Topological recognition of critical transitions in time series of cryptocurrencies

Gidea, Marian; Goldsmith, Daniel; Katz, Yuri A.; Roldan, Pablo; Shmalo, Yonah

doi:10.1016/j.physa.2019.123843

Cited by 53 publications

(34 citation statements)

References 26 publications

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“…Computationally, one area which deserves further exploration is the use of TDA to analyze time-series data (Ravishanker and Chen, 2019) in cancer. This has been done extensively in several other fields including climate analysis (Berwald et al, 2014), tracking stability of dynamical systems (Khasawneh and Munch, 2016), clustering populations of Tribolium flour beetles (Pereira and de Mello, 2015), analyzing motion sensor data during sports activities (Stolz et al, 2017), and financial time series data (Gidea, 2017;Truong, 2017;Gidea and Katz, 2018;Gidea et al, 2020). Though time series oncological data have been analyzed with varying degrees of success (Aoto et al, 2018;Kourou et al, 2020), TDA techniques of any sort have yet to be applied.…”

Section: Discussionmentioning

confidence: 99%

Applications of Topological Data Analysis in Oncology

Bukkuri

Andor

Darcy

2021

Front. Artif. Intell.

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The emergence of the information age in the last few decades brought with it an explosion of biomedical data. But with great power comes great responsibility: there is now a pressing need for new data analysis algorithms to be developed to make sense of the data and transform this information into knowledge which can be directly translated into the clinic. Topological data analysis (TDA) provides a promising path forward: using tools from the mathematical field of algebraic topology, TDA provides a framework to extract insights into the often high-dimensional, incomplete, and noisy nature of biomedical data. Nowhere is this more evident than in the field of oncology, where patient-specific data is routinely presented to clinicians in a variety of forms, from imaging to single cell genomic sequencing. In this review, we focus on applications involving persistent homology, one of the main tools of TDA. We describe some recent successes of TDA in oncology, specifically in predicting treatment responses and prognosis, tumor segmentation and computer-aided diagnosis, disease classification, and cellular architecture determination. We also provide suggestions on avenues for future research including utilizing TDA to analyze cancer time-series data such as gene expression changes during pathogenesis, investigation of the relation between angiogenic vessel structure and treatment efficacy from imaging data, and experimental confirmation that geometric and topological connectivity implies functional connectivity in the context of cancer.

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Section: Discussionmentioning

confidence: 99%

Applications of Topological Data Analysis in Oncology

Bukkuri

Andor

Darcy

2021

Front. Artif. Intell.

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“…The resulting topological summaries, i.e., persistence barcodes, are then used for downstream processing. Within this regime, Gidea et al [15] analyze the dynamics of cryptocurrencies using persistence landscapes [6], Khasawneh et al [21] study chatter classification in synthetic time series from turning processes and Dłotko et al [11] identify periodicity patterns in time series. In [22], Kim et al actually compute one-step forecasts for Bitcoin prices and classify price patterns, essentially feeding barcode statistics as supplementary features to a MLP/CNN-based regression model.…”

Section: Related Workmentioning

confidence: 99%

“…One prime example 1 are topological features, typically obtained via persistent homology [7,13]. In fact, various approaches [31,16,11,21,15] have successfully used topological features for time series analysis, however, mostly in classification settings, for the identification of certain phenomena in dynamical systems, or for purely exploratory analysis (see Section 2).…”

Section: Introductionmentioning

confidence: 99%

Topological Attention for Time Series Forecasting

Zeng,

Graf,

Hofer

et al. 2021

Preprint

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The problem of (point) forecasting univariate time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether local topological properties, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose topological attention, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as N-BEATS, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.

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“…These types of bifurcations are particularly topological in nature, as the solution to the dynamical system changes from a small cluster to a circular structure and sometimes reduces back to a cluster. While persistent homology has been used to study Hopf bifurcations [41][42][43][44], none of the existing methods use zigzag persistence.…”

Section: Bifurcations Using Zigzag (Buzz)mentioning

confidence: 99%

Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

2020

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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. In an experimental setting, this transition could lead to incorrect data or damage to the entire experiment. 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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Topological recognition of critical transitions in time series of cryptocurrencies

Cited by 53 publications

References 26 publications

Applications of Topological Data Analysis in Oncology

Applications of Topological Data Analysis in Oncology

Topological Attention for Time Series Forecasting

Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

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