基于中心Copula函数相似性度量的时间序列聚类方法

针对现实中广泛存在的非线性时间序列数据,提出了一种适用于具有一般相依结构的时间序列聚类的新方法。该方法基于中心Copula函数可以有效度量随机变量之间独立性的特性,采用中心Copula过程捕获时间序列的动态相依结构,采用Cramér-von Mises统计量构造了一种新的时间序列聚类的相似性度量,并给出了该度量的一致性非参数估计及其便于计算的等价形式。实验结果表明,基于新的相似性度量的层次聚类算法不仅适用于非线性时间序列数据,对具有线性相依结构的时间序列数据和实际数据也有较高的聚类质量。

基于新的鲁棒相似性度量的时间序列聚类

针对存在异常值的时间序列数据,提出了一种基于相关系数鲁棒估计的时间序列间的鲁棒广义互相关度量(RGCC)。首先,引入一种鲁棒相关系数代替Pearson相关系数来计算时间序列数据间的协方差矩阵;其次,用新的协方差矩阵的行列式构造两个时间序列间的相似性度量——RGCC;最后,基于该度量计算出序列间的距离矩阵,将其作为聚类算法的输入对数据进行聚类。时间序列聚类仿真实验表明,对存在异常值点的时间序列数据,与基于原始的广义互相关度量(GCC)得到的聚类结果相比,基于RGCC得到的聚类结果明显更接近真实的聚类结果。可见,所提出的新的鲁棒相似性度量完全适用于存在异常值的时间序列数据。

New repairable system model with two types repair based on extended geometric process

A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repair finished. When the system failure, the repairman repair it immediately. The time interval of the preventive repair and the failure correction is described with the extended geometric process. Different from the available replacement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T,N) is considered. The explicit expression of the long-run average cost rate function C(T,N) of the system is derived. Through alternatively minimize the cost rate function C(T,N), the optimal replacement policy (T?,N?) is obtained, and it proves that the optimal policy is unique. Numerical cases illustrate the conclusion, and the sensitivity analysis of the parameters is carried out.

SVAR-GARCH模型的多元波动率估计

考虑SVAR-GARCH模型的多元波动率,提出一种估计波动率的新方法.先利用独立成分分析技术求解因果结构和统计独立的误差项,建立残差项条件协方差阵与误差项条件协方差阵的关系,然后利用单变量GARCH模型的估计结果和识别的因果结构,估计多变量GARCH模型的条件波动的脉冲响应方法,实现多元波动率的估计,该方法可有效减少估计参数.实验结果表明,新方法估计的波动率与能源期货市场的规律相符.

A generalized geometric process based repairable system model with bivariate policy

The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.

两正定矩阵联合对角化盲分离算法

针对具有时间结构的盲分离问题,提出了一种基于两正定矩阵精确联合对角化的盲分离算法。利用多个不同时延统计量构造了两个正定矩阵,以提取出数据的时间结构;再利用所提算法联合对角化构造的两个正定矩阵,得到分离矩阵,进而估计出源信号。所提算法克服了已有算法因采用多个矩阵联合对角化导致的计算量大和采用单个矩阵导致的分离精度低的缺点。计算机仿真结果表明了在有或无噪声情况下,所提算法性能均优于其他对比算法。

Blind source separation with unknown and dynamically changing number of source signals

The contrast function remains to be an open problem in blind source separation （BSS） when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.

Image Denoising via Improved Simultaneous Sparse Coding with Laplacian Scale Mixture

Image denoising is a well-studied problem closely related to sparse coding. Noticing that the Laplacian distribution has a strong sparseness, we use Laplacian scale mixture to model sparse coefficients. With the observation that prior information of an image is relevant to the estimation of sparse coefficients, we introduce the prior information into maximum a posteriori（MAP） estimation of sparse coefficients by an appropriate estimate of the probability density function. Extending to structured sparsity, a nonlocal image denoising model： Improved Simultaneous Sparse Coding with Laplacian Scale Mixture（ISSC-LSM） is proposed. The centering preprocessing, which admits biased-mean of sparse coefficients and saves expensive computation, is done firstly. By alternating minimization and learning an orthogonal PCA dictionary, an efficient algorithm with closed-form solutions is proposed. When applied to noise removal, our proposed ISSC-LSM can capture structured image features, and the adoption of image prior information leads to highly competitive denoising performance. Experimental results show that the proposed method often provides higher subjective and objective qualities than other competing approaches. Our method is most suitable for processing images with abundant self-repeating patterns by effectively suppressing undesirable artifacts while maintaining the textures and edges.