Nonlinear Time Series Prediction Using Chaotic Neural Networks

A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network,the network becomes a chaotic one.For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting,we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation.By selecting the suitable feedback term,the system can escape from the local minima and converge to the global minimum or its approximate solutions,and the forecasting results are better than those of backpropagation algorithm.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is thatit can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. Atime-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the timeevolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate thelocal dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is testedfor the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this predictiontechnique can improve the prediction of chaotic time series.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.     

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of chaotic time series. The effectiveness of the method is demonstrated by applying it to the Hénon map. This study also compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.     

具有增加删除机制的正则化极端学习机的混沌时间序列预测

针对正则化极端学习机的隐层具有随机选择的特性,提出了一种增加删除机制来自适应地确定正则化极端学习机的隐层节点数. 这种机制以对优化目标函数影响的大小作为评价隐层节点优劣的标准,从而淘汰那些比较“差”的节点,将那些比较“优”的节点保留下来,起到一个优化正则化极端学习机隐层节点数的目的. 与已有的只具有增加隐层节点数的机制相比较,本文提出的增加删除机制在减少正则化极端学习机隐层节点数、增强其泛化性能、提高其实时性等方面具有一定的优势. 典型混沌时间序列的实例证明了具有增加删除机制的正则化极端学习机的有效性和可行性. 关键词： 混沌时间序列 人工神经网络 极端学习机     

A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.     

Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network

This paper proposes a co-evolutionary recurrent neural network （CERNN） for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by coevolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets： the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series.     

Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.     

Chaotic Dynamics in Weight Space of Neural Networks

When a special nonlinear self-feedback term is introduced into the dynamical equation of the backpropagation training algorithm for networks, the dynamics in weight space of networks can become chaotic. Chaotic dynamics of the system can help it escape from the most commonplace local minima of the energy. Simulation on the XOR problem and the prediction of chaotic time series have shown that the proposed chaotic training algorithm can converge to the global minimum or its approximate solutions efficiently and dramatically faster than the original backpropagation training algorithm.     

A Multi-Method Survey on the Use of Sentiment Analysis in Multivariate Financial Time Series Forecasting

In practice, time series forecasting involves the creation of models that generalize data from past values and produce future predictions. Moreover, regarding financial time series forecasting, it can be assumed that the procedure involves phenomena partly shaped by the social environment. Thus, the present work is concerned with the study of the use of sentiment analysis methods in data extracted from social networks and their utilization in multivariate prediction architectures that involve financial data. Through an extensive experimental process, 22 different input setups using such extracted information were tested, over a total of 16 different datasets, under the schemes of 27 different algorithms. The comparisons were structured under two case studies. The first concerns possible improvements in the performance of the forecasts in light of the use of sentiment analysis systems in time series forecasting. The second, having as a framework all the possible versions of the above configuration, concerns the selection of the methods that perform best. The results, as presented by various illustrations, indicate, on the one hand, the conditional improvement of predictability after the use of specific sentiment setups in long-term forecasts and, on the other, a universal predominance of long short-term memory architectures.     

基于一种新型聚类算法的RBF神经网络混沌时间序列预测

运用两阶段学习方法构建径向基函数(RBF)神经网络模型预测混沌时间序列.在利用非监督学习算法确定网络隐层中心时,提出了一种基于高斯基的距离度量,并联合输入输出聚类的策略.基于Fisher可分离率设计高斯基距离度量中的惩罚因子,可以提高聚类的性能.而输入输出聚类策略的引入,建立了聚类性能与网络预测性能之间的联系.因此,根据本文方法构建的网络模型,一方面可以加快网络训练的速度,另一方面可以提高预测性能.将该方法对Mackey-Glass, Lorenz和Logistic混沌时间序列进行了预测仿真研究,仿真结果表明了该方法的有效性. 关键词： 混沌时间序列 预测 径向基神经网络 聚类     

A Fusion Transformer for Multivariable Time Series Forecasting: The Mooney Viscosity Prediction Case

Multivariable time series forecasting is an important topic of machine learning, and it frequently involves a complex mix of inputs, including static covariates and exogenous time series input. A targeted investigation of this input data is critical for improving prediction performance. In this paper, we propose the fusion transformer (FusFormer), a transformer-based model for forecasting time series data, whose framework fuses various computation modules for time series input and static covariates. To be more precise, the model calculation consists of two parallel stages. First, it employs a temporal encoder–decoder framework for extracting dynamic temporal features from time series data input, which analyzes and integrates the relative position information of sequence elements into the attention mechanism. Simultaneously, the static covariates are fed to the static enrichment module, which is inspired by gated linear units, to suppress irrelevant information and control the extent of nonlinear processing. Finally, the prediction results are calculated by fusing the outputs of the above two stages. Using Mooney viscosity forecasting as a case study, we demonstrate considerable forecasting performance improvements over existing methodologies and verify the effectiveness of each component of FusFormer via ablation analysis, and an interpretability use case is conducted to visualize temporal patterns of time series. The experimental results prove that FusFormer can achieve accurate Mooney viscosity prediction and improve the efficiency of the tire production process.     

基于在线最小二乘支持向量机回归的混沌时间序列预测

提出了一种基于在线最小二乘支持向量机（LS-SVM）回归的混沌时间序列的预测方法.与离线支持向量机相比，在线最小二乘支持向量机预测方法即使当混沌系统的参数随时间变化时仍然有效.以Chen's混沌系统、Rssler混沌系统、Hénon映射及脑电(EEG)信号四种混沌时 间序列为例评估本文提出的预测方法，结果验证了其混沌时间序列预测的有效性. 关键词： 混沌时间序列 预测 在线学习 支持向量机     

Prediction of Time Series Gene Expression and Structural Analysis of Gene Regulatory Networks Using Recurrent Neural Networks

Methods for time series prediction and classification of gene regulatory networks (GRNs) from gene expression data have been treated separately so far. The recent emergence of attention-based recurrent neural network (RNN) models boosted the interpretability of RNN parameters, making them appealing for the understanding of gene interactions. In this work, we generated synthetic time series gene expression data from a range of archetypal GRNs and we relied on a dual attention RNN to predict the gene temporal dynamics. We show that the prediction is extremely accurate for GRNs with different architectures. Next, we focused on the attention mechanism of the RNN and, using tools from graph theory, we found that its graph properties allow one to hierarchically distinguish different architectures of the GRN. We show that the GRN responded differently to the addition of noise in the prediction by the RNN and we related the noise response to the analysis of the attention mechanism. In conclusion, this work provides a way to understand and exploit the attention mechanism of RNNs and it paves the way to RNN-based methods for time series prediction and inference of GRNs from gene expression data.     

基于模糊边界模块化神经网络的混沌时间序列预测

提出一种模糊边界模块化神经网络（FBMNN）的混沌时间序列预测方法,该方法先对混沌时间序列观测点重构的相空间进行模块化划分,划分点的选取由遗传算法自动寻优.然后定义一个模糊隶属度函数,在划分边界一侧按照一定的模糊隶属度设定模糊边界带,通过模糊化处理,解决了各模块划分点附近预测结果的跳跃问题.最后每一模块,及其模糊边界的样本点都对应一个递归神经网络进行训练,通过预测合成模块输出结果.该方法对三个混沌时间序列基准数据集Mackey-Glass,Lorenz,Henon进行实验,结果表明该方法有效地提高了混沌时间序列预测效果. 关键词： 模糊边界 模块化神经网络 混沌时间序列 预测     

Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks

In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear timeseries, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-meansclustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from thelocal minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glassequation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting resultsare obtained.     

具有选择与遗忘机制的极端学习机在时间序列预测中的应用

针对训练样本贯序输入时的极端学习机 (ELM)训练问题,提出一种具有选择与遗忘机制的极端学习机 (SF-ELM),并研究了其在混沌时间序列预测中的应用. SF-ELM以逐次增加新训练样本的方式实现在线训练,通过引入遗忘因子以减弱旧训练样本的影响,同时以泛化能力为判断依据,对其输出权值进行选择性递推更新. 混沌时间序列在线预测实例表明,SF-ELM是一种有效的ELM在线训练模式. 相比于在线贯序极端学习机,SF-ELM具有更快的在线训练速度和更高的在线预测精度,因此更适于混沌时间序列在线预测. 关键词： 混沌时间序列 时间序列预测 神经网络 极端学习机     

基于Cholesky分解的增量式RELM及其在时间序列预测中的应用

针对应用于混沌时间序列预测的正则极端学习机(RELM)网络结构设计问题,提出一种基于Cholesky分解的增量式RELM训练算法.该算法通过逐次增加隐层神经元的方式自动确定最佳的RELM网络结构,并以Cholesky分解方式计算其输出权值,有效减小了隐层神经元递增过程的计算代价.混沌时间序列预测实例表明,该算法可有效实现最佳RELM网络结构的自动确定,且计算效率高.利用该算法训练后的RELM预测模型具有预测精度高的优点,适用于混沌时间序列预测. 关键词： 神经网络 极端学习机 混沌时间序列 时间序列预测     

Chaotic time series prediction using least squares support vector machines

We propose a new technique of using the least squares support vector machines (LS-SVMs) for making one-step and multi-step prediction of chaotic time series. The LS-SVM achieves higher generalization performance than traditional neural networks and provides an accurate chaotic time series prediction. Unlike neural networks‘ training that requires nonlinear optimization with the danger of getting stuck into local minima, training LS-SVM is equivalent to solving a set of linear equations. Thus it has fast convergence. The simulation results show that LS-SVM has much better potential in the field of chaotic time series prediction.