An investigation into the linear and nonlinear correlation of two music walk sequences

In order to investigate the features of a multiple-part musical score which enhance its appeal to the listener’s ear, this study performs a robust analysis of the correlation between two musical sequences. In the proposed approach, a series of notes are extracted from seven well-known classical pieces of music and are converted into one-variable “music walks”. The linear correlation between pairs of music walks is assessed using the conventional linear correlation coefficient, while the nonlinear correlation is examined using the mutual information concept. The results show that even though two musical time walks may exhibit virtually no linear correlation, they invariably have a certain degree of nonlinear correlation. In other words, to truly understand the correlation between two musical sequences, it is necessary to consider not only the linear correlation between them, but also the nonlinear correlation. In addition, it is shown that the normalized mutual information coefficient between musical sequences has a relatively low value and varies significantly over the course of the musical score. Thus, it can be inferred that the appeal of a musical score stems at least in part from significant variations in both the melody and the rhythm of the constituent parts such that the overall score has a rich and unpredictable property.     

Complex networks in climate dynamics

Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.     

归一化KLD系数及多维序列相关和同步的检测

提出了KLD系数和归一化KLD系数来刻画多维序列的相关结构, 以解决KLD维密度固有的局限性. 利用完全相关和完全不相关的多维序列, 导出KLD维密度的上界和下界函数, 进而导出KLD系数的上界和下界, 在此基础上提出归一化KLD系数. 解析分析和数值仿真都证明, 多维序列相关结构的变化会引起归一化KLD系数线性的变化. 数值仿真还证明, 即使多维序列中仅有其中的两个时间序列的相关结构发生改变, 归一化KLD系数仍能灵敏地检测到. 不仅如此, 归一化KLD系数还可用于非平稳时间序列的分析. 耦合映象格子的数值仿真结果表明, 归一化KLD系数还能够分析非线性系统的相关结构.     

A new complexity measure for time series analysis and classification

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the “Effort To Compress” the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip).     

联合区间高斯过程的近红外光谱波长选择方法及应用

针对近红外光谱应用,提出了一种基于高斯过程(GP)模型的波长选择算法,即联合区间高斯过程(synergy interval gaussian process,siGP)算法。首先将全光谱区域划分为一系列无重复且间距相等的区间,再选取最优的若干个区间联合建立GP模型,由于GP模型具有非线性处理能力,因此该方法可以减少非线性的影响。以红曲菌固态发酵过程中过程参数水分含量和pH值的检测为例,新算法对水分含量、pH值的预测集相关系数(r_p)分别为0.956 4和0.977 3,预测均方根误差(RMSEP)分别为0.012 7和0.161 0,参与建模的数据点由全谱的1 500个分别减少到225个、375个,在对独立样本的预测上,表现出较好的精度。与传统联合区间偏最小二乘(siPLS)波长选择算法对比,siGP算法预测效果更好：对水分含量和pH值,r_p在GP模型预测时提高了3.37%和3.51%,RMSEP在GP模型预测时提高了29.4%和34.8%。表明siGP结合GP模型能够有效选择波长区间以及提高近红外模型的准确性,对进一步实现近红外光谱技术在线检测具有参考价值。     

Three-dimensional Fourier Fringe Analysis

Over the years two-dimensional Fourier Fringe Analysis (2D-FFA) has demonstrated both its capability and its relative robustness in analysing fringe patterns within a short time-frame from static objects. Nowadays, there is an increasing demand to measure dynamic objects. Today 2D-FFA is seen as a fast and flexible method of processing fringe patterns for dynamic objects. But it is still inherently a 2D approach, i.e. it deals with three-dimensional data (video sequences) on an individual 2D frame-by-frame basis. In this paper, a novel three-dimensional Fourier Fringe Analysis (3D-FFA) algorithm is proposed to demodulate fringe pattern sequences taken from dynamic objects. This technique processes the stack of fringe patterns as a single 3D volume, not as a set of individual 2D frames that are each processed in isolation. The proposed algorithm has been evaluated on both computer simulated and real dynamic objects. Results show that the proposed technique is able to demodulate fringe pattern volumes successfully.     

Reconstruction of dynamic structures of experimental setups based on measurable experimental data only

Nowadays, massive amounts of data have been accumulated in various and wide fields, it has become today one of the central issues in interdisciplinary fields to analyze existing data and extract as much useful information as possible from data. It is often that the output data of systems are measurable while dynamic structures producing these data are hidden,and thus studies to reveal system structures by analyzing available data, i.e., reconstructions of systems become one of the most important tasks of information extractions. In the past, most of the works in this respect were based on theoretical analyses and numerical verifications. Direct analyses of experimental data are very rare. In physical science, most of the analyses of experimental setups were based on the first principles of physics laws, i.e., so-called top-down analyses. In this paper, we conducted an experiment of "Boer resonant instrument for forced vibration"(BRIFV) and inferred the dynamic structure of the experimental set purely from the analysis of the measurable experimental data, i.e., by applying the bottomup strategy. Dynamics of the experimental set is strongly nonlinear and chaotic, and it's subjects to inevitable noises. We proposed to use high-order correlation computations to treat nonlinear dynamics; use two-time correlations to treat noise effects. By applying these approaches, we have successfully reconstructed the structure of the experimental setup, and the dynamic system reconstructed with the measured data reproduces good experimental results in a wide range of parameters.     

一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.     

New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.     

基于Raman光谱的人、犬、兔血液鉴别

多物种血液鉴别对于进出口检验检疫、刑事侦检以及野生动物保护等领域尤为重要。传统的血液鉴别方法,在鉴别时常常会对血液样本造成破坏,而Raman光谱作为一种振动光谱可获得物质分子振动、转动信息,进而分析物质组成,为无损血液鉴别技术提供了可能。目前,已经有基于Raman光谱进行血液鉴别的报道,但存在如下两个问题：单一物种样本数量较少,易导致模型欠拟合;均采用线性分类模型,忽略了光谱中非线性因素的影响,降低了模型的分类性能。因此,将支持向量机沿用至Raman光谱血液鉴别中,克服了线性模型只能为光谱中线性关系建模的缺点,有效地吸收了Raman光谱中的非线性关系,实现了对人、犬及兔血液的三分类。实验通过激发波长为785 nm的海洋Raman光谱仪测得共326例样本数据(人110例、犬116例、兔100例),利用Savitzky-Golay平滑滤波、加权最小二乘多项式拟合基线以及矢量归一化等方法对Raman光谱数据进行预处理,并选择2/3的样本数据作为校正集用于模型训练,余下1/3作为测试集用于盲测。与线性分类模型对比实验结果显示,该模型的校正集分类正确率达100%,盲测集分类正确率达93.52%,均优于线性分类模型。实验结果表明,基于支持向量机的分类模型可以用于Raman血液光谱鉴别,具有重要的研究价值和广泛的应用前景。     

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.     

Infrared point target detection with improved template matching

Detecting point targets in infrared images is a difficult task. Template matching is simple and easy to implement for completing this task. However, it has some shortcomings. We propose an improved template matching method for detecting targets. Different from the classic template matching, the projection coefficients obtained from principal component analysis are used as templates and the nonlinear correlation is proposed to measure the similarity, the matching degree. The correlation in original space can not capture the higher-order statistical property of images. So its detection performance is not satisfying. We introduce the nonlinear correlation, which computes the correlation coefficients in a higher-dimensional feature space or even in an infinite-dimensional feature space, to capture the higher-order statistics. The detection performance is improved greatly. Results of experiments show that the improved method is competent to detect infrared point targets.     

高光谱技术结合CARS算法的库尔勒香梨可溶性固形物定量测定

由于高光谱数据量大、维数高,光谱噪声明显、散射严重等特征导致光谱建模时关键变量提取较为困难,同时,高光谱图像的获取会受非单色光、杂散光、温度等多种因素的影响,从而使高光谱数据与待测性质之间有一定非线性关系。为此,提出采用正自适应加权算法(CARS)对可见-近红外高光谱高维数据进行关键变量筛选,并与全光谱和经典变量提取方法SPA,MC-UVE,GA和GA-SPA方法进行比较。以200个库尔勒香梨为研究对象,采用SPXY方法将样本划分为校正集和预测集,校正集和预测集分别包含150个和50个样本。基于不同方法筛选的变量,分别建立线性PLS模型及非线性LS-SVM模型,r2,RMSEP和RPD用于模型性能的评估。综合比较发现,GA,GA-SPA和CARS变量筛选方法能够有效地筛选出原始高光谱数据中具有强信息且对外界影响因素不敏感的变量,适用于高光谱数据关键变量的提取,其中CARS变量筛选效果最佳,基于CARS获取的关键变量构建的非线性LS-SVM库尔勒香梨SSC含量预测模型获得了最优的预测结果,r2_pre,RMSEP和RPD分别为0.851 2,0.291 3和2.592 4。研究表明,CARS方法是一种有效的高光谱关键变量筛选方法,利用高光谱数据,非线性LS-SVM模型比线性PLS模型更适合于香梨品质的定量预测。     

Characteristics of vapor based on complex networks in China

The uneven spatial distribution of stations providing precipitable water vapor (PWV) observations in China hinders the effective use of these data in assimilation, nowcasting, and prediction. In this study, we proposed a complex network framework for exploring the topological structure and the collective behavior of PWV in the mainland of China. We used the Pearson correlation coefficient and transfer entropy to measure the linear and nonlinear relationships of PWV amongst different stations and to set up the undirected and directed complex networks, respectively. Our findings revealed the statistical and geographical distribution of the variables influencing PWV networks and identified the vapor information source and sink stations. Specifically, the findings showed that the statistical and spatial distributions of the undirected and directed complex vapor networks in terms of degree and distance were similar to each other (the common interaction mode for vapor stations and their locations). The betweenness results displayed different features. The largest betweenness ratio for directed networks tended to be larger than that of the undirected networks, implying that the transfer of directed PWV networks was more efficient than that of the undirected networks. The findings of this study are heuristic and will be useful for constructing the best strategy for the PWV data in applications such as vapor observational networks design and precipitation prediction.     

非线性时间序列互信息与Lempel-Ziv复杂度的相关性研究

为探究非线性动力学系统的互信息和复杂度的相关性，用Logistic映射、Lorenz模型和心电RR间期的非线性时间序列作为实验数据，计算多分段延时互信息和多分段Lempel-Ziv复杂度以及它们之间的相关系数.结果表明这些序列的互信息和复杂度呈强负相关，对Logistic方程生成的201个序列的不同段互信息和不同段复杂度之间的相关系数绝对值都大于0.9162，最大达0.9923；对94个心电RR间期序列都大于0.8555，最大达0.9860.研究还发现互信息比复杂度能更敏感地表现出非线性动力系统的特征. 关键词： 相关系数 互信息 Lempel-Ziv 复杂度 心电RR间期     

两分量Bose-Einstein凝聚体的非线性Ramsey干涉

以非线性Rosen-Zener隧穿理论为基础,用两分量Bose-Einstein凝聚体设计了非线性Ramsey干涉计.通过数值模拟实验在时间域上观察到了丰富的Ramsey干涉图样,凝聚体中原子间重要的非线性相互作用导致这些干涉图样明显不同于线性Ramsey干涉时的正弦型条纹.通过进一步对干涉图样作Fourier分析,发现干涉图样的基频能够精确反映系统的非线性和不对称性特征,从而为测量原子的相关性质提供了理论依据. 关键词： Bose-Einstein凝聚 非线性Ramsey干涉 Rosen-Zener隧穿     

Hyperspectral unmixing based on ISOMAP and spatial information

Several nonlinear techniques have recently been proposed for classification and unmixing applications in hyperspectral image processing. A commonly used data-driven approach for treating nonlinear problems employs the geodesic distances on the data manifold as the property of interest. Although this approach often produces better results than linear unmixing algorithms, the graph-based method treats an image as a bag of spectral signatures and ignores the relationship between the pixel and its spatial neighbors. To utilize the spatial distribution of pixels and improve hyperspectral unmixing precision effectively, a new method is proposed for incorporating nonlinear dimension reduction and spatial information, using isometric mapping (ISOMAP) to find significant low-dimensional structures hidden in high-dimensional hyperspectral data. Spatial information is also introduced into the traditional spectral-based endmember search process. A fully constrained least-squares algorithm is used to evaluate the abundance of each endmember. The experimental results for actual images reveal that the performance of the proposed method obtains much better unmixing results than the classical N-FINDR and ISOMAP algorithms.     

基于互信息熵-近红外光谱的过程模式故障检测

近红外光谱分析在工业过程故障检测方面具有独特的优势,是一种准确且高效的方法。结合互信息熵和传统的主成分分析,对近红外光谱特征信息进行提取,通过构建过程的模式来刻画工业过程的运行状态。利用近红外光谱数据,从有机分子含氢基团振动信息中获取工业系统的过程模式,从微观分子层面探索提高工业过程故障检测准确率的有效方法,结合贝叶斯统计学习技术,提出了基于近红外光谱数据的工业过程故障检测技术。针对近红外光谱信息量丰富,谱带较宽,特征性不强的特点,首先对工业过程不同运行状态下的近红外光谱吸光度数据进行一阶导数预处理,采用主成分分析法（principal component analysis,PCA）压缩光谱数据量,扩大不同运行状态下光谱特征信息的差异性,提取光谱的内部特征信息。然后采用互信息熵（mutual information entropy,MIE）作为光谱特征信息相关性度量函数,基于最小冗余最大相关算法进一步减少光谱特征信息间的冗余并最大化光谱特征信息与类别的相关性,弥补了PCA无监督特征波长选择的不足,提出一种基于PCA-MIE的过程模式构建方法,获得的过程模式子集更紧凑更具类别表现力。再利用贝叶斯统计学习算法,根据后验概率对构建的模式子集进行决策,判别生产过程的正常状态和故障状态。由于过程模式子集结合了PCA浓聚方差的优势和互信息熵相关性测度的特征信息选择方法,蕴含了更多的近红外光谱的本质信息与内在规律,从而更能刻画工业过程的运行状态。接着,设置测试准确率TA作为评估标准,用以评价故障检测方法的性能效果。最后利用某化工厂提供的原油脱盐脱水过程近红外光谱数据对所提方法进行验证,并与传统近红外光谱特征信息提取方法PCA和MIE方法性能进行对比分析,结果表明基于PCA-MIE的过程模式故障检测方法几乎在所有维数子集上性能都优于其他两种方法,在特征维数为18维时获得最高的准确率94. 6%,证明了方法的优越性。     

非线性拟合方法用于透射式脉冲红外技术测试碳/碳复合材料的热扩散系数

为了测试碳/碳复合材料的热扩散系数,本文提出了非线性拟合用于透射式脉冲红外检测的数据处理方法.非线性拟合通过循环迭代的方法持续调整拟合参数,让理论值不断逼近实验值,直至获得最佳结果.传统的透射式脉冲红外成像技术利用半高时间法测试材料的热扩散系数,但通常会受到采集时间不足和信噪比差的限制.本文提出的非线性拟合方法可以有效消除或减弱这两种影响.在使用该方法之前,首先选用常见的304不锈钢评估了该方法的测量精度及拟合长度对测试结果的影响.结果显示304不锈钢的测量精度达到0.3%,且当拟合长度不小于半高时间法采集时间的1/5时,拟合长度对非线性拟合结果影响很小.随后使用该拟合方法测试了不同厚度的碳/碳复合材料试件,并通过热扩散系数测量结果分析了试件之间的热参数差异性和材料自身的均匀性.     

Probing through bond connectivities with MQMAS NMR

Polarization transfer from quadrupolar (27Al) to spin-1/2 (31P) nuclei via J-coupling is employed to measure two-dimensional 27Al-31P heteronuclear correlation spectra with isotropic resolution. The proposed experiment, MQ-J-HETCOR, uses multiple quantum magic angle spinning (MQMAS) NMR for elimination of the second-order quadrupolar broadening and INEPT, INEPTR, INEPT+ and DEPT sequences for the polarization transfer. The experimental conditions leading to best sensitivity and resolution are detailed using AlPO4-14 as a test sample.