Inspired by the well-known permutation entropy (PE), an effective image encoding scheme for chaotic time series, Triad State Space Construction (TSSC), is proposed. The TSSC image can recognize higher-order temporal patterns and identify new forbidden regions in time series motifs beyond the Bandt-Pompe probabilities. The Convolutional Neural Network (ConvNet) is widely used in image classification. The ConvNet classifier based on TSSC images (TSSC-ConvNet) are highly accurate and very robust in the chaotic signal classification.
University of Oxford（牛津大学）；United Kingdom Atomic Energy Authority（英国原子能管理局）
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some of the most challenging real-life applications is to train different neural networks on a data set from a dynamical system with a basic or low-dimensional phase space and then use these networks to classify univariate time series of a dynamical system with more intricate or high-dimensional phase space. We illustrate this generalisation approach using the log…
In the time-series analysis, the time series motifs and the order patterns in time series can reveal general temporal patterns and dynamic features. Triadic Motif Field (TMF) is a simple and effective time-series image encoding method based on triadic time series motifs. Electrocardiography (ECG) signals are time-series data widely used to diagnose various cardiac anomalies. The TMF images contain the features characterizing the normal and Atrial Fibrillation (AF) ECG signals. Considering the quasi-periodic characteristics of ECG signals, the dynamic features can be extracted from the TMF imag…
Center of Nanomaterials for Renewable Energy（纳米材料可再生能源中心）；State Key Laboratory of Electrical Insulation and Power Equipment（电力设备电气绝缘国家重点实验室）；School of Electrical Engineering（电气工程学院）；Xi’an Jiaotong University（西安交通大学）
Time series motifs play an important role in the time series analysis. The motif-based time series clustering is used for the discovery of higher-order patterns or structures in time series data. Inspired by the convolutional neural network (CNN) classifier based on the image representations of time series, motif difference field (MDF) is proposed. Compared to other image representations of time series, MDF is simple and easy to construct. With the Fully Convolution Network (FCN) as the classifier, MDF demonstrates the superior performance on the UCR time series dataset in benchmark with other…
School of Computing, Electronics and Mathematics, Coventry University UK（考文垂大学计算机、电子与数学系）
Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new traject…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis testing and investigates potential differences in discriminant statistics between the given empirical sample and its surrogate counterparts. The choice and estimation of the discriminant statistics can be challenging across short time series. Also, conclusion based on a single empirical sample is an inherent limitation. The present study proposes a recurrent neur…
Neural Network Entropy (NNetEn): Entropy-Based EEG Signal and Chaotic Time Series Classification, Python Package for NNetEn Calculation
Institute of Physics and Technology, Petrozavodsk State University（彼得罗扎沃茨克国立大学物理与技术学院）；Kuwait College of Science and Technology（科威特科学技术学院）；Vels Institute of Sciences, Technology, and Advanced Studies（维尔斯科学技术与高等研究院）；Damghan University（达姆甘大学）
National Institute of Advanced Studies（国家高等研究院）；PES University（PES大学）
Inspired by chaotic firing of neurons in the brain, we propose ChaosNet -- a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luroth Series (GLS) which has been shown in earlier works to possess very useful properties for compression, cryptography and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on ChaosNet that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning…
Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）；Jadavpur University（贾达普大学）；Calcutta Institute of Engineering and Management（加尔各答工程与管理学院）
This contribution reports an application of MultiFractal Detrended Fluctuation Analysis, MFDFA based novel feature extraction technique for automated detection of epilepsy. In fractal geometry, Multifractal Detrended Fluctuation Analysis MFDFA is a popular technique to examine the self-similarity of a nonlinear, chaotic and noisy time series. In the present research work, EEG signals representing healthy, interictal (seizure free) and ictal activities (seizure) are acquired from an existing available database. The acquired EEG signals of different states are at first analyzed using MFDFA. To r…
National Institute of Advanced Studies（国家先进研究所）；Indian Institute of Science Campus（印度科学研究所校区）；Consciousness Studies Programme（意识研究项目）；Indian Institute of Science（印度科学研究所）；Indian Institute of Science Campus, Bengaluru, India（印度科学研究所校区，班加罗尔，印度）
There has been empirical evidence of presence of non-linearity and chaos at the level of single neurons in biological neural networks. The properties of chaotic neurons inspires us to employ them in artificial learning systems. Here, we propose a Neurochaos Learning (NL) architecture, where the neurons used to extract features from data are 1D chaotic maps. ChaosFEX+SVM, an instance of this NL architecture, is proposed as a hybrid combination of chaos and classical machine learning algorithm. We formally prove that a single layer of NL with a finite number of 1D chaotic neurons satisfies the U…
A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps
Department of Computer Science and Information Systems (CSIS)（计算机科学与信息系统系）；Adjunct Faculty, Consciousness Studies Programme, National Institute of Advanced Studies, IISc Campus, Bengaluru, 560012, Karnataka, India（意识研究项目兼职教员，国家高级研究院，IISc校区，班加罗尔，560012，卡纳塔克邦，印度）
The University of Trans-Disciplinary Health Sciences And Technology（跨学科健康科学与技术大学）；National Institute of Advanced Studies（国家高级研究院）；Institute of Computer Science of the Czech Academy of Sciences（捷克科学院计算机科学研究所）
Discovering cause-effect from observational data is an important but challenging problem in science and engineering. In this work, a recently proposed brain inspired learning algorithm namely-\emph{Neurochaos Learning} (NL) is used for the classification of cause-effect from simulated data. The data instances used are generated from coupled AR processes, coupled 1D chaotic skew tent maps, coupled 1D chaotic logistic maps and a real-world prey-predator system. The proposed method consistently outperforms a five layer Deep Neural Network architecture for coupling coefficient values ranging from …
Hyperparameter-Free Neurochaos Learning Algorithm for Classification
Department of Mathematics（数学系）；Amrita Vishwa Vidyapeetham（阿米特大学）；Complex Systems Programme（复杂系统计划）；National Institute of Advanced Studies（国家高级研究机构）；Indian Institute of Science（印度科学学院）
Chaotic Map based Compression Approach to Classification
BITS Pilani K K Birla Goa Campus（BITS Pilani K K Birla 果阿校区）；National Institute of Advanced Studies（国家高级研究院）；Norwegian Institute of Science and Technology（挪威科学技术研究院）
Classification accuracy provided by a machine learning model depends a lot on the feature set used in the learning process. Feature Selection (FS) is an important and challenging pre-processing technique which helps to identify only the relevant features from a dataset thereby reducing the feature dimension as well as improving the classification accuracy at the same time. The binary version of Whale Optimization Algorithm (WOA) is a popular FS technique which is inspired from the foraging behavior of humpback whales. In this paper, an embedded version of WOA called Embedded Chaotic Whale Surv…
Making a simple model by choosing a limited number of features with the purpose of reducing the computational complexity of the algorithms involved in classification is one of the main issues in machine learning and data mining. The aim of Feature Selection (FS) is to reduce the number of redundant and irrelevant features and improve the accuracy of classification in a data set. We propose an efficient ISPSO-GLOBAL (Improved Seeding Particle Swarm Optimization GLOBAL) method which investigates the specified iterations to produce prominent features and store them in storage list. The goal is to…
The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the enormous practical success of AI, these algorithms are only loosely inspired from the biological brain and do not mimic any of the fundamental properties of neurons in the brain, one such property being the chaotic firing of biological neurons. This motivates us to develop a novel neuronal architecture where the individual neurons are intrinsically chaotic in natur…
Institute for Basic Science（基础科学研究所）；Korea University of Science and Technology（韩国科学技术大学）
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional Lyapunov exponent computation is far from converging. We show the robustness of the neural network to varying control parameters, in particular we train with one set of control parameters, and succes…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and bio…
Russian Quantum Center（俄罗斯量子中心）；University of New South Wales（新南威尔士大学）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算机科学联合中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；QuTech, Delft Technical University（代尔夫特理工大学量子技术研究所）；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）；National University of Science and Technology MISIS（国立科技大学米西斯）
Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and many-body systems. We realize neural network algorithms that perform a classification between regular and chaotic behavior in quantum billiard models with remarkably high accuracy. We use the variational autoencoder for autosupervised classification of regular/chaotic wave functions, as well as demonstrating that variational autoencoders could be used as a tool f…
University of Cambridge（剑桥大学）；Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）；TU Munich（慕尼黑工业大学）
An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their prediction and control. In this paper, we propose a data-driven methodology for the prediction and control of extreme events in a chaotic shear flow. The approach is based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent dataset. The objective is five-fold. First, we exploit ad-hoc metrics fro…
Time series are ubiquitous and therefore inherently hard to analyze and ultimately to label or cluster. With the rise of the Internet of Things (IoT) and its smart devices, data is collected in large amounts any given second. The collected data is rich in information, as one can detect accidents (e.g. cars) in real time, or assess injury/sickness over a given time span (e.g. health devices). Due to its chaotic nature and massive amounts of datapoints, timeseries are hard to label manually. Furthermore new classes within the data could emerge over time (contrary to e.g. handwritten digits), whi…
