scholarly journals ­­­Control and Anti-control of Chaos Based on the Moving Largest Lyapunov Exponent Using Reinforcement Learning

2021 ◽  
Author(s):  
Yanyan Han ◽  
Jianpeng Ding ◽  
Lin Du ◽  
Youming Lei
Keyword(s):  
Reinforcement Learning ◽  
Lyapunov Exponent ◽  
Clustering Algorithm ◽  
Moving Average ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Control Of Chaos ◽  
Linear Region ◽  
Data Set ◽  
Density Peaks

Abstract In this work, we propose a method of control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning. In this method, we design a reward function for the reinforcement learning according to the moving largest Lyapunov exponent, which is similar to the moving average but computes the corresponding largest Lyapunov exponent using a recently updated time series with a fixed, short length. We adopt the density peaks-based clustering algorithm to determine a linear region of the average divergence index so that we can obtain the largest Lyapunov exponent of the small data set by fitting the slope of the linear region. We show that the proposed method is fast and easy to implement through controlling and anti-controlling typical systems such as the Henon map and Lorenz system.

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

scholarly journals Clusterdv, a simple density-based clustering method that is robust, general and automatic

2017 ◽  
Author(s):  
João C. Marques ◽  
Michael B. Orger
Keyword(s):  
Clustering Algorithm ◽  
Underlying Structure ◽  
Data Sets ◽  
Natural Phenomena ◽  
Cluster Number ◽  
Data Set ◽  
Density Peaks ◽  
Wide Range ◽  
Cluster Shape ◽  
Fully Automatic

AbstractHow to partition a data set into a set of distinct clusters is a ubiquitous and challenging problem. The fact that data varies widely in features such as cluster shape, cluster number, density distribution, background noise, outliers and degree of overlap, makes it difficult to find a single algorithm that can be broadly applied. One recent method, clusterdp, based on search of density peaks, can be applied successfully to cluster many kinds of data, but it is not fully automatic, and fails on some simple data distributions. We propose an alternative approach, clusterdv, which estimates density dips between points, and allows robust determination of cluster number and distribution across a wide range of data, without any manual parameter adjustment. We show that this method is able to solve a range of synthetic and experimental data sets, where the underlying structure is known, and identifies consistent and meaningful clusters in new behavioral data.Author summarIt is common that natural phenomena produce groupings, or clusters, in data, that can reveal the underlying processes. However, the form of these clusters can vary arbitrarily, making it challenging to find a single algorithm that identifies their structure correctly, without prior knowledge of the number of groupings or their distribution. We describe a simple clustering algorithm that is fully automatic and is able to correctly identify the number and shape of groupings in data of many types. We expect this algorithm to be useful in finding unknown natural phenomena present in data from a wide range of scientific fields.

scholarly journals Density Peaks Clustering Based on Feature Reduction and Quasi-Monte Carlo

2022 ◽  
Vol 2022 ◽  
pp. 1-17
Author(s):  
Zhihui Hu ◽  
Xiaoran Wei ◽  
Xiaoxu Han ◽  
Guang Kou ◽  
Haoyu Zhang ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
High Dimensional Data ◽  
Original Data ◽  
Feature Reduction ◽  
High Dimensional ◽  
Data Sampling ◽  
Data Set ◽  
Quasi Monte Carlo ◽  
Density Peaks ◽  
Density Peaks Clustering

Density peaks clustering (DPC) is a well-known density-based clustering algorithm that can deal with nonspherical clusters well. However, DPC has high computational complexity and space complexity in calculating local density ρ and distance δ , which makes it suitable only for small-scale data sets. In addition, for clustering high-dimensional data, the performance of DPC still needs to be improved. High-dimensional data not only make the data distribution more complex but also lead to more computational overheads. To address the above issues, we propose an improved density peaks clustering algorithm, which combines feature reduction and data sampling strategy. Specifically, features of the high-dimensional data are automatically extracted by principal component analysis (PCA), auto-encoder (AE), and t-distributed stochastic neighbor embedding (t-SNE). Next, in order to reduce the computational overhead, we propose a novel data sampling method for the low-dimensional feature data. Firstly, the data distribution in the low-dimensional feature space is estimated by the Quasi-Monte Carlo (QMC) sequence with low-discrepancy characteristics. Then, the representative QMC points are selected according to their cell densities. Next, the selected QMC points are used to calculate ρ and δ instead of the original data points. In general, the number of the selected QMC points is much smaller than that of the initial data set. Finally, a two-stage classification strategy based on the QMC points clustering results is proposed to classify the original data set. Compared with current works, our proposed algorithm can reduce the computational complexity from O n 2 to O N n , where N denotes the number of selected QMC points and n is the size of original data set, typically N ≪ n . Experimental results demonstrate that the proposed algorithm can effectively reduce the computational overhead and improve the model performance.

scholarly journals TOWARDS AUTOMATIC EPILEPTIC SEIZURE DETECTION IN EEGS BASED ON NEURAL NETWORKS AND LARGEST LYAPUNOV EXPONENT

2014 ◽  
pp. 36-47
Author(s):  
Vladimir Golovko ◽  
Svetlana Artsiomenka ◽  
Volha Kisten ◽  
Victor Evstigneev
Keyword(s):  
Neural Networks ◽  
Lyapunov Exponent ◽  
Epileptic Seizure ◽  
Seizure Detection ◽  
Epileptic Activity ◽  
Largest Lyapunov Exponent ◽  
Eeg Signals ◽  
Paroxysmal Activity ◽  
Data Set ◽  
Epileptic Seizure Detection

Over the past few decades, application of neural networks and chaos theory to electroencephalogram (EEG) analysis has grown rapidly due to the complex and nonlinear nature of EEG data. We report a novel method for epileptic seizure detection that is depending on the maximal short-term Lyapunov exponent (STLmax). The proposed approach is based on the automatic segmentation of the EEG into time segments that correspond to epileptic and non-epileptic activity. The STL-max is then computed from both categories of EEG signal and used for classification of epileptic and non-epileptic EEG segments throughout the recording. Neural network techniques are proposed both for segmentation of EEG signals and computation of STLmax. The data set from hospital have been used for experiments performing. It consists of 21 records during 8 seconds of eight adult patients. Furthermore the publicly available data were used for experiments. The main advantages of presented neural technique is its ability to detect rapidly the small EEG time segments as the epileptic or non-epileptic activity, training without desired data set about epileptic and non-epileptic activity in EEG signals. The proposed approach permits to detect exactly the epileptic and non-epileptic EEG segments of different duration and shape in order to identify a pathological activity in a remission state as well as detect a paroxysmal activity in a preictal period.

Multivariate Time Series Prediction Based on a Simple RBF Network

2012 ◽  
Vol 566 ◽  
pp. 97-102
Author(s):  
Jian Hui Xi ◽  
Hai Dan Wang ◽  
Li Ying Jiang
Keyword(s):  
Time Series ◽  
Clustering Algorithm ◽  
Time Series Prediction ◽  
Multivariate Time Series ◽  
Nonlinear Function ◽  
Small Data ◽  
Data Set ◽  
Rbf Network ◽  
Training Samples ◽  
Local Search Procedure

Improvement on defining hidden layer’s clustering centers of RBF network is greatly important for the network modeling and prediction, especially for multivariate time series. This paper firstly uses a linear function and a nonlinear function respectively to detect the linear correlations and the nonlinear correlations of the time series. And a small data set which includes effective information of the system is defined. Then, a local search procedure is introduced to optimize K-means clustering algorithm, which is aimed at quickly and effectively adjusting hidden layer’s clustering centers. Finally, input other training samples to determine network weights, LS or its improved method can be selected. Simulation results show that compared with that of conventional RBF network, with the same number of hidden layer’s nodes, the RBF network model in this paper gets better prediction accuracy.

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