False Neighbors Research Articles

Dynamical systems theory applied to short walking trials

Human walking is an extremely complex neuromuscular activity whose simplicity disappears when an attempt is made to provide a quantitative description of the process. The dynamical systems theory provides a framework for analyzing the stability and chaotic nature of dynamical systems, employing Floquet multipliers (FM) and long and short-term Lyapunov exponents (LE), respectively. This report compares FM and LE from three methods: method A (false nearest neighbors and numerical approximation), method B (false nearest neighbors and semi-analytical technique) and method C (singular value decomposition and semi-analytical technique). Data from 33 healthy older adults with no history of falls were used to explain the dynamic system. A surrogate center of mass trajectory was calculated for the analysis of sway in the transverse plane. Results revealed methodological differences in LE and FM calculations with semi-analytical solutions providing closer approximations to observed gait behavior. The long-term LE from Methods A and B were similar, but other LE pairings differed. Method A’s short-term LE indicated chaotic gaits for all subjects, while long-term LE from Methods A and B indicated chaos for half the subjects. Method C showed non-chaotic gait for most subjects. Method B’s FM indicated over 30% of subjects had unstable gait. Method C yielded values of LE and FM that most closely matched the subjects’ gait patterns. This study offers a methodological foundation for gait analysis using short time-series data, facilitating deeper insights into both stability and chaos within gait dynamics.

MNN: Mixed nearest-neighbors for self-supervised learning

In contrastive self-supervised learning, positive samples are typically drawn from the same image but in different augmented views, resulting in a limited source of positive samples. An effective way to alleviate this problem is to incorporate the relationship between samples, which involves including the top-K nearest neighbors of positive samples. However, the issue of false neighbors (i.e., neighbors that do not belong to the same category as the positive sample) is a significant yet often overlooked challenge. In this paper, we present a simple self-supervised learning framework called Mixed Nearest-Neighbors (MNN) for Self-Supervised Learning. The primary objective of the MNN is to enhance the robustness and accuracy of the model by strategically incorporating synthesized neighboring samples. Specifically, our proposed method utilizes image mixture to mitigate the effects of noise introduced by false neighbors, while adopting an intuitive weighting strategy that effectively integrates these synthesized neighbors into the model. The linear evaluation of MNN on CIFAR-10, CIFAR,100, STL-10, and Tiny ImageNet shows an improvement of 0.41% to 1.96% over the previous state-of-the-art (SOTA) methods and 1.82% to 8.8% over the Mean Shift (MSF) method. Furthermore, the proposed components can be seamlessly integrated into other self-supervised learning algorithms to enhance their performance. Code is available at https://github.com/pc-cp/MNN.

Revealing alterations in heart rate fluctuations during the progression of Chagas disease.

The heart rate variability (HRV) continually evolves throughout life, reflecting modifications in the architecture of the sinoatrial node (SAN) and in the regulation of heart rate by the autonomic nervous system (ANS). Both can be considerably affected by Chagas disease, causing important changes in the complex nature of HRV. We aim to evaluate the ability of an index based on the false nearest neighbors method (FN10) to reflect these changes during disease progression. We perform a retrospective, descriptive, and cross-sectional study analyzing HRV time series of participants with Chagas disease. We determine the dependence of FN10 on age and sex in a healthy population, and then evaluate FN10 in individuals with Chagas disease. In the healthy population, FN10 has a scaling behavior with age, which is independent of sex. In Chagas disease, some individuals show FN10 values significantly above those seen in the healthy population. We relate the findings to the pathophysiological mechanisms that determine the progression of the disease. The results indicate that FN10 may be a candidate prognostic biomarker for heart disease.

TPANet: A novel triple parallel attention network approach for remaining useful life prediction of lithium-ion batteries

Accurate remaining useful life (RUL) prediction for lithium-ion batteries (LIBs) is important for proper equipment operation. Among the numerous existing studies on battery research, data-driven approaches have gained significant attention because they obviate the need for complex chemical and physical modeling of battery processes. However, in most current data-driven methods, the sliding window size values are determined empirically, which affects both the time required for model prediction and the prediction accuracy. To address this issue, this paper proposes a two-stage prediction method for battery capacity aging trajectories. In the first stage, a false nearest neighbor (FNN) technique is utilized to infer the sliding window size of the battery, reducing the error associated with manually selecting the sliding window size. In the second stage, a novel triple parallel attention network (TPANet) based on convolutional neural networks (CNNs) and attention units is developed, which extracts the input battery capacity degradation features through a parallel mechanism. The introduction of attention units in each parallel branch allows the model to enhance the capture of capacity regeneration phenomena as well as long-term dependence on input data. The proposed approach is validated on two publicly available datasets as well as a battery developed by ourselves. Diverse simulation results demonstrate the ability of the proposed approach to accurately predict the RUL of LIBs in a short time with broad generalization capabilities.

Complexity of hydrometeorological variables: false nearest neighbour algorithm

ABSTRACT This study examines the complexity of hydrometeorological variables in the Savitri River basin in India. Specifically, the study estimates the dimensionality of daily rainfall, runoff, maximum temperature, minimum temperature, pan evaporation, relative humidity, sunshine duration, and wind speed observed during 2000–2010 at two stations (Kangule and Birwadi). The false nearest neighbour (FNN) algorithm is employed to estimate the dimensionality of each variable. The dimensionality represents the number of variables dominantly governing the system. The FNN dimension values of the eight daily hydrometeorological time series from each station range between 4 and 7, which may be considered as exhibiting a medium level of complexity. Among the eight series, wind speed is found to be the least complex, whereas minimum temperature and sunshine duration are the most complex. An attempt is also made to examine the effect of temporal scale on the complexity of the hydrometeorological variables, by analysing the hourly rainfall and runoff series from the two stations. The results indicate that, for both rainfall and runoff, hourly data (finer scale) exhibits greater complexity, with two to three additional influential variables. The present results have important implications for hydrometeorological modelling, prediction, and disaster management in the small and flood-prone Savitri River basin.

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network, we propose a convolutional neural network (CNN)-long short-term memory (LSTM) prediction model based on the incremental attention mechanism. Firstly, a traversal search is conducted through the traversal layer for finite parameters in the phase space. Then, an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria (DWC). The phase space parameters that best meet DWC are selected and fed into the input layer. Finally, the constructed CNN-LSTM network extracts spatiotemporal features and provides the final prediction results. The model is verified using Logistic, Lorenz, and sunspot chaotic time series, and the performance is compared from the two dimensions of prediction accuracy and network phase space structure. Additionally, the CNN-LSTM network based on incremental attention is compared with LSTM, CNN, recurrent neural network (RNN), and support vector regression (SVR) for prediction accuracy. The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy. Also, the algorithm to estimate the phase space parameter is compared with the traditional CAO, false nearest neighbor, and C–C, three typical methods for determining the chaotic phase space parameters. The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks, including CNN-LSTM, LSTM, CNN, RNN, and SVR.

DOWN: Dynamic Order Weighted Network for Fine-grained Category Discovery

Discovering fine-grained categories from coarsely-labeled data is a practical and challenging task, which can adapt models to fine-grained sub-categories and reduce significant annotation costs. In the absence of fine-grained labels, previous works have encountered challenges in modeling fine-grained semantic correlation within data effectively and efficiently. In response to this challenge, we propose DOWN: Dynamic Order Weighted Network, which systematically explores and exploits semantic structures within data and reduces the effect of noisy samples. Specifically, a multi-task pre-training paradigm is initially employed to acquire both general and coarse-grained knowledge. Subsequently, we retrieve a candidate neighbor set for a given query and then sort the retrieved neighbors based on semantic similarity to capture relative orders between data, which enhances model capability to distinguish false-positive neighbors. To optimize the utilization of semantic structures of data and mitigate the impact of false neighbors, we introduce a weighting mechanism with exponential decay functions for the sorted neighbors based on order distances. Considering the incremental growth of the model’s capability during training, we dynamically adjust the base of the exponential decay function, which progressively augments the weights for tail samples, thus achieving equilibrium between exploitation of neighborhood information and avoidance of neighborhood noise. Moreover, we theoretically justify the effectiveness of our model from three perspectives. Extensive experiments on three benchmark datasets validate both effectiveness and efficiency of our model over SOTA models. Our code and data are available at https://github.com/Lackel/DOWN.

Generalized synchronization in a tritrophic food web metacommunity

Complete synchronization among the metacommunity is known to elevate the risk of their extinction due to stochasticity and other environmental perturbations. Owing to the inherent heterogeneous nature of the metacommunity, we demonstrate the emergence of generalized synchronization among the patches of dispersally connected tritrophic food web using the framework of an auxiliary system approach and the mutual false nearest neighbor. We find that the critical value of the dispersal rate increases significantly with the size of the metacommunity for both unidirectional and bidirectional dispersals, which in turn corroborates that larger metacommunities are more stable than smaller ones. Further, we find that the critical value of the dispersal for the onset of generalized synchronization is smaller(larger) for bidirectional dispersal than that for unidirectional dispersal for smaller(larger) metacommunities. Most importantly, complete synchronization error remains finite even after the onset of generalized synchronization in a wider range of dispersal rate elucidating that the latter can serve as an early warning signal for the extinction of the metacommunity.

Chaotic dynamics of diatomic systems in an electromagnetic field: Dynamical and topological invariants

An advanced combined quantum-dynamic and chaos-geometric method for analysis, modelling, and forecasting of the chaotic dynamics of diatomic molecules in an intense electromagnetic field is presented. The method is based on the use of the non-stationary theory of the Schrödinger equation in the approximation of the density functional and the methods of the theory of chaos and dynamic systems for the analysis of time series of polarization and other characteristics of diatomic molecules in an intense electromagnetic field. In particular, the latter includes the Gottwald-Melbourne test, the correlation integral method , fractal and multifractal formalism, average mutual information, false nearest neighbours, surrogate data algorithms, analysis on the basis of the Lyapunov's exponents, Kolmogorov entropy, nonlinear forecast models based on algorithms of optimized predicted trajectories, B-spline approximations. As an illustration, the advanced data for the dynamical and topological invariants (correlation dimension, embedding dimension, Kaplan-York dimension, Lyapunov's exponents, Kolmogorov entropy, etc.) for the diatomic ZrO molecule in a linearly polarized electromagnetic field are listed.

A novel resonance attractor evaluation method for traveling wave vibration of thin-walled gears: Modeling and experiments

Thin-walled gears have high power density and are the main gear type in aeronautical applications, but threatened by the traveling wave vibration (TWV). In this paper, a novel resonance attractor evaluation (RAE) method is proposed to describe this dynamics characteristic for the complex thin-walled gear drivetrain. The unsteady responses of the drivetrain are discretized into different time-series subsets, and each subset is reconstructed into a high-dimensional mapping phase space based on the average mutual information and the false nearest neighbor theory. Finally, the TWV is identified from the evolution of attractor features—which are quantified by indicators: the boundary radius and the phase point expansion rate. To verify the proposed method, a high-speed transmission experiment involving thin-walled bevel gears is designed, and the RAE model is established based on the proposed methodology and compared with the experimental results. Results show that this model accurately identifies resonance frequencies and describes rotation speed bands that excite the TWV. The proposed methodology provides a theoretical basis for introducing the phase space reconstruction method into the TWV study and for the safe operation of aero-engine gears.

Effective precursors for self-organization of complex systems into a critical state based on dynamic series data

Many different precursors are known, but not all of which are effective, i.e., giving enough time to take preventive measures and with a minimum number of false early warning signals. The study aims to select and study effective early warning measures from a set of measures directly related to critical slowing down as well as to the change in the structure of the reconstructed phase space in the neighborhood of the critical transition point of sand cellular automata. We obtained a dynamical series of the number of unstable nodes in automata with stochastic and deterministic vertex collapse rules, with different topological graph structure and probabilistic distribution law for pumping of automata. For these dynamical series we computed windowed early warning measures. We formulated the notion of an effective measure as the measure that has the smallest number of false signals and the longest early warning time among the set of early warning measures. We found that regardless of the rules, topological structure of graphs, and probabilistic distribution law for pumping of automata, the effective early warning measures are the embedding dimension, correlation dimension, and approximation entropy estimated using the false nearest neighbors algorithm. The variance has the smallest early warning time, and the largest Lyapunov exponent has the greatest number of false early warning signals. Autocorrelation at lag-1 and Welch’s estimate for the scaling exponent of power spectral density cannot be used as early warning measures for critical transitions in the automata. The efficiency definition we introduced can be used to search for and investigate new early warning measures. Embedding dimension, correlation dimension and approximation entropy can be used as effective real-time early warning measures for critical transitions in real-world systems isomorphic to sand cellular automata such as microblogging social network and stock exchange.

A chaotic investigation on pollutant parameters of a wastewater treatment facility using false nearest neighbour algorithm

A chaotic investigation on pollutant parameters of a wastewater treatment facility using false nearest neighbour algorithm

Nonlinear modeling of sparkling drink bubbles using a physics informed long short term memory network

Bubble dynamics exist in many physical phenomena from the interaction between atmosphere and ocean, to food science of champagne bubbles. Bubble sound has recently been found to be a new way to understand bubbles and bubble dynamics. In this paper, we collect bubble sounds of different types of sparkling drinks, namely, sparkling water, beer, and champagne, and use the experimental data to construct a data driven model for sparkling bubbles. We apply dynamical reconstruction theory to the measured data and use false nearest neighbor, correlation dimension, and largest Lyapunov exponent to verify that the sparkling drink bubble dynamic is nonlinear and chaotic. Based on the derived physical principle on bubble pressure, we propose a novel physics informed long short term memory (PI-LSTM) neural network as a time series predictor to form a data driven with physics guidance model for bubble dynamics. It is shown here that the proposed PI-LSTM is effective in modeling the bubble sound data with improved accuracy compared to standard predictors including LSTM, multi-layer neural network and decision tree. The predictive analysis supports the nonlinear behavior of the bubble sound signals and demonstrates results consistent with the chaotic analysis.

Semantic and sentiment trajectories of literary masterpieces

The paper deals with semantic and sentiment trajectories of literary masterpieces (we used corpora of 12 languages of various language families), composed of individual embeddings or n-grams. We ascertain that, for all languages, semantic and sentiment trajectories are markedly chaotic: positive largest Lyapunov exponents; ‘entropy-complexity’ pairs belonging to the ‘chaotic’ area of the respective plane; the distinctive ‘chaotic’ drop of the number of false nearest neighbours at a particular value of an embedding dimension. The Russian language turns out to be more ‘chaotic’ than, for example, the English one; we attribute this fact to the free order of words. The Esperanto language, for various ‘approaches’ to different Indo-European languages. The results do not corroborate its claim to be equidistant from all languages. However, it seems to be equidistant from all Indo-European languages. These characteristics are utilised in order to develop a method to compare styles of an original masterpiece and its translations (to automatically assess translation quality). It appears that machine translations are still worse than human ones, however, for example, the Facebook translation is comparable with them.

A new fault diagnosis of rolling bearing based on phase-space reconstruction and convolutional neural network

PurposeTo solve the problem that the traditional methods miss key information in the process of bearing fault identification, this paper aims to apply the phase-space reconstruction (PSR) theory and intelligent diagnosis techniques to extend the one-dimensional vibration signal to the high-dimensional phase space to reveal the system information implied in the univariate time series of the vibration signal.Design/methodology/approachIn this paper, a new method based on the PSR technique and convolutional neural network (CNN) is proposed. First, the delay time and the embedding dimension are determined by the C-C method and the false nearest neighbors method, respectively. Through the coordinate delay reconstruction method, the two-dimensional signal is constructed, and this information is saved in a set of gray images. Then, a simple and efficient convolutional network is proposed. Finally, the phase diagrams of different states are used as samples and input into a two-dimensional CNN for learning modeling to construct a PSR-CNN fault diagnosis model.FindingsThe proposed PSR-CNN model is tested on two data sets and compared with support vector machine (SVM), k-nearest neighbor (KNN) and Markov transition field methods, and the comparison results showed that the method proposed in this paper has higher accuracy and better generalization performance.Originality/valueThe method proposed in this paper provides a reliable solution in the field of rolling bearing fault diagnosis.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2023-0113/

Testing the complexity and chaotic nature of wave-dominated turbulent flows

This study employs chaos theory concepts to investigate the complexity and chaotic nature of surface-generated waves in comparison to steady-flow state. The flows are generated through laboratory-flume experiments. Two separate tests are carried out: steady-flow test; and test with the addition of waves to the steady-flow under identical flow conditions. For wave addition, two-different frequencies of wave (i.e., 1.1 Hz and 2.1 Hz) are considered. Two chaos theory-based approaches are employed to determine the complexity and chaotic nature of wave-current dynamics: False nearest neighbour (FNN) method; and Lyapunov exponent method. An effort is also made to confirm and understand the results from these chaos-theory methods with the results from the wavelet and Shannon entropy methods. The results from the chaos-theory methods suggest optimistic evidence of the presence of chaotic behaviour in the combined wave-current cases. The results show that greater complexity is found at the near-bed region with aperiodic nature of the eddy scales and the complexity becomes less when moving towards the near-surface region. These results are well supported by the tests with wavelet and Shannon entropy methods. The results further reveal that the complexity for the steady-flow case is high and the complexity decreases with the addition of waves.

NARX-Elman Based Mach Number Prediction and Model Migration of Wind Tunnel Conditions

Mach number, as an important index to judge the system performance in wind tunnel tests, its stability determines the quality of the flow field of this wind tunnel and needs to be controlled precisely. Due to the complex process in the wind tunnel test, it is difficult to ensure the smooth operation of the Mach number by the traditional control strategy, therefore, a Mach number prediction model based on a nonlinear autoregressive exogenous model (NARX)-Elman is proposed in this paper. Firstly, the NARX model is adopted as the basic framework of this model, the false nearest neighbor (FNN) is used for model order solving, and the Elman network is used for dynamic nonlinear fitting of the model. Secondly, considering the wind tunnel system with multiple conditions and the high cost of conducting complete data experiments, a new model migration method, the input-output slope/bias correction-genetic algorithm (IOSBC-GA), is proposed, which uses IOSBC method as the basic framework to construct the migration model based on the historical condition model and a small amount of data of the new condition, and uses GA to find the slope of deviation in the new model and correct the input-output relationship between the old and new conditions, so as to establish the model for the new condition. By comparing the model respectively with the traditional algorithm and the model built without migration, the root mean square error (RMSE) and the maximum deviation (MD) of this model are less than 0.001, indicating that the model has high prediction accuracy.

Using scaling-region distributions to select embedding parameters

Reconstructing state-space dynamics from scalar data using time-delay embedding requires choosing values for the delay τ and the dimension m. Both parameters are critical to the success of the procedure and neither is easy to formally validate. While embedding theorems do offer formal guidance for these choices, in practice one has to resort to heuristics, such as the average mutual information (AMI) method of Fraser & Swinney for τ or the false near neighbor (FNN) method of Kennel et al. for m. Best practice suggests an iterative approach: one of these heuristics is used to make a good first guess for the corresponding free parameter and then an “asymptotic invariant” approach is then used to firm up its value by, e.g., computing the correlation dimension or Lyapunov exponent for a range of values and looking for convergence. This process can be subjective, as these computations often involve finding, and fitting a line to, a scaling region in a plot: a process that is generally done by eye and is not immune to confirmation bias. Moreover, most of these heuristics do not provide confidence intervals, making it difficult to say what “convergence” is. Here, we propose an approach that automates the first step, removing the subjectivity, and formalizes the second, offering a statistical test for convergence. Our approach rests upon a recently developed method for automated scaling-region selection that includes confidence intervals on the results. We demonstrate this methodology by selecting values for the embedding dimension for several real and simulated dynamical systems. We compare these results to those produced by FNN and validate them against known results—e.g., of the correlation dimension—where these are available. We note that this method extends to any free parameter in the theory or practice of delay reconstruction.

How complex is COVID-19: Spatiotemporal variation of chaotic nature of the virus in Indian states.

Like other pandemics, COVID-19 also created a huge socioeconomic imbalance and distress in people. Often, every pandemic is characterized as chaotic and complex. Hence, the nature of the virus spread and deaths should be analyzed to prepare for the next similar pandemic. In this analysis, the popular and well-known time series in chaos theory is implemented, and the results are deduced for the states of India. The phase space reconstruction algorithm is implemented, and false nearest neighbor (FNN) method is applied to determine the dimensionality, and also Lyapunov exponent of the time series is estimated. The chaotic nature of COVID-19 cases showed a less severe and low complexity, with the FNN dimension range of 3-5, whereas the COVID-19 deaths showed moderate complexity with FNN dimensions 2-7. Policymakers should take action on medical availability in rural states and control people's movement in highly populated areas.

Nonlinear Model Order Selection: A GMM Clustering Approach Based on a Genetic Version of EM Algorithm

Choosing an accurate model order is one of the important sections in system identification. Traditionally, the model order selection of a nonlinear system depends on a predetermined model. However, it requires excess calculation and is impossible to get rid of the trouble of the structural design of the model, once the specific model was determined. A false nearest neighbor (FNN) algorithm that only relies on input-output data to estimate the model order is proposed here. Due to the FNN algorithm is sensitive to its own threshold which is a crucial constant for evaluating the model structure, Gaussian mixture model (GMM) clustering based on a genetic version of the expectation-maximization (EM) algorithm and minimum description length (MDL) criterion is developed in this paper, where the order can be determined without relying on a specific model. The GMM clustering is proposed to calculate the threshold of the FNN. Then, the genetic algorithm and MDL criteria are embedded to optimize the calculation of the EM algorithm as reduce the influence of initial values and not prone to fall into local extreme values as well. Three examples are given here to indicate the superiority of this technique: simulation of a strongly nonlinear system, isothermal polymerization process, and Van der Vusse reaction in relevant reference. Finally, some typical modeling methods are conducted to confirm the validity of this approach.