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.     

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.     

A granular time series approach to long-term forecasting and trend forecasting

To overcome the “curse of dimensionality” (which plagues most predictors (predictive models) when carrying out long-term forecasts) and cope with uncertainty present in many time series, in this study, we introduce a concept of granular time series which are used to long-term forecasting and trend forecasting. A technique of fuzzy clustering is used to construct information granules on a basis of available numeric data present in the original time series. In the sequel, we develop a forecasting model which captures the essential relationships between such information granules and in this manner constructs a fundamental forecasting mechanism. It is demonstrated that the proposed model comes with a number of advantages which manifest when processing a large number of data. Experimental evidence is provided through a series of examples using which we quantify the performance of the forecasting model and provide with some comparative analysis.     

Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.     

虚拟环境下大数据智能并行聚类方法研究

为了减少虚拟环境下大数据运行时间,数据运行时能够反映出一定的规律性和特殊的分类性,需要对虚拟环境下大数据进行智能并行聚类。当前大数据聚类方法是根据K-均值聚类方法不断地进行大数据样本分类的调整,经过多次计算调整后达到数据并行聚类的效果,但每当有新的大数据流入时,都需要对当前全部数据进行K-均值聚类,计算过程复杂,聚类效率低。为此,提出了一种基于MapReduce的虚拟环境下大数据智能并行聚类方法。首先在虚拟环境下大数据中抽取小规模数据集并确定大数据簇的质心,采用Single法对所抽样的小规模数据进行聚类,获得虚拟环境下大数据属性的均值,利用最小距离分类规则将大数据属性的均值快速地向数据簇的真实中心移动,依据Davies-bouldin指标假设一个数据簇离散度参数,在此参数值中选出大数据智能并行聚类相似度最大值,最后利用聚类相似度最大值得到Davies-bouldin指数,以Davies-bouldin指数为基础将多个类别的质心间距以及聚类离散度指定阈值合并为一个类并进行迭代计算,得到数据最佳聚类中心位置,由此完成虚拟环境下大数据智能并行聚类。仿真实验结果证明,所提方法提高了大数据智能并行聚类的灵活性和普遍适用性,减少了聚类时间,并适合应用于教育技术领域,不仅可以使教育技术网络数据更加合理化,而且更加规范化。     

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.     

An Improved K-Means Algorithm Based on Evidence Distance

The main influencing factors of the clustering effect of the k-means algorithm are the selection of the initial clustering center and the distance measurement between the sample points. The traditional k-mean algorithm uses Euclidean distance to measure the distance between sample points, thus it suffers from low differentiation of attributes between sample points and is prone to local optimal solutions. For this feature, this paper proposes an improved k-means algorithm based on evidence distance. Firstly, the attribute values of sample points are modelled as the basic probability assignment (BPA) of sample points. Then, the traditional Euclidean distance is replaced by the evidence distance for measuring the distance between sample points, and finally k-means clustering is carried out using UCI data. Experimental comparisons are made with the traditional k-means algorithm, the k-means algorithm based on the aggregation distance parameter, and the Gaussian mixture model. The experimental results show that the improved k-means algorithm based on evidence distance proposed in this paper has a better clustering effect and the convergence of the algorithm is also better.     

Long memory and volatility clustering: Is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomenon is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.     

A modified region growing algorithm for multi-colored image object segmentation

A hybrid algorithm based on seeded region growing and k-means clustering was proposed to improve image object segmentation result. A user friendly segmentation tool was provided for the definition of objects,then k-means algorithm was utilized to cluster the selected points into k seeds-clusters, finally the seeded region growing algorithm was used for object segmentation. Experimental results show that the proposed method is suitable for segmentation of multi-colored object, while conventional seeded region growing methods can only segment uniform-colored object.     

Grafting of higher-order correlations of real financial markets into herding models

In this work, we graft the volatility clustering observed in empirical financial time series into the Equiluz and Zimmermann (EZ) model, which was introduced to reproduce the herding behaviors of a financial time series. The original EZ model failed to reproduce the empirically observed power-law exponents of real financial data. The EZ model ordinarily produces a more fat-tailed distribution compared to real data, and a long-range correlation of absolute returns that underlie the volatility clustering. As it is not appropriate to capture the empirically observed correlations in a modified EZ model, we apply a sorting method to incorporate the nonlinear correlation structure of a real financial time series into the generated returns. By doing so, we observe that the slow convergence of distribution of returns is well established for returns generated from the EZ model and its modified version. It is also found that the modified EZ model leads to a less fat-tailed distribution.     

Complex network analysis in inclined oil--water two-phase flow

Complex networks have established themselves in recent years as being particularly suitable and flexible for representing and modelling many complex natural and artificial systems. Oil--water two-phase flow is one of the most complex systems. In this paper, we use complex networks to study the inclined oil--water two-phase flow. Two different complex network construction methods are proposed to build two types of networks, i.e. the flow pattern complex network (FPCN) and fluid dynamic complex network (FDCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used for identifying three inclined oil--water flow patterns. To investigate the dynamic characteristics of the inclined oil--water two-phase flow, we construct 48 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of the inclined oil--water two-phase flow. In this paper, from a new perspective, we not only introduce a complex network theory into the study of the oil--water two-phase flow but also indicate that the complex network may be a powerful tool for exploring nonlinear time series in practice.     

基于选择性支持向量机集成的混沌时间序列预测

提出了一种基于聚类的选择性支持向量机集成预测模型.为提高支持向量机集成的泛化能力，采用自组织映射和K均值聚类算法结合的聚类组合算法，从每簇中选择出精度最高的子支持向量机进行集成，可以保证子支持向量机有较高精度并提高了子支持向量机之间的差异度.该方法能以较小的代价显著提高支持向量机集成的泛化能力.采用该方法对Mackey-Glass混沌时间序列和Lorenz系统生成的混沌时间序列进行预测实验，结果表明可以对混沌时间序列进行准确预测，验证了该方法的有效性. 关键词： 支持向量机 集成 混沌时间序列 聚类     

一种基于误差补偿的多元混沌时间序列混合预测模型

针对多元混沌时间序列的预测问题, 考虑到单纯改进储备池算法无法明显地提高预测精度, 提出一种基于误差补偿的时间序列混合预测模型. 实际观测的数据既包含线性特征又包含非线性特征. 首先利用自回归移动平均模型预测线性特征, 使得残差数据仅含非线性特征; 然后, 建立正则化回声状态网络模型预测; 最后, 将非线性部分的预测值与线性部分的预测值相加, 以实现高精度的多元混沌时间序列预测. 基于Lorenz和太阳黑子-黄河径流量时间序列的仿真实验验证了本文所提模型的有效性. 关键词： 回声状态网络 混沌 多元时间序列预测 误差补偿     

基于改进K均值聚类的机械故障智能检测

针对传统的K均值聚类算法在机械故障检测的过程中,由于对于K值的选择具有较强的主观性,最后极易得到局部最优解,而非全局最优解,降低了机械故障检测的准确性。提出一种改进K均值聚类的机械故障智能检测方法。将K均值聚类算法与粒子群算法相结合,在迭代处理的过程中,结合K均值进行优化,即将粒子群算法中的子代个体利用K均值聚类进行运算获取局部最优解,并使用这些个体继续参与迭代处理,这样能够提高算法的收敛速度,避免陷入局部最优解,获得准确的机械故障信号特征。实验结果表明,利用K均值倾斜特征提取的机械故障智能检测算法进行机械故障检测,能够有效提高故障检测的准确性,取得了令人满意的效果。     

Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine

The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.     

The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

According to the Einstein, Weinberg, and M?ller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by Ayón-Beato and García. The results show that the energy associated with the definitions of Einstein and Weinberg are the same, but M?ller not. Using the power series expansion, we find out that the first two terms in the expression are the same as the energy distributions of the Reissner-Nordstr?m solution, and the third term could be used to survey the factualness between numerous solutions of the Einstein field equations coupled to a nonlinear electrodynamics.     

Correlation Functions of an Autonomous Stochastic System with Nonlinear Time Delays

The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences between the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonlinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.     

Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.     

光电延迟反馈系统几种混沌路径的仿真分析

对非线性光电延迟反馈系统的响应时间序列进行数值分析.模型反馈循环中加入带通滤波器,建立非线性光电延迟反馈系统的数学模型.用龙格-库塔数值分析方法,通过调节参数,发现两种产生混沌信号的路径.设置特定φ时,在低反馈增益情况下,系统输出快速方波信号或慢速周期震荡信号,随着反馈增益的增加,系统输出出现复杂周期信号或混沌breather现象;在高反馈增益时,系统输出从不同的动力特性变成混沌状态.     

时序建模方法在滑油光谱分析中的应用

本文讨论了时序建模方法在机械设备滑油光谱分析中的应用。通过运用ＡＲ模型对采集的航空发动机滑油光谱数据进行时序建模和预测分析,获得了满意的效果。这一成果,为机械设备的状态监控和故障预报提供了一种实用方法。