基于GM(0,N)模型的三元区间数序列预测

在工程和经济领域,很多数据序列具有很强的振荡性,这些振荡序列用区间数表示将包含更多信息.三元区间数不仅包含系统特征的上下界,还在中间增加一个偏好值,对三元区间数序列的预测研究具有很好的应用价值.为了使灰色模型GM(0,N)能够直接对三元区间数序列建模,改进了GM(0,N)模型方程的参数设置,将整体贡献系数和滞后项系数取为精确数,而将线性修正项系数和补偿系数设为三元区间数,从而对三元区间数的不同界点进行线性修正和补偿.进一步,为了提高对振荡序列的预测精度,结合马尔科夫预测和序列转换方法对模型的预测序列进行修正. 通过对我国用电量和社会消费品零售总额的预测,表明了所提出的三元区间数多变量灰色模型比单变量灰色模型和区间数序列转换为精确数序列再预测的方法效果更好.     

基于特征点转换的时间序列符号化方法

将时序数据有效地映射到特征空间是时间序列相似性搜索的一个关键问题。文章结合时间序列符号化思想与分段线性表示中分段点选取的思想,提出一种基于特征点转换的时间序列符号化方法FPTS。该方法能有效提取序列的形状特征,在降维和除噪的同时保留序列的极值点特性,支持基于动态时间弯曲距离的相似性度量,克服传统的符号化方法受限于精确匹配的缺陷。实验证明了该方法的准确性和高效性。     

不确定时间序列的规约方法

为提高不确定时间序列的查询效率,在对不确定时间序列数据集进行建模的基础上,提出由不确定时间序列向确定时间序列的 3种规约方法,分别为概率最大法、混合规约法和均值法,并给出具体的规约过程。实验结果表明,上述3种规约方法能减少时间序列的不确定性,为其相似性匹配、搜索和查询操作提供依据。     

基于Haar小波的时间序列相似度量算法的实现

时间序列相似性搜索问题中,涉及到维数简约,对数据进行变换应用于时间序列数据的降维。在详细了解时间序列数据库相似搜索技术的基础上,本文选择Haar小波来处理时间序列,提供了系数子集的良好近似,用C＋＋语言实现基于Haar小波的时间序列相似度量算法。当需要线性数据时．Haar小波变换能够快速且容易的计算出在时间序列和简单编码的长度。     

基于形态表示的时间序列相似性搜索

时间序列是一类重要的复杂数据 ,时间序列知识发现正成为知识发现的研究热点之一 ,时间序列的相似性搜索是时间序列知识发现的重要方面 .提出一种新的基于形态表示的时间序列相似性搜索机制 .该机制采用逐段线性化技术 ,将复杂的时间序列曲线简化为多个直线段 .同时 ,结合时间序列的符号表示思想 ,构造了基于云模型的形态概念树 ,提出了时间序列的形态描述方法——基于云模型的时间序列表示法 ,并在此基础上采用增强动态编程算法实现了时间序列的相似性搜索 .     

时间序列的夹角距离及相似性搜索

提出一种面向相似性搜索的时间序列近似表示和度量方法.在自适应分段线性表示的基础上,使用相邻线段间的夹角构成的角度序列近似表示时间序列,并给出夹角距离度量方法的概念和基本性质的证明过程.序列的夹角距离克服了用点距离度量相似性时鲁棒性差以及物理概念不明确等缺陷,而且具有平移和旋转不变性的突出优点.对人工数据和实际股票数据进行相似搜索,实验结果证明该方法的有效性.     

基于波动特征的时间序列数据挖掘

针对相似度搜索是时间序列数据挖掘的基础,构造鲁棒的动态时间弯曲距离是相似性研究的关键,考虑时间序列特征点的重要意义,引入一种时间序列波动点的抽取方法,采用二叉特征树结构对原序列进行再表达.该方法既提取了序列整体趋势信息,又有效约减了数据维数.对多个数据集的层次聚类实验表明,在保证较高准确率情况下,该方法显著提高了DTW的计算效率.     

基于相关反馈的时间序列相似性搜索

传统的基于相关反馈的时间序列相似性搜索是将正反馈和负反馈融合在一起创建新查询向量,这样并没有充分利用负反馈序列的价值,而且容易对初始查询向量进行过多的更改。本文提出一种基于反馈的时间序列相似搜索方法,将反馈的正相关和负相关序列分开处理,最终的相似序列不但要与正相关序列相似,还要尽量与负相关序列不相似。在UCR数据集上的实验结果表明,本文提出的相似搜索方法与传统的基于反馈的相似搜索方法相比,在某些数据集上可以提高查询的准确率以及查全率。     

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。     

QAR数据多维子序列的相似性搜索

QAR数据的高维度以及维度之间不确定的相互关联性,使得原有低维空间上度量时间序列的相似性的方法不再适用,另一方面由于民航行业的特殊性,利用QAR数据进行相似性搜索来确定飞行故障,对相似性的定义也有特殊的要求。通过专家经验结合一种层次分析算法来确定飞行故障所关联的属性维度的重要性,对QAR数据的多维子序列进行符号化表示,并利用k-d树的特殊性质建立索引,使QAR数据多维子序列的快速相似性搜索成为可能,结合形状和距离对相似性进行定义和度量,实验证明查找速度快,准确度较为满意。     

Finding relevant sequences in time series containing crisp, interval, and fuzzy interval data

Finding similar sequences in time series has received much attention and is a widely studied topic. Most existing approaches in the time series area focus on the efficiency of algorithms but seldom provide a means to handle imprecise data. In this paper, a more general approach is proposed to measure the distance of time sequences containing crisp values, intervals, and fuzzy intervals as well. The concept of distance measurement and its associated dynamic-programming-based algorithms are described. In addition to finding the sequences with similar evolving trends, a means of finding the sequences with opposite evolving tendencies is also proposed, which is usually omitted in current related research but could be of great interest to many users.     

A new approach for determining the length of intervals for fuzzy time series

In the implementations of fuzzy time series forecasting, the identification of interval lengths has an important impact on the performance of the procedure. However, the interval length has been chosen arbitrarily in many papers. Huarng developed a new approach which is called ratio-based lengths of intervals in order to identify the length of intervals. In our paper, we propose a new approach which uses a single-variable constrained optimization to determine the ratio for the length of intervals. The proposed approach is applied to the two well-known time series, which are enrollment data at The University of Alabama and inventory demand data. The obtained results are compared to those of other methods. The proposed method produces more accurate predictions for the future values of used time series.     

Determining relevance of imprecise temporal intervals for cultural heritage information retrieval

Time is an essential concept in cultural heritage applications. Instances of temporal concepts such as time intervals are used for the annotation of cultural objects and also for querying datasets containing information about these objects. Hence it is important to match query and annotation intervals by examining their similarity or closeness. One of the problems is that in many cases time intervals are imprecise. For example, the boundaries of the “Pre-Roman age” and the “Roman age” are inherently imprecise and it may be difficult to distinguish them with clear-cut intervals. In this paper we apply the fuzzy set theory to model imprecise time intervals in order to determine relevance of the relationship between two time intervals. We present a method for matching query and annotation intervals based on their weighted mutual overlapping and closeness. We present (1) methods for calculating these weights to produce a combined measure and (2) results of comparing the combined measure with human evaluators as a case study. The case study takes into consideration archaeological temporal information, which is in most cases inherently fuzzy, and therefore offers a particularly complex and challenging scenario. The results show that our new combined measure that utilizes different weighted measures together in rankings, performs the best in terms of precision and recall. It should be used when ranking annotation intervals according to a given query interval in cultural heritage information retrieval. Our approach intends to be generalizable: overlapping and closeness may be calculated between any two fuzzy temporal intervals. The presented procedure of using user evaluation results as a basis for assigning weights for overlapping and closeness could potentially be used to reveal weights in other domains and purposes as well.     

A non-linear clustering method for fuzzy time series: Histogram damping partition under the optimized cluster paradox

The aim of this paper is to investigate the problem of finding the efficient number of clusters in fuzzy time series. The clustering process has been discussed in the existing literature, and a number of methods have been suggested. These methods have several drawbacks, especially the lack of cluster shape and quantity optimization. There are two critical dimensions in a fuzzy time series clustering: the selection of a proper interval for fuzzy clusters and the optimization of the membership degrees among the fuzzy cluster set. The existing methods for the interval selection assume that the intended data has a short-tailed distribution, and the cluster intervals are established in identical lengths (e.g. Song and Chissom, 1994; Chen, 1996; Yolcu et al., 2009). However, the time series data (particularly in economic research) is rarely short-tailed and mostly converges to long-tail distribution because of the boom-bust market behavior. This paper proposes a novel clustering method named histogram damping partition (HDP) to define sub-clusters on the standard deviation intervals and truncate the histogram of the data by a constraint based on the coefficient of variation. The HDP approach can be used for many different kinds of fuzzy time series models at the clustering stage.     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

Fuzzifying Allen's Temporal Interval Relations

When the time span of an event is imprecise, it can be represented by a fuzzy set, called a fuzzy time interval. In this paper, we propose a framework to represent, compute, and reason about temporal relationships between such events. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events (ldquoRoosevelt died before the beginning of the Cold Warrdquo) but also imprecise relationships (ldquoRoosevelt died just before the beginning of the Cold Warrdquo). We show that, unlike previous models, our model is a generalization that preserves many of the properties of the 13 relations Allen introduced for crisp time intervals. Furthermore, we show how our model can be used for efficient fuzzy temporal reasoning by means of a transitivity table. Finally, we illustrate its use in the context of question answering systems.     

NOE TS fuzzy modelling of nonlinear dynamic systems with uncertainties using symbolic interval-valued data

An approach to Nonlinear Output Error (NOE) modelling using Takagi–Sugeno (TS) fuzzy model for a class of nonlinear dynamic systems having variability in their outputs is presented. Furthermore, the approach is compared and graphically illustrated with other alternate approaches on the basis of interval data and interval membership functions. Assuming the identification method can be repeated offline a number of times under similar conditions, multiple input–output time series can be obtained from the underlying system. These time series are pre-processed using the techniques of statistics and probability theory to generate the envelopes of response (curves outlining the upper and lower extremes of response) at each time instant. Two types of envelopes are described in this research: the max–min envelopes and the envelopes based on the confidence intervals provided by extended Chebyshev's inequality. By incorporating interval data in fuzzy modelling and using the theory of symbolic interval-valued data, a TS fuzzy model with interval antecedent and consequent parameters is obtained. This algorithm provides a model for predicting the expected response as well as envelopes. In order to validate the presented model, a simulation case study is devised in this paper. Moreover, it is demonstrated on the real data obtained from an electro-mechanical throttle valve.     

INTUITIONISTIC FUZZY SETS BASED METHOD FOR FUZZY TIME SERIES FORECASTING

Fuzzy time series models are of great interest in forecasting when the information is imprecise and vague. However, the major problem in fuzzy time series forecasting is the accuracy of the forecasted values. In the present study we propose a hybrid method of forecasting based on fuzzy time series and intuitionistic fuzzy sets. The proposed model is a simplified computational approach that uses the degree of nondeterminacy to establish fuzzy logical relations on time series data. The developed model was implemented on the historical enrollment data for the University of Alabama and the forecasted values were compared with the results of existing methods to show its superiority. The suitability of the proposed method was also examined in forecasting market share prices of the State Bank of India on the Bombay Stock Exchange, India.     

基于核估计和区间聚类的数据流中异常模式发现

研究数据流中异常模式发现问题。为保证可以随时输出当前的异常模式,引入一种简单且有效的数据结构——三层时间区间嵌套模式(TTI),来监测数据流。对新到数据是否为异常加以判断评价的标准不是预先分配的静止阈值,而是由算法(KIC:核估计和置信区间聚类分析)计算得到的动态阈值,从而在仅占用很小内存的前提下提高了算法的准确性。设计的SWMA算法进一步降低了时间和空间复杂度。最后分别在模拟线性模型、非线性模型及带时间戳的真实数据流上对方法的准确性、可行性和时效性进行了验证。     

An effective neural network and fuzzy time series-based hybridized model to handle forecasting problems of two factors

Fuzzy time series forecasting method has been applied in several domains, such as stock market price, temperature, sales, crop production and academic enrollments. In this paper, we introduce a model to deal with forecasting problems of two factors. The proposed model is designed using fuzzy time series and artificial neural network. In a fuzzy time series forecasting model, the length of intervals in the universe of discourse always affects the results of forecasting. Therefore, an artificial neural network- based technique is employed for determining the intervals of the historical time series data sets by clustering them into different groups. The historical time series data sets are then fuzzified, and the high-order fuzzy logical relationships are established among fuzzified values based on fuzzy time series method. The paper also introduces some rules for interval weighing to defuzzify the fuzzified time series data sets. From experimental results, it is observed that the proposed model exhibits higher accuracy than those of existing two-factors fuzzy time series models.