Combining Measures of Signal Complexity and Machine Learning for Time Series Analyis: A Review

Measures of signal complexity, such as the Hurst exponent, the fractal dimension, and the Spectrum of Lyapunov exponents, are used in time series analysis to give estimates on persistency, anti-persistency, fluctuations and predictability of the data under study. They have proven beneficial when doing time series prediction using machine and deep learning and tell what features may be relevant for predicting time-series and establishing complexity features. Further, the performance of machine learning approaches can be improved, taking into account the complexity of the data under study, e.g., adapting the employed algorithm to the inherent long-term memory of the data. In this article, we provide a review of complexity and entropy measures in combination with machine learning approaches. We give a comprehensive review of relevant publications, suggesting the use of fractal or complexity-measure concepts to improve existing machine or deep learning approaches. Additionally, we evaluate applications of these concepts and examine if they can be helpful in predicting and analyzing time series using machine and deep learning. Finally, we give a list of a total of six ways to combine machine learning and measures of signal complexity as found in the literature.

Exploring Neural Signal Complexity as a Potential Link between Creative Thinking, Intelligence, and Cognitive Control

Functional connectivity studies have demonstrated that creative thinking builds upon an interplay of multiple neural networks involving the cognitive control system. Theoretically, cognitive control has generally been discussed as the common basis underlying the positive relationship between creative thinking and intelligence. However, the literature still lacks a detailed investigation of the association patterns between cognitive control, the factors of creative thinking as measured by divergent thinking (DT) tasks, i.e., fluency and originality, and intelligence, both fluid and crystallized. In the present study, we explored these relationships at the behavioral and the neural level, based on N = 77 young adults. We focused on brain-signal complexity (BSC), parameterized by multi-scale entropy (MSE), as measured during a verbal DT and a cognitive control task. We demonstrated that MSE is a sensitive neural indicator of originality as well as inhibition. Then, we explore the relationships between MSE and factor scores indicating DT and intelligence. In a series of across-scalp analyses, we show that the overall MSE measured during a DT task, as well as MSE measured in cognitive control states, are associated with fluency and originality at specific scalp locations, but not with fluid and crystallized intelligence. The present explorative study broadens our understanding of the relationship between creative thinking, intelligence, and cognitive control from the perspective of BSC and has the potential to inspire future BSC-related theories of creative thinking.

Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS

Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.

EEG Signal Complexity Is Reduced During Resting-State in Fragile X Syndrome

Introduction: Fragile X syndrome (FXS) is a genetic disorder caused by a mutation of the fragile X mental retardation 1 gene (FMR1). FXS is associated with neurophysiological abnormalities, including cortical hyperexcitability. Alterations in electroencephalogram (EEG) resting-state power spectral density (PSD) are well-defined in FXS and were found to be linked to neurodevelopmental delays. Whether non-linear dynamics of the brain signal are also altered remains to be studied.Methods: In this study, resting-state EEG power, including alpha peak frequency (APF) and theta/beta ratio (TBR), as well as signal complexity using multi-scale entropy (MSE) were compared between 26 FXS participants (ages 5–28 years), and 7 neurotypical (NT) controls with a similar age distribution. Subsequently a replication study was carried out, comparing our cohort to 19 FXS participants independently recorded at a different site.Results: PSD results confirmed the increased gamma, decreased alpha power and APF in FXS participants compared to NT controls. No alterations in TBR were found. Importantly, results revealed reduced signal complexity in FXS participants, specifically in higher scales, suggesting that altered signal complexity is sensitive to brain alterations in this population. The replication study mostly confirmed these results and suggested critical points of stagnation in the neurodevelopmental curve of FXS.Conclusion: Signal complexity is a powerful feature that can be added to the electrophysiological biomarkers of brain maturation in FXS.

The Application of Complexity Analysis in Brain Blood-Oxygen Signal

One of the daunting features of the brain is its physiology complexity, which arises from the interaction of numerous neuronal circuits that operate over a wide range of temporal and spatial scales, enabling the brain to adapt to the constantly changing environment and to perform various cognitive functions. As a reflection of the complexity of brain physiology, the complexity of brain blood-oxygen signal has been frequently studied in recent years. This paper reviews previous literature regarding the following three aspects: (1) whether the complexity of the brain blood-oxygen signal can serve as a reliable biomarker for distinguishing different patient populations; (2) which is the best algorithm for complexity measure? And (3) how to select the optimal parameters for complexity measures. We then discuss future directions for blood-oxygen signal complexity analysis, including improving complexity measurement based on the characteristics of both spatial patterns of brain blood-oxygen signal and latency of complexity itself. In conclusion, the current review helps to better understand complexity analysis in brain blood-oxygen signal analysis and provide useful information for future studies.

Signal complexity indicators of health status in clinical EEG

Brain signal variability changes across the lifespan in both health and disease, likely reflecting changes in information processing capacity related to development, aging and neurological disorders. While signal complexity, and multiscale entropy (MSE) in particular, has been proposed as a biomarker for neurological disorders, most observations of altered signal complexity have come from studies comparing patients with few to no comorbidities against healthy controls. In this study, we examined whether MSE of brain signals was distinguishable across patient groups in a large and heterogeneous set of clinical-EEG data. Using a multivariate analysis, we found unique timescale-dependent differences in MSE across various neurological disorders. We also found MSE to differentiate individuals with non-brain comorbidities, suggesting that MSE is sensitive to brain signal changes brought about by metabolic and other non-brain disorders. Such changes were not detectable in the spectral power density of brain signals. Our findings suggest that brain signal complexity may offer complementary information to spectral power about an individual’s health status and is a promising avenue for clinical biomarker development.

High-Density EEG in a Charles Bonnet Syndrome Patient during and without Visual Hallucinations: A Case-Report Study

Charles Bonnet syndrome (CBS) is a rare clinical condition characterized by complex visual hallucinations in people with loss of vision. So far, the neurobiological mechanisms underlying the hallucinations remain elusive. This case-report study aims at investigating electrical activity changes in a CBS patient during visual hallucinations, as compared to a resting-state period (without hallucinations). Prior to the EEG, the patient underwent neuropsychological, ophthalmologic, and neurological examinations. Spectral and connectivity, graph analyses and signal diversity were applied to high-density EEG data. Visual hallucinations (as compared to resting-state) were characterized by a significant reduction of power in the frontal areas, paralleled by an increase in the midline posterior regions in delta and theta bands and by an increase of alpha power in the occipital and midline posterior regions. We next observed a reduction of theta connectivity in the frontal and right posterior areas, which at a network level was complemented by a disruption of small-worldness (lower local and global efficiency) and by an increase of network modularity. Finally, we found a higher signal complexity especially when considering the frontal areas in the alpha band. The emergence of hallucinations may stem from these changes in the visual cortex and in core cortical regions encompassing both the default mode and the fronto-parietal attentional networks.

Derived loss of signal complexity and plasticity in a genus of weakly electric fish

Signal plasticity can maximize the usefulness of costly animal signals such as the electric organ discharges (EODs) of weakly electric fishes. Some species of the order Gymnotiformes rapidly alter their EOD amplitude and duration in response to circadian cues and social stimuli. How this plasticity is maintained across related species with different degrees of signal complexity is poorly understood. In one genus of weakly electric gymnotiform fish (Brachyhypopomus) only one species, B. bennetti, produces a monophasic signal while all other species emit complex biphasic or multiphasic EOD waveforms produced by two overlapping but asynchronous action potentials in each electric organ cell (electrocyte). One consequence of this signal complexity is the suppression of low-frequency signal content that is detectable by electroreceptive predators. In complex EODs, reduction of the EOD amplitude and duration during daytime inactivity can decrease both predation risk and the metabolic cost of EOD generation. We compared EOD plasticity and its underlying physiology in Brachyhypopomus focusing on B. bennetti. We found that B. bennetti exhibits minimal EOD plasticity, but that its electrocytes retained vestigial mechanisms of biphasic signaling and vestigial mechanisms for modulating the EOD amplitude. These results suggest that this species represents a transitional phenotypic state within a clade where signal complexity and plasticity were initially gained and then lost. Signal mimicry, mate recognition, and sexual selection are potential factors maintaining the monophasic EOD phenotype in the face of detection by electroreceptive predators.