Three perspectives on complexity: entropy, compression, subsymmetry

Nagaraj, Nithin; Balasubramanian, Karthi

doi:10.1140/epjst/e2016-60347-2

Cited by 25 publications

(20 citation statements)

References 47 publications

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“…Now for this notion of ''complexity'', that has been referred to in this section several times, there is no single unique definition. As noted in Nagaraj & Balasubramanian (2017b), Shannon entropy (Shannon, 1948;Cover & Thomas, 2012) is a very popular and intuitive measure of complexity. A low value of Shannon entropy indicates high redundancy and structure (low complexity) in the data and a high value indicates low redundancy and high randomness (high complexity).…”

Section: Dynamical Complexity (Dc) and Dynamical Compression-compleximentioning

confidence: 99%

“…ETC is defined as the effort to compress the input sequence using the lossless compression algorithm known as Non-sequential Recursive Pair Substitution (NSRPS). It has been demonstrated that both LZ and ETC outperform Shannon entropy in accurately characterizing the dynamical complexity of both stochastic (Markov) and deterministic chaotic systems in the presence of noise (Nagaraj & Balasubramanian, 2017a;Nagaraj & Balasubramanian, 2017b). Further, ETC has shown to reliably capture complexity of very short time series where even LZ fails (Nagaraj & Balasubramanian, 2017a), and for analyzing short RR tachograms from healthy young and old subjects (Balasubramanian & Nagaraj, 2016).…”

Section: Dynamical Complexity (Dc) and Dynamical Compression-compleximentioning

confidence: 99%

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Data-based intervention approach for Complexity-Causality measure

Kathpalia

Nagaraj

2019

PeerJ Computer Science

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Causality testing methods are being widely used in various disciplines of science. Model-free methods for causality estimation are very useful, as the underlying model generating the data is often unknown. However, existing model-free/data-driven measures assume separability of cause and effect at the level of individual samples of measurements and unlike model-based methods do not perform any intervention to learn causal relationships. These measures can thus only capture causality which is by the associational occurrence of ‘cause’ and ‘effect’ between well separated samples. In real-world processes, often ‘cause’ and ‘effect’ are inherently inseparable or become inseparable in the acquired measurements. We propose a novel measure that uses an adaptive interventional scheme to capture causality which is not merely associational. The scheme is based on characterizing complexities associated with the dynamical evolution of processes on short windows of measurements. The formulated measure, Compression-Complexity Causality is rigorously tested on simulated and real datasets and its performance is compared with that of existing measures such as Granger Causality and Transfer Entropy. The proposed measure is robust to the presence of noise, long-term memory, filtering and decimation, low temporal resolution (including aliasing), non-uniform sampling, finite length signals and presence of common driving variables. Our measure outperforms existing state-of-the-art measures, establishing itself as an effective tool for causality testing in real world applications.

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Section: Dynamical Complexity (Dc) and Dynamical Compression-compleximentioning

confidence: 99%

Section: Dynamical Complexity (Dc) and Dynamical Compression-compleximentioning

confidence: 99%

Data-based intervention approach for Complexity-Causality measure

Kathpalia

Nagaraj

2019

PeerJ Computer Science

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“…It should be noted that both LZ and ETC are complexity measures derived from lossless data compression algorithms (hence we term them as compression-complexity measures). It has been demonstrated that both LZ and ETC outperform Shannon Entropy in characterizing complexity of noisy time series of short length arising out of stochastic (markov) and chaotic systems [37,39,40]. Further, ETC consistently performs better than LZ in a number of applications as shown in recently published literature [39][40][41][42].…”

Section: • Strength Of the Hydrogen Bondsmentioning

confidence: 81%

“…It has been demonstrated that both LZ and ETC outperform Shannon Entropy in characterizing complexity of noisy time series of short length arising out of stochastic (markov) and chaotic systems [37,39,40]. Further, ETC consistently performs better than LZ in a number of applications as shown in recently published literature [39][40][41][42]. For details of how to compute LZ and ETC on actual input sequences, we refer the readers to [22,37,43].…”

Section: • Strength Of the Hydrogen Bondsmentioning

confidence: 98%

Automatic Identification of SARS Coronavirus using Compression-Complexity Measures

Balasubramanian

Nagaraj

2020

Preprint

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Finding vaccine or specific antiviral treatment for global pandemic of virus diseases (such as the ongoing COVID-19) requires rapid analysis, annotation and evaluation of metagenomic libraries to enable a quick and efficient screening of nucleotide sequences. Traditional sequence alignment methods are not suitable and there is a need for fast alignment-free techniques for sequence analysis. Information theory and data compression algorithms provide a rich set of mathematical and computational tools to capture essential patterns in biological sequences. In 2013, our research group (Nagaraj et al., Eur. Phys. J. Special Topics 222(3-4), 2013) has proposed a novel measure known as Effort-To-Compress (ETC) based on the notion of compression-complexity to capture the information content of sequences. In this study, we propose a compression-complexity based distance measure for automatic identification of SARS coronavirus strains from a set of viruses using only short fragments of nucleotide sequences. We also demonstrate that our proposed method can correctly distinguish SARS-CoV-2 from SARS-CoV-1 viruses by analyzing very short segments of nucleotide sequences. This work could be extended further to enable medical practitioners in automatically identifying and characterizing SARS coronavirus strain in a fast and efficient fashion using short and/or incomplete segments of nucleotide sequences. Potentially, the need for sequence assembly can be circumvented.NoteThe main ideas and results of this research were first presented at the International Conference on Nonlinear Systems and Dynamics (CNSD-2013) held at Indian Institute of Technology, Indore, December 12, 2013. In this manuscript, we have extended our preliminary analysis to include SARS-CoV-2 virus as well.

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“…Now for this notion of "complexity", that has been referred to in this section several times, there is no single unique definition. As noted in Nagaraj and Balasubramanian (2017b), Shannon entropy (Cover and Thomas, 2012) is a very popular and intuitive measure of complexity. A low value of Shannon entropy indicates high redundancy and structure (low complexity) in the data and a high value indicates low redundancy and high randomness (high complexity).…”

Section: /19mentioning

confidence: 99%

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Supplemental Information 2: MATLAB Toolbox for Computation of Compression-Complexity Causality Measure

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Causality testing methods are being widely used in various disciplines of science. Modelfree methods for causality estimation are very useful as the underlying model generating the data is often unknown. However, existing model-free measures assume separability of cause and effect at the level of individual samples of measurements and unlike modelbased methods do not perform any intervention to learn causal relationships. These measures can thus only capture causality which is by the associational occurrence of 'cause' and 'effect' between well separated samples. In real-world processes, often 'cause' and 'effect' are inherently inseparable or become inseparable in the acquired measurements. We propose a novel measure that uses an adaptive interventional scheme to capture causality which is not merely associational. The scheme is based on characterizing complexities associated with the dynamical evolution of processes on short windows of measurements. The formulated measure, Compression-Complexity Causality is rigorously tested on simulated and real datasets and its performance is compared with that of existing measures such as Granger Causality and Transfer Entropy. The proposed measure is robust to presence of noise, long-term memory, filtering and decimation, low temporal resolution (including aliasing), non-uniform sampling, finite length signals and presence of common driving variables. Our measure outperforms existing state-of-the-art measures, establishing itself as an effective tool for causality testing in real world applications.

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Three perspectives on complexity: entropy, compression, subsymmetry

Cited by 25 publications

References 47 publications

Data-based intervention approach for Complexity-Causality measure

Data-based intervention approach for Complexity-Causality measure

Automatic Identification of SARS Coronavirus using Compression-Complexity Measures

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