A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification

Chung, Yu-Min; Hu, Chuan-Shen; Lo, Yu‐Lun; Wu, Hau‐Tieng

doi:10.48550/arxiv.1908.06856

Cited by 3 publications

(5 citation statements)

References 80 publications

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“…However none of the methods mentioned use topological features. In direct comparison, the authors in [5] use similar persistent homology based approaches, however they use a different featurization method and they test their method across many databases. They perform three different classification tasks: (1) sleep vs. wake, (2) REM vs. NREM, and (3) wake vs. REM vs. NREM.…”

Section: Resultsmentioning

confidence: 99%

“…Our accuracies for the two class classification problem are over 70% for all patients. We acknowledge that we are only using 8 patients, while the datasets used in [5] are much larger, so it is not a direct comparison. However, the consistency of our results across these 8 patients with varying OSA severity seems promising that it would extend to larger datasets.…”

Section: Resultsmentioning

confidence: 99%

“…Existing applications include studying machining dynamics [11,12,13], gene expression [21,2], financial data [15], and video data [28,26]. Additionally, [5] used topological methods for time series analysis of sleep-wake states. Our goal is to explore the use of persistent homology to classify sleep states in PSG data.…”

Section: Sleep State Analysis Using Persistent Homologymentioning

confidence: 99%

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Classifying sleep states using persistent homology and Markov chain: a Pilot Study

Tymochko,

Singhal,

Heo

2020

Preprint

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Obstructive sleep Apnea (OSA) is a form of sleep disordered breathing characterized by frequent episodes of upper airway collapse during sleep. Pediatric OSA occurs in 1-5% of children and can related to other serious health conditions such as high blood pressure, behavioral issues, or altered growth. OSA is often diagnosed by studying the patient's sleep cycle, the pattern with which they progress through various sleep states such as wakefulness, rapid eye-movement, and non-rapid eye-movement. The sleep state data is obtained using an overnight polysomnography test that the patient undergoes at a hospital or sleep clinic, where a technician manually labels each 30 second time interval, also called an "epoch," with the current sleep state. This process is laborious and prone to human error. We seek an automatic method of classifying the sleep state, as well as a method to analyze the sleep cycles. This article is a pilot study in sleep state classification using two approaches: first, we'll use methods from the field of topological data analysis to classify the sleep state and second, we'll model sleep states as a Markov chain and visually analyze the sleep patterns. In the future, we will continue to build on this work to improve our methods.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Sleep State Analysis Using Persistent Homologymentioning

confidence: 99%

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Classifying sleep states using persistent homology and Markov chain: a Pilot Study

Tymochko,

Singhal,

Heo

2020

Preprint

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“…In [14], authors defined a new distance on the space of persistence diagram and used this new distance to classify time series. In [20] and [5], authors used TDA tools to analyze physiological signals.…”

Section: Introductionmentioning

confidence: 99%

A Persistent Homology Approach to Time Series Classification

Chung¹,

Cruse²,

Lawson³

2020

Preprint

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Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that tracks changes in topological information. These changes can be recorded in multi-sets known as persistence diagrams. Converting information stored in persistence diagrams into a form compatible with modern machine learning algorithms is a major vein of research in TDA. Persistence curves, a recently developed framework, provides a canonical and flexible way to encode the information presented in persistence diagrams into vectors. In this work, we propose a new set of metrics based on persistence curves. We prove the stability of the proposed metrics. Finally, we apply these metrics to the UCR Time Series Classification Archive. These empirical results show that our metrics perform better than the relevant benchmark in most cases and warrant further study.

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“…Specifically, persistent homology has been shown to quantify features of a time series such as periodic and quasiperiodic behavior [28,31,36,23,40] or chaotic and periodic behavior [25,18]. Existing applications in time series analysis include studying machining dynamics [19,20,41,18,42,21,17], gene expression [28,4], financial data [13], video data [38,37], and sleepwake states [10,39]. These applications typically involve summarizing the underlying topological shape of each time series in a persistence diagram then using additional methods to analyze the resulting collection of persistence diagrams.…”

Section: Introductionmentioning

confidence: 99%

Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

Tymochko,

Munch,

Khasawneh

2020

Preprint

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Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. While standard persistent homology has been used in this setting, it usually requires analyzing a collection of persistence diagrams, which in turn drives up the computational cost considerably. Using zigzag persistence, we can capture topological changes in the state space of the dynamical system in only one persistence diagram. Here we present Bifurcations using ZigZag (BuZZ), a one-step method to study and detect bifurcations using zigzag persistence. The BuZZ method is successfully able to detect this type of behavior in two synthetic examples as well as an example dynamical system.

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A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification

Cited by 3 publications

References 80 publications

Classifying sleep states using persistent homology and Markov chain: a Pilot Study

Classifying sleep states using persistent homology and Markov chain: a Pilot Study

A Persistent Homology Approach to Time Series Classification

Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

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