tauzin, Guillaume; Lupo, Umberto; Tunstall, Lewis C.; Pérez, Julian Burella; Caorsi, Matteo; Wojciech, Reise,; Medina-Mardones, Anibal M.; Dassatti, Alberto; Hess, Kathryn

doi:10.48550/arxiv.2004.02551

Cited by 12 publications

(11 citation statements)

References 6 publications

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“…This system is part of the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via Welsh Government. Persistent homology calculations were performed using giotto-tda [47]…”

Section: Acknowledgments 17mentioning

confidence: 99%

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Sale,

Giansiracusa,

Lucini

2021

Preprint

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We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

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Section: Acknowledgments 17mentioning

confidence: 99%

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Sale,

Giansiracusa,

Lucini

2021

Preprint

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“…We acknowledge the University of Turin's and Polytechnic University of Turin's High Performance Centre for Artificial Intelligence (HPC4AI) for providing us with the following computational resources: • GPU: Nvidia Tesla T4 (not used yet) Moreover, the implementation described in the previous paragraphs is largely based on the following libraries: TDA's feature extraction with giotto-tda [29], hyperparameter optimization scikit-optimize [30] along with Machine Learning algorithms implementation with scikit-learn [31].…”

Section: Hardware Support and Codementioning

confidence: 99%

Topological Data Analysis (TDA) Techniques Enhance Hand Pose Classification from ECoG Neural Recordings

Azeglio¹,

Bernardo²,

Penna³

et al. 2021

Preprint

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Electrocorticogram (ECoG) well characterizes hand movement intentions and gestures. In the present work we aim to investigate the possibility to enhance hand pose classification, in a Rock-Paper-Scissor -and Rest -task, by introducing topological descriptors of time series data. We hypothesized that an innovative approach based on topological data analysis can extract hidden information that are not detectable with standard Brain Computer Interface (BCI) techniques. To investigate this hypothesis, we integrate topological features together with power band features and feed them to several standard classifiers, e.g. Random Forest, Gradient Boosting. Model selection is thus completed after a meticulous phase of bayesian hyperparameter optimization. With our method, we observed robust results in terms of accuracy for a four-labels classification problem, with limited available data. Through feature importance investigation, we conclude that topological descriptors are able to extract useful discriminative information and provide novel insights. Since our data are restricted to single-patient recordings, generalization might be limited. Nevertheless, our method can be extended and applied to a wide range of neurophysiological recordings and it might be an intriguing point of departure for future studies.

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“…Later, it became clear that the simplicial complex language was a natural formalism for explicitly representing biological and physical systems. For example, simplicial complexes have been used to represent neural recordings [82,49], classify images [195,51,62], and describe the mesoscale architecture of brain networks [193,194,161,184,153]. Even more recent work has focused on defining generative models to construct simplicial complexes with given topological features [47].…”

Section: Simplicial Complexesmentioning

confidence: 99%

The why, how, and when of representations for complex systems

Torres¹,

Blevins²,

Bassett³

et al. 2020

Preprint

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Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific strategies that are seldom revisited or questioned, and the siloing of ideas within a domain due to inconsistency of complex systems language. In this work we offer basic, domain-agnostic language in order to advance towards a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system and data collected, then moving through different mathematical formalisms for encoding the observed data (i.e. graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each formalism. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of one relation among the parts of a system may influence the existence of another relation. We discuss how dependencies may arise and how they may alter interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and choice of mathematical representation influence the results. We hope this work can serve as an opportunity of reflection for experienced complexity scientists, as well as an introductory resource for new researchers.

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giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration

Cited by 12 publications

References 6 publications

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Topological Data Analysis (TDA) Techniques Enhance Hand Pose Classification from ECoG Neural Recordings

The why, how, and when of representations for complex systems

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