不确定时间序列的相似性匹配问题

确定性时间序列的相似性匹配方法都没有考虑数据的不确定性,而现实世界中传感器采集到的数据往往是不确定的,现有的时间序列的相似性匹配方法不适用于这些领域.针对此问题,将不确定性时间序列做预处理,把它分为横向时间维和纵向概率维,首先把给定的不确定时间序列用Haar小波变换进行压缩变换,在此基础上,对得到的不确定性时间序列概率维作纵向处理,提出一种选代表方法,即采用概率最大法、均值法等选出一条确定的时间序列.通过这2种预处理后,对得到的确定性时间序列进行降维和索引,根据查询序列和数据库中的时间序列中的各自的不确定性进行组合,分别提出对应组合的相似性匹配算法.     

不确定时间序列的降维及相似性匹配

不确定时间序列的每个时间点上对应一个可能取值的集合,无法给出其确定值,这种不确定性给时间序列降维处理和相似性匹配带来巨大挑战,现有的时间序列降维方法和相似性匹配算法已经无法适用。针对此问题,提出了描述统计模型,将不确定时间序列归约为3条确定时间序列,通过离散傅里叶变换（discrete Fou-rier transform,DFT）、离散余弦变换（discrete cosine transform,DCT）、离散小波变换（discrete wavelet trans-form,DWT）对模型下不确定时间序列降维;根据模型特点,提出了以观察值区间和区间集中趋势为核心的相似性匹配算法。经过实验验证,描述统计模型下DCT和DWT有良好的降维效果,提出的相似匹配算法与现有算法相比提高了匹配准确率。     

不确定时间序列的统计降维方法

由于不确定时间序列的长度很长,并且每个采样点的取值具有不确定性,导致了维度灾难和庞大的可能世界集,给不确定时间序列相似性匹配带来了巨大的困难,因此对不确定时间序列降维是实现对其方便存储、快速查询和相似性匹配的首要任务。不确定时间序列普遍采用小波变换的降维方法,但是该方法没有考虑到采样点之间的相关性。为解决该问题,提出一种基于概率统计和数据相关性的降维方法,该方法将不确定时间序列分为概率维度和时间维度,并分别对两维度进行降维。在时间维度,根据采样点之间的相关性,使用某个采样点代表后续相关度高的采样点;在概率维度,使用大概率点表示相邻的小概率点。实验效果表明:使用该方法对不确定时间序列进行降维后,降维序列可以保持原序列的变化趋势,压缩程度显著,并且可近似地恢复原序列。     

改进的符号化时间序列处理方法

符号化聚集近似是一种有效的时间序列数据离散化降维方法,为了扩展非等维符号化时间序列相似性度量的解决方案,提出了一种新方法。首先将关键点提取技术应用在符号化算法中对时间序列进行降维处理,然后利用文中提出的方法对非等长的时间序列进行局部等维处理,再符号化;最后采用不同的方法进行相似度对比计算。实验结果表明,这种方法是简单而有效的,并且使非等长符号化时间序列的相似性度量及聚类方法得到了拓展。     

基于SAX的时间序列相似性度量方法*

符号化表示是一种有效的时间序列降维技术,其相似性度量是诸多挖掘任务的基础。基于SAX(sym-bolic aggregate approximation)的距离MINDIST_PAA_iSAX不满足对称性,在时间序列挖掘中具有局限性,提出了对称的度量Sym_PAA_SAX,且下界于欧拉距离。在真实数据集和合成数据集上的实验说明下界紧密性较好,相似搜索错报率较低。     

面向相似性查询的时间序列距离度量方法述评

从一元时间序列和多元时间序列两个方面对当前提出的主要时间序列距离度量方法进行了述评.深入分析了各种算法的原理和特点,比较了算法对时间序列形变的支持情况以及时间复杂度.从客观上讲,各种算法之间并不具有绝对的优劣关系,每种算法的原理和特点各异,适用的问题领域也不一样.对于工程应用中选择时间序列距离度量方法具有指导意义,同时对于设计新的距离度量方法也具有参考价值.     

基于EMD方法的时间序列分层相似性匹配算法

时间序列数据挖掘是时态数据挖掘的一个重要方面;针对金融时间序列非稳定、非线性的特点;使用EMD方法进行序列趋势的提取;得到了原始时间序列的长期趋势。在此基础上提出了子序列分层匹配算法;首先进行时间序列趋势的粗匹配;在结果集中进一步进行细节匹配;与传统方法相比;提高了相似性匹配的效率;减少了结果集的冗余。     

时间序列的模糊匹配方法

一个时间序列可以定义为一系列的数值,每一个数值代表一个时间点的值。在数据库和数据仓库应用中,时间序列数据是一类非常重要的数据类型。时间序列的相似性的判定,有基于欧几里得距离的判定方法和包络线方法。欧几里得距离方法对序列中的噪声很敏感,而且欧几里得距离随着序列长度的增加而变大。Rakesh Agrawal等所提出的方法,是将匹配的子序列按顺序连接来判定两个序列的相似性,如果一个子序列落入另一个子序列的包络线区间内(如图1),那么认为这两个于序列是匹配的,例外的数据被忽略,该方法的本质是在两个序列中包含一定比率的相匹配的子序列。该方法避免了欧几里得距离的缺点,任意长度序列的相似性的判定使用统一的标准。但是相似性的判定在包络线边界处发生了突变。     

寻找地震相关地区的时间序列相似性匹配算法

把时间序列相似性匹配的基本概念和方法引入到地震预报的应用中.在分析现阶段时间序列研究成果的基础上,结合大量地震历史源数据和领域专家经验知识,提出了有关地震地区相关性的地震相似度定义和地震序列相似性匹配模型,并通过大量实验模拟对该模型进行了反复验证,实现了基于地震相似度的时间序列相似性匹配算法.同时,通过分析我国地震活动频繁区域近20年来的地震历史数据,应用地震区域序列相似性匹配算法进行了固定时间差的粗粒度和细粒度纵向序列相似性实验分析,取得了可信度较高的实验结果,为地震学预测的应用研究提供了较好的技术支持.     

时间序列序列模式的相似性研究

时间序列序列模式相似性的度量是从时间序列中获取时序关联规则的重要环节。一般情况下,距离度量法只能度量相同长度序列模式的相似性。借用动态时间弯曲距离的思想,这种基于非线性弯曲技术的算法可以获得很高的识别、匹配精度。在定义元模式相似性的基础上,定义了序列模式的动态时间弯曲距离,最后用两个不同时间序列进行仿真实验,可以得到不同长度的序列的相似度。     

基于三角不等式的时间序列相似性搜索算法

由于传统的时序相似性度量方式不满足距离三角不等式关系,影响后续的相似性搜索及关联规则的获取,在时序符号化的基础上,提出一种满足三角不等式的符号化距离度量方式。与MINDIST_PAA_SAX和Sym_PAA_SAX度量方式进行比较,其结果表明,该度量方式在异常检测和相似性查询上具有较好的优越性。实验结果表明,该方法在相似性搜索及关联规则的获取方面具有更高的可信度。     

Prediction of uncertain structural responses using fuzzy time series

Numerical methods for the prediction of uncertain structural responses with the aid of fuzzy time series are presented. Uncertain data, uncertain measured actions, and uncertain structural responses over time are considered as time series comprised of fuzzy data. Uncertain data are described by means of a new incremental fuzzy representation, which permits a complete and accurate estimation of uncertainty. The fuzzy time series are regarded as realizations of a fuzzy random process. Methods for identification and quantification of the underlying fuzzy random process are developed. The concepts of model-free and of model-based forecasting are addressed. These concepts enable the prediction of data in the form of optimal forecasts, fuzzy forecast intervals, and fuzzy random forecasts. The algorithms are demonstrated by way of practical examples.     

基于特征点分段的多元时间序列相似性搜索

现有的各种多元时间序列相似性搜索方法难以准确高效地完成搜索任务。提出了一种基于特征点分段的多元时间序列相似性搜索算法,提取所定义的用于分段的特征点,分段后将原时间序列转化为模式序列,该模式序列能够很好地保留原序列的全局形状特征,再用分层匹配的方法进行相似性搜索。实验结果表明,该方法能够有效刻画序列的全局形状特征,通过分层匹配保留局部的相似性,同时提高搜索准确率。     

Prediction method of autoregressive moving average models for uncertain time series

ABSTRACT

Time series analysis is based on the continuous regularity of the development of objective things to predict the next value depending on observed values. Based on time series analysis, we present autoregressive moving average models to predict the next future value for an uncertain time series. In this paper, imprecise observations and disturbance terms are regarded as uncertain variables and assume that the latter are satisfied uncertain normal distribution. The prediction models of uncertain time series are established combining the knowledge of autoregressive model and uncertainty theory. Therefore, the interval range of the next future value is predicted based on the reliability constraint. As an illustration to compare with the numerical examples of the existing prediction method, the innovations and effectiveness of the work are further demonstrated by the computational results.     

基于趋势的时间序列相似性度量和聚类研究

由于时间序列的长度很大,并且不确定时间序列在每个采样点的取值具有不确定性,导致时间序列在相似性匹配和聚类挖掘中时间复杂度很高,为了解决该问题,提出了基于趋势的时间序列相似性度量方法和聚类方法.其中基于趋势的相似性度量方法根据时间序列的整体变化趋势,将时间序列映射为短的趋势符号序列,并利用各趋势的一阶连接性指数和塔尼莫特系数完成相似性度量;基于趋势的聚类方法通过定义趋势高度,并对趋势符号序列迭代进行区间划分和趋势判断,并以此构建趋势树,最后将趋势树根节点中趋势符号相同的序列聚集为一类.实验结果表明:a)五种趋势符号的一阶连接性指数可唯一地表示一条时间序列;b)基于趋势的相似性度量方法在多项式时间内可有效完成时间序列的相似性匹配;c)基于趋势的聚类方法将序列的相似性度量和聚类过程集中在一起,聚类效果显著.     

基于关键点的不同长度时间序列相似性度量

目前,时间序列的相似性大多是在原始序列上进行判断和比较的,原始序列维度较高,计算量大,不利于相似性比较。提出了新的关键点（转折点或极值点）算法,除利用常用的极值法求非单调序列的关键点外,还提出了求单调序列关键点的新算法,利用该算法可以压缩时间序列,降低维度,又能保持序列的轮廓。在关键点时间序列上提出了新的相似性判定算法,利用该算法可计算任意两序列的相似度,并且提高了相似性判定的鲁棒性,减少人为干预设置阈值带来的影响。实验结果表明,基于时间序列关键点的相似性算法能很好地判定任意两序列的相似性,减少了计算量,提高了鲁棒性及减少人为干扰,对时间序列数据挖掘中的聚类与预测有很好的帮助作用。     

Forecasting daily time series using periodic unobserved components time series models

A periodic time series analysis is explored in the context of unobserved components time series models that include stochastic time functions for trend, seasonal and irregular effects. Periodic time series models allow dynamic characteristics (autocovariances) to depend on the period of the year, month, week or day. In the standard multivariate approach one can interpret a periodic time series analysis as a simultaneous treatment of typically yearly time series where each series is related to a particular season. Here, the periodic analysis applies to a vector of monthly time series related to each day of the month. Particular focus is on the forecasting performance and therefore on the underlying periodic forecast function, defined by the in-sample observation weights for producing (multi-step) forecasts. These weight patterns facilitate the interpretation of periodic model extensions. A statistical state space approach is used to estimate the model and allows for irregularly spaced observations in daily time series. Recent algorithms are adopted for the computation of observation weights for forecasting based on state space models with regressor variables. The methodology is illustrated for daily Dutch tax revenues that appear to have periodic dynamic properties. The dimension of our periodic unobserved components model is relatively large as we allow each element (day) of the vector of monthly time series to have a changing seasonal pattern. Nevertheless, even with only five years of data we find that the increased periodic flexibility can help in out-of-sample forecasting for two extra years of data.     

Weighted dynamic time warping for time series classification

Dynamic time warping (DTW), which finds the minimum path by providing non-linear alignments between two time series, has been widely used as a distance measure for time series classification and clustering. However, DTW does not account for the relative importance regarding the phase difference between a reference point and a testing point. This may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition. Therefore, we propose a novel distance measure, called a weighted DTW (WDTW), which is a penalty-based DTW. Our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers. The rationale underlying the proposed distance measure is demonstrated with some illustrative examples. A new weight function, called the modified logistic weight function (MLWF), is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point. By applying different weights to adjacent points, the proposed algorithm can enhance the detection of similarity between two time series. We show that some popular distance measures such as DTW and Euclidean distance are special cases of our proposed WDTW measure. We extend the proposed idea to other variants of DTW such as derivative dynamic time warping (DDTW) and propose the weighted version of DDTW. We have compared the performances of our proposed procedures with other popular approaches using public data sets available through the UCR Time Series Data Mining Archive for both time series classification and clustering problems. The experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

改进的SIFT邻域投票图像匹配算法

针对传统图像匹配算法在几何差异场景下匹配精度低的问题,提出一种改进SIFT特征描述符和邻域投票相结合的图像匹配算法。使用8个邻域像素的平均值代替原始极值点,通过SIFT提取图像中的特征点,利用Sobel算子计算特征点的梯度幅度和方向,结合8个仿射形式的同心圆邻域生成64维描述符,根据欧氏距离确定初始匹配点,采用邻域投票的方法剔除错误的匹配点,实现图像的精确匹配。实验结果表明,该算法在显著提高匹配精度的同时缩短了匹配时间,对复杂场景的匹配性能明显提升。