Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

The properties of complex networks derived from applying a compression algorithm to time series subject to symbolic ordinal-based encoding is explored. The information content of compression codewords can be used to detect forbidden symbolic patterns indicative of nonlinear determinism. The connectivity structure of ordinal-based compression networks summarized by their minimal cycle basis structure can also be used in tests for nonlinear determinism, in particular, detection of time irreversibility in a signal.

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Are all the word ranking methods the same?

International Journal of Modern Physics C ◽

10.1142/s0129183121501448 ◽

2021 ◽

pp. 2150144

Author(s):

Elham Najafi ◽

Alireza Valizadeh ◽

Amir H. Darooneh

Keyword(s):

Complex System ◽

Time Series ◽

Spatial Distribution ◽

Time Series Analysis ◽

Complex Networks ◽

Rank Correlation ◽

Ranking Methods ◽

Series Analysis ◽

Maximum Value

Text as a complex system is commonly studied by various methods, like complex networks or time series analysis, in order to discover its properties. One of the most important properties of each text is its keywords, which are extracted by word ranking methods. There are various methods to rank words of a text. Each method differently ranks words according to their frequency, spatial distribution or other word properties. Here, we aimed to explore how similar various word ranking methods are. For this purpose, we studied the rank correlation of some important word ranking methods for number of sample texts with different subjects and text sizes. We found that by increasing text size the correlation between ranking methods grows. It means that as the text size increases, the associated word ranks calculated by different ranking methods converge. Also, we found out that the rank correlations of word ranking methods approach their maximum value in the case of large enough texts.

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Learning in Feedforward Neural Networks Accelerated by Transfer Entropy

Entropy ◽

10.3390/e22010102 ◽

2020 ◽

Vol 22 (1) ◽

pp. 102 ◽

Cited By ~ 1

Author(s):

Adrian Moldovan ◽

Angel Caţaron ◽

Răzvan Andonie

Keyword(s):

Neural Networks ◽

Time Series ◽

Information Transfer ◽

Feedforward Neural Networks ◽

Theoretical Method ◽

Transfer Entropy ◽

Training Algorithms ◽

Training Algorithm ◽

Neural Connections ◽

Feedback Connections

Current neural networks architectures are many times harder to train because of the increasing size and complexity of the used datasets. Our objective is to design more efficient training algorithms utilizing causal relationships inferred from neural networks. The transfer entropy (TE) was initially introduced as an information transfer measure used to quantify the statistical coherence between events (time series). Later, it was related to causality, even if they are not the same. There are only few papers reporting applications of causality or TE in neural networks. Our contribution is an information-theoretical method for analyzing information transfer between the nodes of feedforward neural networks. The information transfer is measured by the TE of feedback neural connections. Intuitively, TE measures the relevance of a connection in the network and the feedback amplifies this connection. We introduce a backpropagation type training algorithm that uses TE feedback connections to improve its performance.

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FROM TIME SERIES TO COMPLEX NETWORKS: AN OVERVIEW

Recent Advances in Predicting and Preventing Epileptic Seizures ◽

10.1142/9789814525350_0010 ◽

2013 ◽

Author(s):

S. BIALONSKI ◽

K. LEHNERTZ

Keyword(s):

Time Series ◽

Complex Networks

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Reciprocal characterization from multivariate time series to multilayer complex networks

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5112799 ◽

2020 ◽

Vol 30 (1) ◽

pp. 013137 ◽

Cited By ~ 3

Author(s):

Yi Zhao ◽

Xiaoyi Peng ◽

Michael Small

Keyword(s):

Time Series ◽

Complex Networks ◽

Multivariate Time Series

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A sliding window-based algorithm for faster transformation of time series into complex networks

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5112782 ◽

2019 ◽

Vol 29 (10) ◽

pp. 103121 ◽

Cited By ~ 2

Author(s):

Rafael Carmona-Cabezas ◽

Javier Gómez-Gómez ◽

Eduardo Gutiérrez de Ravé ◽

Francisco José Jiménez-Hornero

Keyword(s):

Time Series ◽

Complex Networks ◽

Sliding Window

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PROBING COMPLEX NETWORKS FROM MEASURED TIME SERIES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412502367 ◽

2012 ◽

Vol 22 (10) ◽

pp. 1250236 ◽

Cited By ~ 9

Author(s):

LIANG HUANG ◽

YING-CHENG LAI ◽

MARY ANN F. HARRISON

Keyword(s):

Time Series ◽

Complex Networks ◽

Network Topology ◽

Efficient Method ◽

Relative Importance ◽

Computationally Efficient ◽

Heuristic Argument ◽

Principal Eigenvector ◽

Measured Time ◽

Potential Applications

We propose a method to detect nodes of relative importance, e.g. hubs, in an unknown network based on a set of measured time series. The idea is to construct a matrix characterizing the synchronization probabilities between various pairs of time series and examine the components of the principal eigenvector. We provide a heuristic argument indicating the existence of an approximate one-to-one correspondence between the components and the degrees of the nodes from which measurements are obtained. The striking finding is that such a correspondence appears to be quite robust, which holds regardless of the detailed node dynamics and of the network topology. Our computationally efficient method thus provides a general means to address the important problem of network detection, with potential applications in a number of fields.

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