Algorithms for generating surrogate data for sparsely quantized time series

The method of surrogate data is frequently used for a statistical examination of nonlinear properties underlying original data. If surrogate data sets are generated by a null hypothesis that the data are derived by a linear process, a rejection of the hypothesis means that the original data have more complex properties. However, we found that if an algorithm for generating surrogate data, for example, amplitude adjusted Fourier transformed, is applied to sparsely quantized data, there are large discrepancies between their power spectrum and that of the original data in lower frequency regions. We performed some simulations to confirm that these errors often lead to false rejections.In this paper, in order to prevent such drawbacks, we advance an extended hypothesis, and propose two improved algorithms for generating surrogate data that reduce the discrepancies of the power spectra. We also confirm the validity of the two improved algorithms with numerical simulations by showing that the extended null hypothesis can be rejected if the time series is produced from chaotic dynamical systems. Finally, we applied these algorithms for analyzing financial tick data as a real example; then we showed that the extended null hypothesis cannot be rejected because the nonlinear statistics or nonlinear prediction errors exhibited are the same as those of the original financial tick time series.     

Interpreting non-random signatures in biomedical signals with Lempel-Ziv complexity

Lempel-Ziv complexity (LZ) [J. Ziv, A. Lempel, On the complexity of finite sequences, IEEE Trans. Inform. Theory 22 (1976) 75-81] and its variants have been used widely to identify non-random patterns in biomedical signals obtained across distinct physiological states. Non-random signatures of the complexity measure can occur under nonlinear deterministic as well as non-deterministic settings. Surrogate data testing have also been encouraged in the past in conjunction with complexity estimates to make a finer distinction between various classes of processes. In this brief letter, we make two important observations (1) Non-Gaussian noise at the dynamical level can elude existing surrogate algorithms namely: Phase-randomized surrogates (FT) amplitude-adjusted Fourier transform (AAFT) and iterated amplitude-adjusted Fourier transform (IAAFT). Thus any inference nonlinear determinism as an explanation for the non-randomness is incomplete (2) Decrease in complexity can be observed even across two linear processes with identical auto-correlation functions. The results are illustrated with a second-order auto-regressive process with Gaussian and non-Gaussian innovations. AR(2) processes have been used widely to model several physiological phenomena, hence their choice. The results presented encourage cautious interpretation of non-random signatures in experimental signals using complexity measures.     

脊小波变换域模糊自适应图像增强算法

提出了基于脊小波(ridgelet)变换域的模糊自适应图像增强算法,利用脊小波变换在表示图像线性奇异边缘时具有独特的优越性,达到突出边缘和抑制噪声的目的。利用频域内傅里叶投影变换定理,提出优化有限拉东(Radon)变换系数顺序的方法,使得拉东变换后图像的折回现象得到改善;利用广义模糊集合概念和最大模糊熵原理,提出一种自适应设置模糊增强函数方法,使得增强后的图像在抑制噪声、增强特征方面达到较好折衷。通过模拟实验显示,该算法优于传统的增强方式,在低信噪比情况(2.5~5.5 dB)下,其边缘检测概率大于二维小波增强方式约50%。应用于含有局部线形裂纹的路面病害图像的增强,可以将裂纹信号基本增强出来,且对路面上离散的油滴、石子等点噪声抑制较好。     

非最小相位线性非高斯序列的替代数据检验

替代数据法作为检验时间序列非线性和混沌的统计方法获得了广泛应用.常用的替代数据法的零假设为“原序列来自(经过单调静态非线性变换的)平稳线性高斯随机过程”.拒绝此假设,并不能说明序列必然来自确定性的非线性动力系统,非最小相位的线性非高斯序列也会导致基于相位随机化的替代数据检验拒绝此假设 关键词： 替代数据 时间序列分析 非线性 非最小相位     

Adaptive and efficient nonlinear channel equalization for underwater acoustic communication

We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear (piecewise linear) channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of conventional nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furthermore, the equalization algorithm should be completely adaptive, since due to the highly non-stationary nature of the underwater medium, the optimal mean squared error (MSE) equalizer as well as the best piecewise linear equalizer changes in time. To this end, we introduce an adaptive piecewise linear equalization algorithm that not only adapts the linear equalizer at each region but also learns the complete hierarchical structure with a computational complexity only polynomial in the number of nodes of the tree. Furthermore, our algorithm is constructed to directly minimize the final squared error without introducing any ad-hoc parameters. We demonstrate the performance of our algorithms through highly realistic experiments performed on practical field data as well as accurately simulated underwater acoustic channels.     

Generalized and Improved （G＇/G）-Expansion Method Combined with Jacobi Elliptic Equation

In this article, we propose an alternative approach of the generalized and improved （G＇/G）-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.     

Correlation dimension: A pivotal statistic for non-constrained realizations of composite hypotheses in surrogate data analysis

Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.

In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.

This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses.     

基于最大似然多项式回归的鲁棒语音识别

本文针对最大似然线性回归算法线性假设的缺点,将多项式回归方法用于模型自适应,构建了基于最大似然多项式回归的非线性模型自适应算法。该算法在对数谱域用多项式回归方法,逼近每个Mel子带上识别环境模型均值与训练环境模型均值之间的非线性关系。多项式系数通过EM算法和最大似然准则从识别环境下的少量自适应数据中估计。实验结果表明,二阶多项式就可以较好地逼近模型均值的非线性环境变换关系。在噪声补偿和说话人自适应实验中,最大似然多项式回归算法的误识率都明显低于最大似然线性回归算法。本文算法较好地克服了线性模型自适应算法线性假设的缺陷,可同时减小噪声,和说话人的改变或其它因素对语音识别系统的影响,尤其适合说话人和噪声的联合自适应。      

Novel optical image encryption scheme based on fractional Mellin transform

A novel nonlinear image encryption scheme is proposed by introducing the fractional Mellin transform (FrMT) into the field of image security. As a nonlinear transform, FrMT is employed to get rid of the potential insecurity of the optical image encryption system caused by the intrinsic object-image relationship between the plaintext and the ciphertext. Different annular domains of the original image are transformed by FrMTs of different orders, and then the outputs are further encrypted by comprehensively using fractional Fourier transform (FrFT), amplitude encoding and phase encoding. The keys of the encryption algorithm include the orders of the FrMTs, the radii of the FrMT domains, the order of the FrFT and the phases generated in the further encryption process, thus the key space is extremely large. An optoelectronic hybrid structure for the proposed scheme is also introduced. Numerical simulations demonstrate that the proposed algorithm is robust with noise immunity, sensitive to the keys, and outperforms the conventional linear encryption methods to counteract some attacks.     

Stationarity tests for financial time series

Much attention has been paid in recent years to the study of the order of integration of a time series, i.e. the number of differences that are necessary to transform it into a stationary series. The relevance of the subject arises because most of time series analysis in economics and finance are based on the stationarity hypothesis. In the paper we present the most common tests for the null hypothesis of stationarity, and apply them to study the order of integration in a Spanish financial series namely the IBEX-35, using unit root tests as well. We find empirical evidence of a unit root in the series.     

Testing nonlinear Markovian hypotheses in dynamical systems

We present a statistical approach for detecting the Markovian character of dynamical systems by analyzing their flow of information. Especially in the presence of noise which is mostly the case for real-world time series, the calculation of the information flow of the underlying system via the concept of symbolic dynamics is rather problematic since one has to use infinitesimal partitions. We circumvent this difficulty by measuring the information flow indirectly. More precisely, we calculate a measure based on higher order cumulants which quantifies the statistical dependencies between the past values of the time series and the point r steps ahead. As an extension of Theiler's method of surrogate data (Theiler et al., 1992) this cumulant based information flow (a function of the look-ahead r) is used as the discriminating statistic in testing the observed dynamics against a hierarchy of null hypotheses corresponding to nonlinear Markov processes of increasing order. This procedure is iterative in the sense that whenever a null hypothesis is rejected new data sets can be generated corresponding to better approximations of the original process in terms of information flow. Since we use higher order cumulants for calculating the discriminating statistic our method is also applicable to small data sets. Numerical results on artificial and real-world examples including non-chaotic, nonlinear processes, autoregressive models and noisy chaos show the effectiveness of our approach.     

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     

Detecting nonlinearity of action surface EMG signal

The action surface EMG (ASEMG) signal contains the electrical properties of limb muscle contraction that undergo many complex transitions in limb different movement states; however, because of the small data nature of this kind signal, it is not clear whether its essence is stochastic or deterministic nonlinear (even chaotic). In this Letter, we show for the first time that ASEMG has deterministic nonlinear character by using the surrogate data method. Furthermore, we study the nonlinear dynamic features of ASEMG by computing its correlation dimension and applying correlation dimension as test statistics. These results indicate that ASEMG is a high-dimension nonlinear signal (even chaotic). In addition, this Letter improves the surrogate data method based on Fourier transform (FT) algorithm to avoid limitations of the previous FT algorithm.     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers

In this paper we describe efficient methods to obtain the stationary states of linear and nonlinear photonic systems, which have gained particular interest in the field of integrated and nonlinear optics. While the methods presented are directly applicable to optical physics, they are also general and should be of interest in a broad range of phenomena presently under study in other areas of physics and engineering. The strategy consists in combining the use of classical methods, such as inverse iteration or the Newton method, together with modern, nonstationary linear solvers, such as SYMMLQ or GMRES, in order to obtain efficient numerical computations to problems involving large matrices. We have selected several example problems in order to discuss the practical implementation details, not normally described in the present literature. Moreover, the problems we have selected provide a backdrop to contrast and motivate the use of different methods for systems which are symmetric and non-symmetric, single and multi-component, and also real and complex. Information relative to numerical performance of the different algorithms, including a survey for a nonsymmetric problem, which requires the adjustment of a restarting parameter for the GMRES algorithm, is also presented.     

NIRS feature extraction based on deep auto-encoder neural network

As a secondary analysis method, Near Infrared Spectroscopy (NIRS) needs an effective feature extraction method to improve the model performance. Deep auto-encoder (DAE) can build up an adaptive multilayer encoder network to transform the high-dimensional data into a low-dimensional code with both linear and nonlinear feature combinations. To evaluate its capability, we experimented on the spectra data obtained from different categories of cigarette with the method of DAE, and compared with the principal component analysis (PCA). The results showed that the DAE can extract more nonlinear features to characterize cigarette quality. In addition, the DAE also got the linear distribution of cigarette quality by its nonlinear transformation of features. Finally, we employed k-Nearest Neighbor (kNN) to classify different categories of cigarette with the features extracted by the linear transformation methods as PCA and wavelet transform-principal component analysis (WT-PCA), and the nonlinear transformation methods as DAE and isometric mapping (ISOMAP). The results showed that the pattern recognition mode built on features extracted by DAE was provided with more validity.     

Generalized wavelet transform based on the convolution operator in the linear canonical transform domain

The wavelet transform (WT) and linear canonical transform (LCT) have been shown to be powerful tool for optics and signal processing. In this paper, firstly, we introduce a novel time-frequency transformation tool coined the generalized wavelet transform (GWT), based on the idea of the LCT and WT. Then, we derive some fundamental results of this transform, including its basis properties, inner product theorem and convolution theorem, inverse formula and admissibility condition. Further, we also discuss the time-fractional-frequency resolution of the GWT. The GWT is capable of representing signals in the time-fractional-frequency plane. Last, some potential applications of the GWT are also presented to show the advantage of the theory. The GWT can circumvent the limitations of the WT and the LCT.     

Speech enhancement method based on low-rank approximation in a reproducing kernel Hilbert space

Speech signal is corrupted unavoidably by noisy environment in subway, factory, and restaurant or speech from other speakers in speech communication. Speech enhancement methods have been widely studied to minimize noise influence in different linear transform domain, such as discrete Fourier transform domain, Karhunen-Loeve transform domain or discrete cosine transform domain. Kernel method as a nonlinear transform has received a lot of interest recently and is commonly used in many applications including audio signal processing. However this kind of method typically suffers from the computational complexity. In this paper, we propose a speech enhancement algorithm using low-rank approximation in a reproducing kernel Hilbert space to reduce storage space and running time with very little performance loss in the enhanced speech. We also analyze the root mean squared error bound between the enhanced vectors obtained by the approximation kernel matrix and the full kernel matrix. Simulations show that the proposed method can improve the computation speed of the algorithm with the approximate performance compared with that of the full kernel matrix.     

Maximum likelihood polynomial regression for robust speech recognition

The linear hypothesis is the main disadvantage of maximum likelihood linear regression (MLLR).This paper applies the polynomial regression method to model adaptation and establishes a nonlinear model adaptation algorithm using maximum likelihood polynomial regression(MLPR)for robust speech recognition.In this algorithm,the nonlinear relationship between training and testing Gaussian means in every Mel channel is approximated by a set of polynomials and the polynomial coefficients are estimated from adaptation data in test environment using the expectation-maximization(EM)algorithm and maximum likelihood(ML) criterion.The experimental results show that the second-order polynomial can approximate the actual nonlinear function better and in noise compensation and speaker adaptation,the word error rates of MLPR are significantly lower than those of MLLR.The proposed MLPR algorithm overcomes the limitation of linear hypothesis well and can decrease the impact of noise,speaker and other factors simultaneously.It is especially suitable for joint adaptation of speaker and noise.