Approach to an irregular time series on the basis of the fractal theory
Abstract
We present a technique to measure the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval. First we apply it to a fractional Brownian function [1] which has a property of self-similarity for all scales, and we can get the stable and precise fractal dimension. This technique is also applied to the observational data of natural phenomena. It does not show self-similarity all over the scale but has a different self-similarity across the characteristic time scale. The present method gives us a stable characteristic time scale as well as the fractal dimension.
References (11)
- P. Grassberger et al.
Measuring the strangeness of strange attractors
Physica D
(1983) - B. Mandelbrot
Fractals: Form, Chance and Dimension
(1977) - B. Mandelbrot et al.
Some long-run properties of geophysical records
Water Resource Research
(1969) - D. Rulle
Five turbulent problems
Physica D
(1983) - K.J. Falconer
The Geometry of fractal sets
(1985)
Cited by (1757)
Reliable automatic sleep stage classification based on hybrid intelligence
2024, Computers in Biology and MedicineSleep staging is a vital aspect of sleep assessment, serving as a critical tool for evaluating the quality of sleep and identifying sleep disorders. Manual sleep staging is a laborious process, while automatic sleep staging is seldom utilized in clinical practice due to issues related to the inadequate accuracy and interpretability of classification results in automatic sleep staging models. In this work, a hybrid intelligent model is presented for automatic sleep staging, which integrates data intelligence and knowledge intelligence, to attain a balance between accuracy, interpretability, and generalizability in the sleep stage classification. Specifically, it is built on any combination of typical electroencephalography (EEG) and electrooculography (EOG) channels, including a temporal fully convolutional network based on the U-Net architecture and a multi-task feature mapping structure. The experimental results show that, compared to current interpretable automatic sleep staging models, our model achieves a Macro-F1 score of 0.804 on the ISRUC dataset and 0.780 on the Sleep-EDFx dataset. Moreover, we use knowledge intelligence to address issues of excessive jumps and unreasonable sleep stage transitions in the coarse sleep graphs obtained by the model. We also explore the different ways knowledge intelligence affects coarse sleep graphs by combining different sleep graph correction methods. Our research can offer convenient support for sleep physicians, indicating its significant potential in improving the efficiency of clinical sleep staging.
We applied four fractal dimension estimation algorithms on the temporal electrical impedance signal of normal MDCK type II cell cultures monitored by ECIS technique and showed that the fractal dimension due to micromotion allows discriminating processes not sensed by the spectral impedance of the culture. In this work we subjected cell cultures to electric current damage and drug exposure to analyze the changes in the fractal structure of the temporal signal. Among the changes presented and detected are the differentiation between a healthy monolayer and one exposed to a drug, as well as the distinction between a seeding process and a wound-healing process performed by electric current. The four algorithms used were validated by applying them on topological functions of known fractal dimension, a study that determined the necessary conditions for a correct estimation.
Fractal Dimension as a discriminative feature for high accuracy classification in motor imagery EEG-based brain-computer interface
2024, Computer Methods and Programs in BiomedicineThe brain-computer interface (BCI) technology acquires human brain electrical signals, which can be effectively and successfully used to control external devices, potentially supporting subjects suffering from motor impairments in the interaction with the environment. To this aim, BCI systems must correctly decode and interpret neurophysiological signals reflecting the intention of the subjects to move. Therefore, the accurate classification of single events in motor tasks represents a fundamental challenge in ensuring efficient communication and control between users and BCIs. Movement-associated changes in electroencephalographic (EEG) sensorimotor rhythms, such as event-related desynchronization (ERD), are well-known features of discriminating motor tasks. Fractal dimension (FD) can be used to evaluate the complexity and self-similarity in brain signals, potentially providing complementary information to frequency-based signal features.
In the present work, we introduce FD as a novel feature for subject-independent event classification, and we test several machine learning (ML) models in behavioural tasks of motor imagery (MI) and motor execution (ME).
Our results show that FD improves the classification accuracy of ML compared to ERD. Furthermore, unilateral hand movements have higher classification accuracy than bilateral movements in both MI and ME tasks.
These results provide further insights into subject-independent event classification in BCI systems and demonstrate the potential of FD as a discriminative feature for EEG signals.
Heart rate complexity helps mortality prediction in the intensive care unit: A pilot study using artificial intelligence
2024, Computers in Biology and MedicineIn intensive care units (ICUs), accurate mortality prediction is crucial for effective patient management and resource allocation. The Simplified Acute Physiology Score II (SAPS-2), though commonly used, relies heavily on comprehensive clinical data and blood samples. This study sought to develop an artificial intelligence (AI) model utilizing key hemodynamic parameters to predict ICU mortality within the first 24 h and assess its performance relative to SAPS-2.
We conducted an analysis of select hemodynamic parameters and the structure of heart rate curves to identify potential predictors of ICU mortality. A machine-learning model was subsequently trained and validated on distinct patient cohorts. The AI algorithm’s performance was then compared to the SAPS-2, focusing on classification accuracy, calibration, and generalizability.
The study included 1298 ICU admissions from March 27th, 2015, to March 27th, 2017. An additional cohort from 2022 to 2023 comprised 590 patients, resulting in a total dataset of 1888 patients. The observed mortality rate stood at 24.0%. Key determinants of mortality were the Glasgow Coma Scale score, heart rate complexity, patient age, duration of diastolic blood pressure below 50 mmHg, heart rate variability, and specific mean and systolic blood pressure thresholds. The AI model, informed by these determinants, exhibited a performance profile in predicting mortality that was comparable, if not superior, to the SAPS-2.
The AI model, which integrates heart rate and blood pressure curve analyses with basic clinical parameters, provides a methodological approach to predict in-hospital mortality in ICU patients. This model offers an alternative to existing tools that depend on extensive clinical data and laboratory inputs. Its potential integration into ICU monitoring systems may facilitate more streamlined mortality prediction processes.
In-phase matrix profile: A novel method for the detection of major depressive disorder
2024, Biomedical Signal Processing and ControlMajor depressive disorder (MDD) is the leading cause of disability worldwide. Reliable detection of MDD is the basis for early and successful intervention in treating the disorder and preventing disability. We introduce a novel feature extraction method, the in-phase matrix profile (pMP), which is specifically adapted for electroencephalographic (EEG) signals. Methods: The pMP characterizes general self-similarity of an EEG signal. The method extracts overlapping one-second-long subsegments from an EEG signal segment, calculates Euclidean distances between all possible subsegment pairs, and subsequently uses the distance values, where subsegments are most in phase, to calculate pMP. The method was applied to the resting-state eyes-closed EEG data of an MDD group and age- and gender-matched healthy controls (66 subjects). Higuchi's fractal dimension (HFD) values were calculated for the same groups for comparison. Results: Both pMP and HFD values were higher in MDD. The pMP successfully distinguished MDD and control group in all 30 EEG channels. In contrast, HFD resulted in statistically significant group distinguishability in 13 (43%) channels located mainly in the central region of the head. The highest classification accuracy for pMP was 73% and for HFD 67%. Conclusion: The present article shows that pMP outperforms HFD in detecting MDD and is a promising method for future MDD studies. Significance: The pMP is a sensitive parameter-free method for detecting MDD that can be used in future studies and is a potential method to reach clinical use for diagnosing MDD.
Detection of long-range correlation causing multifractality in H time series of geomagnetic field over the Northern Hemisphere during quiet geomagnetic conditions
2024, Advances in Space ResearchThe generation of geomagnetic time series frequently involves intricate spatio-temporal dynamics, wherein nonlinearity and scaling emerge as pivotal mechanisms. The present work investigates the fractal properties of geomagnetic field, and its sources during quiet geomagnetic conditions, by analyzing the horizontal component data of 1 min resolution (H time series) from different latitude regions. Analysis using Auto Correlation Function (ACF), Power spectrum analysis (PSA), Rescaled range analysis (R/S) and Detrended Fluctuation Analysis (DFA) gave indications of the presence of long-range correlations, fractal properties and scaling behaviour of quiet period H time series data. The strong q dependence of generalized Hurst exponent h(q) and scaling exponent Ʈ(q), obtained from the Multifractal Detrended Fluctuation Analysis (MFDFA) method, confirmed the multifractal behaviour of quiet period H time series. The multifractal source analysis of the quiet period H time series with its shuffled and surrogate time series data revealed that, the multifractal characteristics are caused almost entirely by the long-range correlations between small and large fluctuations. The analysis of the latitudinal variations in the multifractal characteristics is also performed as a part of the work, by considering H time series belonging to various latitudes under almost same longitude. The observed decrease in the generalized Hurst exponent values with increase in latitude indicates the change in the multifractal characteristics of the time series with latitude. Also the work revealed that, the H time series from high latitude region shows anti-persistent behaviour, even when the H time series from observatories located at the low and mid latitude regions exhibiting persistent behaviour. The change in the persistence, anti-persistence behaviour can be related to the strength of Earth’s magnetic field.