Symbolic dynamics and complexity in a physiological time series

A general approach to non-stationary data from a non-linear dynamical time series is presented. As an application, the RR intervals extracted from the 24 h electrocardiograms of 60 healthy individuals 16–64 yr of age are analyzed with the use of a sliding time window of 100 intervals. This procedure maps the original time series into a time series of the given complexity measure. The state of the system is then given by the properties of the distribution of the complexity measure. The relation of the complexity measures to the level of the catecholamine hormones in the plasma, their dependence on the age of the subject, their mutual correlation and the results of surrogate data tests are discussed. Two different approaches to analyzing complexity are used: pattern entropy as a measure of statistical order and algorithmic complexity as a measure sequential order in heart rate variability. These two complexity measures are found to reflect different aspects of the neuroregulation of the heart. Finally, in some subjects (usually younger persons) the two complexity measures depend on their age while in others (mostly older subjects) they do not – in which case the correlation between is lost.     

Data Clustering Based on Maximization of Outlier Factor

There exist many data clustering algorithms, but they can not adequately handle the number of clusters or cluster shapes. Their performance mainly depends on a choice of algorithm parameters. Our approach to data clustering and algorithm does not require the parameter choice; it can be treated as a natural adaptation to the existing structure of distances between data points. The outlier factor introduced by the author specifies a degree of being an outlier for each data point. The outlier factor notion is based on the difference between the frequency distribution of interpoint distances in a given dataset and the corresponding distribution of uniformly distributed points. Then data clusters can be determined by maximizing the outlier factor function. The data points in dataset are divided into clusters according to the attractor regions of local optima. An experimental evaluation of the proposed algorithm shows that the proposed method can identify complex cluster shapes. Key advantages of the approach are: good clustering properties for datasets with comparatively large amount of noise (an additional data points), and an absence of important parameters which adequate choice determines the quality of results.     

AR模型辨识的稀疏结构迭代算法

模型估计是机器学习领域一个重要的研究内容,动态数据的模型估计是系统辨识和系统控制的基础.针对AR时间序列模型辨识问题,证明了在给定阶数下AR模型参数的最小二乘估计本质上也是一种矩估计.根据结构风险最小化原理,通过对模型拟合度和模型复杂度的折衷,提出了基于稀疏结构迭代的AR序列模型估计算法,并讨论了基于广义岭估计的最优正则化参数选取规则.数值结果表明,方法能以节省参数的方式有效地实现AR模型的辨识,比矩估计法结果有明显改善.     

Model-based clustering and segmentation of time series with changes in regime

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the Expectation?CMaximization (EM) algorithm. Within the context of a railway application, this paper introduces a novel mixture model for dealing with time series that are subject to changes in regime. The proposed approach, called ClustSeg, consists in modeling each cluster by a regression model in which the polynomial coefficients vary according to a discrete hidden process. In particular, this approach makes use of logistic functions to model the (smooth or abrupt) transitions between regimes. The model parameters are estimated by the maximum likelihood method solved by an EM algorithm. This approach can also be regarded as a clustering approach which operates by finding groups of time series having common changes in regime. In addition to providing a time series partition, it therefore provides a time series segmentation. The problem of selecting the optimal numbers of clusters and segments is solved by means of the Bayesian Information Criterion. The ClustSeg approach is shown to be efficient using a variety of simulated time series and real-world time series of electrical power consumption from rail switching operations.     

Linear relations in time series models. II

In this paper an asymptotic theory is developed for a new time series model which was introduced in a previous paper [5]. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in the sense that they have the same asymptotic distribution as the maximum likelihood estimators.     

Boundary-variation solution of eigenvalue problems for elliptic operators

We present an algorithm which, based on certain properties of analytic dependence, constructs boundary perturbation expansions of arbitrary order for eigenfunctions of elliptic PDEs. The resulting Taylor series can be evaluated far outside their radii of convergence—by means of appropriate methods of analytic continuation in the domain of complex perturbation parameters. A difficulty associated with calculation of the Taylor coefficients becomes apparent as one considers the issues raised by multiplicity: domain perturbations may remove existing multiple eigenvalues and criteria must therefore be provided to obtain Taylor series expansions for all branches stemming from a given multiple point. The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work. While our proofs, constructions and numerical examples are given for eigenvalue problems for the Laplacian operator in the plane, other elliptic operators can be treated similarly.     

Individual forecasting behavior

Participants of a laboratory experiment judgmentally forecast a time series. In order to support their forecasts they are given a highly correlated indicator with a constant lead period of one. The subjects are not given any other information than the time series realizations and have to base their forecasts on pure eyeballing/chart-reading. Standard economic models do not appropriately account for the features of individual forecasts: These are typically affected by intra- and inter-individual instability of behavior. We extend the scheme theory by Otwin Becker for the explanation of individual forecasts by simple schemes based on visually perceived characteristics of the time series. We find that the forecasts of most subjects can be explained very accurately by only a few schemes.     

Time series modeling of Army Mission Command communication networks: an event-driven analysis

We examine the communication time series of a fully-networked Army coalition command and control organization. The network comprised two echelons of command, at the Division and Brigade levels, over a 2-week military scenario exercise involving a Mission Command staff communicating over email and phone. We used time series analysis to predict the communications record based on an external work variable of the number of important scenario events occurring across time. After taking into account structural features of the time series—decreasing communications over time, a network crash, and the transition between weeks—we examined the remaining variability in email and phone communication. We found that the exercise scenario events were not a significant predictor of the Divisional communications, which were best fit by an auto-regressive model of order 1, meaning that the best predictor of the volume of communications at a given time point was the volume of communications on the immediately preceding time point. The occurrence of scenario events, however, did predict the Brigade communication time series, which were well fit by a lag dependent variable model. These results demonstrate that Brigade communications responded to and could be predicted by battlefield events, whereas the Division communications were only predicted by their own past values. These results highlight the importance of modeling environmental work events to predict organizational communication time series and suggest that network communications are perhaps increasingly dependent upon battlefield events for lower echelons of command closer to the tactical edge.     

Innovations algorithm asymptotics for periodically stationary time series with heavy tails

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In this case, the sample covariances on which the innovations algorithm are based are known to be asymptotically stable. The asymptotic results developed here are useful to determine which model parameters are significant. In the process, we also compute the asymptotic distributions of least squares estimates of parameters in an autoregressive model.     

A recursive algorithm for nonlinear least-squares problems

The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown. A. Alessandri and M. Cuneo were partially supported by the EU and the Regione Liguria through the Regional Programmes of Innovative Action (PRAI) of the European Regional Development Fund (ERDF). M. Sanguineti was partially supported by a grant from the PRIN project ‘New Techniques for the Identification and Adaptive Control of Industrial Systems’ of the Italian Ministry of University and Research.     

Risk evaluation of diabetes mellitus by relation of chaotic globals to HRV

This study's aim is to analyze heart rate dynamics in subjects with diabetes by measures of heart rate variability (HRV). The correlation of chaotic global parameters in the two cohorts is able to assess the probability of cardiac failure and other dynamical diseases. Adults (46) were divided into two equal groups. The autonomic evaluation consisted of measuring HRV for 30 min in supine position in absence of any physical, sensory, or pharmacological stimuli. Chaotic global parameters are able to statistically determine which series of electrocardiograph interpeak intervals in short time‐series are diabetic and which are not. The chaotic forward parameter that applies all three parameters is suggested to be the most appropriate and robust algorithm. This was decided after tests for normality; followed by one‐way analysis of variance (ANOVA1); (P < 0.09) and Kruskal–Wallis technique (P < 0.03). Principal component analysis implied two components represent 99.8% of total variance. Therefore, diabetes is a disease which reduces the chaotic response and, as such may be termed a dynamical condition such as are cardiac arrest, asthma, and epilepsy. © 2014 Wiley Periodicals, Inc. Complexity 20: 84–92, 2015     

Hierarchical hesitant fuzzy K-means clustering algorithm简

Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.     

Bayesian cylindrical data modeling using Abe–Ley mixtures

This paper proposes a Metropolis–Hastings algorithm based on Markov chain Monte Carlo sampling, to estimate the parameters of the Abe–Ley distribution, which is a recently proposed Weibull-Sine-Skewed-von Mises mixture model, for bivariate circular-linear data. Current literature estimates the parameters of these mixture models using the expectation-maximization method, but we will show that this exhibits a few shortcomings for the considered mixture model. First, standard expectation-maximization does not guarantee convergence to a global optimum, because the likelihood is multi-modal, which results from the high dimensionality of the mixture’s likelihood. Second, given that expectation-maximization provides point estimates of the parameters only, the uncertainties of the estimates (e.g., confidence intervals) are not directly available in these methods. Hence, extra calculations are needed to quantify such uncertainty. We propose a Metropolis–Hastings based algorithm that avoids both shortcomings of expectation-maximization. Indeed, Metropolis–Hastings provides an approximation to the complete (posterior) distribution, given that it samples from the joint posterior of the mixture parameters. This facilitates direct inference (e.g., about uncertainty, multi-modality) from the estimation. In developing the algorithm, we tackle various challenges including convergence speed, label switching and selecting the optimum number of mixture components. We then (i) verify the effectiveness of the proposed algorithm on sample datasets with known true parameters, and further (ii) validate our methodology on an environmental dataset (a traditional application domain of Abe–Ley mixtures where measurements are function of direction). Finally, we (iii) demonstrate the usefulness of our approach in an application domain where the circular measurement is periodic in time.     

The Generalized Arc Routing Problem

This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed.     

Panel data analysis: a survey on model-based clustering of time series

Clustering is a widely used statistical tool to determine subsets in a given data set. Frequently used clustering methods are mostly based on distance measures and cannot easily be extended to cluster time series within a panel or a longitudinal data set. The paper reviews recently suggested approaches to model-based clustering of panel or longitudinal data based on finite mixture models. Several approaches are considered that are suitable both for continuous and for categorical time series observations. Bayesian estimation through Markov chain Monte Carlo methods is described in detail and various criteria to select the number of clusters are reviewed. An application to a panel of marijuana use among teenagers serves as an illustration.     

标准粒子群优化算法的收敛性分析

研究标准粒子群优化算法在经验区域的各个子区域内的收敛和发散行为,分析系统特征根与算法参数的关系,得到一系列结论.数值仿真实验展示不同子区域内的算法参数对粒子位置和粒子速度运动轨迹的不同影响,进一步验证本文结论的正确性.     

Some robust objectives of FCM for data analyzing

There are many data clustering techniques available to extract meaningful information from real world data, but the obtained clustering results of the available techniques, running time for the performance of clustering techniques in clustering real world data are highly important. This work is strongly felt that fuzzy clustering technique is suitable one to find meaningful information and appropriate groups into real world datasets. In fuzzy clustering the objective function controls the groups or clusters and computation parts of clustering. Hence researchers in fuzzy clustering algorithm aim is to minimize the objective function that usually has number of computation parts, like calculation of cluster prototypes, degree of membership for objects, computation part for updating and stopping algorithms. This paper introduces some new effective fuzzy objective functions with effective fuzzy parameters that can help to minimize the running time and to obtain strong meaningful information or clusters into the real world datasets. Further this paper tries to introduce new way for predicting membership, centres by minimizing the proposed new fuzzy objective functions. And experimental results of proposed algorithms are given to illustrate the effectiveness of proposed methods.     

Efficient construction of a smooth nonparametric family of empirical distributions and calculation of bootstrap likelihood

This paper considers the efficient construction of a nonparametric family of distributions indexed by a specified parameter of interest and its application to calculating a bootstrap likelihood for the parameter. An approximate expression is obtained for the variance of log bootstrap likelihood for statistics which are defined by an estimating equation resulting from the method of selecting the first-level bootstrap populations and parameters. The expression is shown to agree well with simulations for artificial data sets based on quantiles of the standard normal distribution, and these results give guidelines for the amount of aggregation of bootstrap samples with similar parameter values required to achieve a given reduction in variance. An application to earthquake data illustrates how the variance expression can be used to construct an efficient Monte Carlo algorithm for defining a smooth nonparametric family of empirical distributions to calculate a bootstrap likelihood by greatly reducing the inherent variability due to first-level resampling.     

Identification of a nonlinear circuit

The identification of a differential equation underlying a measured time series is a prerequisite for numerous types of applications. In the validation of a proposed parameterized model one often faces the dilemma that it is hard to decide whether possible discrepancies between the measured time series and the simulated model output are caused by an inappropriate model or by wrongly specified parameters in a correct type of model. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a nonlinear chaotically oscillating circuit where we finally obtain an extremely accurate reconstruction of the observed attractor.     

When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone.