Multiplex visibility graphs to investigate recurrent neural network dynamics

Bianchi, Filippo Maria; Livi, Lorenzo; Alippi, Cesare; Jenssen, Robert

doi:10.1038/srep44037

Cited by 37 publications

(31 citation statements)

References 67 publications

(105 reference statements)

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“…Each model is configured with the same hyperparameters in all the experiments. Since reservoirs are sensitive to the hyperparameter setting [47], a fine-tuning with independent cross-validation for each task is usually more important in classic RC models than in RNNs trained with gradient descent, such as LSTM and GRU. Nevertheless, we show that the proposed rmESN achieves competitive results even with fixed the hyperparameters.…”

Section: Methodsmentioning

confidence: 99%

Reservoir Computing Approaches for Representation and Classification of Multivariate Time Series

Bianchi

Scardapane

Løkse

et al. 2021

IEEE Trans. Neural Netw. Learning Syst.

Self Cite

136

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Section: Methodsmentioning

confidence: 99%

Reservoir Computing Approaches for Representation and Classification of Multivariate Time Series

Bianchi

Scardapane

Løkse

et al. 2021

IEEE Trans. Neural Netw. Learning Syst.

Self Cite

136

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“…Bianchi et al (2017) used multiplex visibility networks method based on the weighted HVG algorithm (Section 3.1.5) where the edge weights are given by:

w_{i, j} = 1 / \sqrt{{(j - i)}^{2} + {(Y_{i} - Y_{j})}^{2}}

, incorporating temporal and amplitude information of the data. They studied topological measures of the networks to characterize neuron activations.…”

Section: Mapping Multivariate Time Series Into Complex Networkmentioning

confidence: 99%

Time series analysis via network science: Concepts and algorithms

Silva

Ribeiro

et al. 2021

WIREs Data Min & Knowl

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There is nowadays a constant flux of data being generated and collected in all types of real world systems. These data sets are often indexed by time, space, or both requiring appropriate approaches to analyze the data. In univariate settings, time series analysis is a mature field. However, in multivariate contexts, time series analysis still presents many limitations. In order to address these issues, the last decade has brought approaches based on network science. These methods involve transforming an initial time series data set into one or more networks, which can be analyzed in depth to provide insight into the original time series. This review provides a comprehensive overview of existing mapping methods for transforming time series into networks for a wide audience of researchers and practitioners in machine learning, data mining, and time series. Our main contribution is a structured review of existing methodologies, identifying their main characteristics, and their differences. We describe the main conceptual approaches, provide authoritative references and give insight into their advantages and limitations in a unified way and language. We first describe the case of univariate time series, which can be mapped to single layer networks, and we divide the current mappings based on the underlying concept: visibility, transition, and proximity. We then proceed with multivariate time series discussing both single layer and multiple layer approaches. Although still very recent, this research area has much potential and with this survey we intend to pave the way for future research on the topic. This article is categorized under: Fundamental Concepts of Data and Knowledge > Data Concepts Fundamental Concepts of Data and Knowledge > Knowledge Representation

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“…if node i corresponds to a future time than node j, and are visible to each other, then there is connection from i®j but not i¬j 35 . There is also a technique to map multivariate time series into multiplex graphs 36 that may enable analysis of multi-modality monitoring data from the injury site e.g. ISP, tissue oxygen and microdialysis.…”

Section: Discussionmentioning

confidence: 99%

Visibility Graph Analysis of Intraspinal Pressure Signal Predicts Functional Outcome in Spinal Cord Injured Patients

Chen

Gallagher

Hogg

et al. 2018

Journal of Neurotrauma

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To guide management of patients with acute spinal cord injuries, we developed intraspinal pressure monitoring from the injury site. Here, we examine the complex fluctuations in the intraspinal pressure signal using network theory. We analyzed 7097 h of intraspinal pressure data from 58 patients with severe cord injuries. Intraspinal pressure signals were split into hourly windows. Each window was mapped into a visibility graph as follows. Vertical bars were drawn at 0.1 Hz representing signal amplitudes. Each bar produced a node, thus totalling 360 nodes per graph. Two nodes were linked with an edge if the straight line through the nodes did not intersect a bar. We computed several topological metrics for each graph including diameter, modularity, eccentricity, and small-worldness. Patients were followed up for 20 months on average. Our data show that the topological structure of intraspinal pressure visibility graphs is highly sensitive to pathological events at the injury site, including cord compression (high intraspinal pressure), ischemia (low spinal cord perfusion pressure), and deranged autoregulation (high spinal pressure reactivity index). These pathological changes correlate with long graph diameter, high modularity, high eccentricity and reduced small-worldness. In a multivariate logistic regression model, age, neurological status on admission, and average node eccentricity were independent predictors of neurological improvement. We conclude that analysis of intraspinal pressure fluctuations after spinal cord injury as graphs, rather than as time series, captures clinically important information. Our novel technique may be applied to other signals recorded from injured central nervous system (CNS); for example, intracranial pressure, tissue metabolite, and oxygen levels.

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Multiplex visibility graphs to investigate recurrent neural network dynamics

Cited by 37 publications

References 67 publications

Reservoir Computing Approaches for Representation and Classification of Multivariate Time Series

Reservoir Computing Approaches for Representation and Classification of Multivariate Time Series

Time series analysis via network science: Concepts and algorithms

Visibility Graph Analysis of Intraspinal Pressure Signal Predicts Functional Outcome in Spinal Cord Injured Patients

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