Persistence Paths and Signature Features in Topological Data Analysis

Chevyrev, Ilya; Nanda, Vidit; Oberhauser, Harald

doi:10.1109/tpami.2018.2885516

Cited by 57 publications

(41 citation statements)

References 26 publications

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“…The signature S(X) completely characterises a path X up to tree-like equivalence and is invariant to reparameterisation [5]. The usefulness of signatures as features of sequential data was demonstrated theoretically for non-parametric hypothesis testing [4] and algebraic geometry [6] as well as in numerous machine learning applications [7], for example: in healthcare [8][9][10][11][12], finance [13], computer vision [14,15], topological data analysis [16] and deep signature learning [17].…”

Section: The Signature Of a Pathmentioning

confidence: 99%

The Signature-Based Model for Early Detection of Sepsis from Electronic Health Records in the Intensive Care Unit

Morrill¹,

Kormilitzin²,

Nevado‐Holgado³

et al. 2019

2019 Computing in Cardiology Conference (CinC)

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Optimal feature selection leads to enhanced efficiency and accuracy when developing both supervised and unsupervised machine-learning models. In this work, a new signature-based regression model is proposed to automatically identify a patient's risk of sepsis based on physiological data streams and to make a positive or negative prediction of sepsis for every time interval since admission to the intensive care unit. The gradient boosting machine algorithm that uses the features at the current time-points and the signature features extracted from the time-series to model the longitudinal effects of sepsis yields the utility function score of 0.360 (officially ranked 1st, team name: 'Can I get your Signature?') on the full test set. The signature method shows a systematic and competitive approach to model sepsis by learning from health data streams.

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Section: The Signature Of a Pathmentioning

confidence: 99%

The Signature-Based Model for Early Detection of Sepsis from Electronic Health Records in the Intensive Care Unit

Morrill¹,

Kormilitzin²,

Nevado‐Holgado³

et al. 2019

2019 Computing in Cardiology Conference (CinC)

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“…Betti curves are advantageous because they permit the calculation of a mean curve, next to providing an easy-to-evaluate distance and kernel method. Chevyrev et al ( 2018 ) used this representation—and related “paths” derived from a persistence diagram and its representations—to solve classification tasks, using random forests and support vector machine classifiers. One drawback of the Betti curves is their limited expressive power.…”

Section: Surveymentioning

confidence: 99%

A Survey of Topological Machine Learning Methods

Hensel

Moor

Rieck

2021

Front. Artif. Intell.

111

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The last decade saw an enormous boost in the field of computational topology: methods and concepts from algebraic and differential topology, formerly confined to the realm of pure mathematics, have demonstrated their utility in numerous areas such as computational biology personalised medicine, and time-dependent data analysis, to name a few. The newly-emerging domain comprising topology-based techniques is often referred to as topological data analysis (TDA). Next to their applications in the aforementioned areas, TDA methods have also proven to be effective in supporting, enhancing, and augmenting both classical machine learning and deep learning models. In this paper, we review the state of the art of a nascent field we refer to as “topological machine learning,” i.e., the successful symbiosis of topology-based methods and machine learning algorithms, such as deep neural networks. We identify common threads, current applications, and future challenges.

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“…For example, persistence landscapes (Bubenik, 2015) map persistence diagrams into a Banach space, specifically L p space. More examples include persistence image (Adams et al, 2017), generalized persistence landscapes (Berry et al, 2020), persistence path (Chevyrev et al, 2018), persistence codebook (Zelinski et al, 2020), persistence curves (Chung and Lawson, 2019), kernel based methods (Reininghaus et al, 2015;Kusano et al, 2016), and persistent entropy (Chintakunta et al, 2015;Atienza et al, 2019b). These methods have been studied and applied to different applications.…”

Section: Data Analysis With Persistence Diagram and Commonly Considermentioning

confidence: 99%

A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

Chung

et al. 2021

Front. Physiol.

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Persistent homology is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general pipeline to apply persistent homology to study time series, particularly the instantaneous heart rate time series for the heart rate variability (HRV) analysis. The first step is capturing the shapes of time series from two different aspects—the persistent homologies and hence persistence diagrams of its sub-level set and Taken's lag map. Second, we propose a systematic and computationally efficient approach to summarize persistence diagrams, which we coined persistence statistics. To demonstrate our proposed method, we apply these tools to the HRV analysis and the sleep-wake, REM-NREM (rapid eyeball movement and non rapid eyeball movement) and sleep-REM-NREM classification problems. The proposed algorithm is evaluated on three different datasets via the cross-database validation scheme. The performance of our approach is better than the state-of-the-art algorithms, and the result is consistent throughout different datasets.

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Persistence Paths and Signature Features in Topological Data Analysis

Cited by 57 publications

References 26 publications

The Signature-Based Model for Early Detection of Sepsis from Electronic Health Records in the Intensive Care Unit

The Signature-Based Model for Early Detection of Sepsis from Electronic Health Records in the Intensive Care Unit

A Survey of Topological Machine Learning Methods

A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

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