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1、学校代码： 10327学号： MG10021008硕士 学位 论文基于值半径复函数的时间序列表达研究院专系：业：信息工程学院计算机应用技术研 究 方 向：图像处理、数据挖掘姓名：杨基文指 导 教 师：完 成 日 期：答 辩 日 期：吴 刚（副教授）2012 年 12 月 20 日2013 年 3 月 13 日RESEARCH OF TIME SERIESREPRESENTATION BASED ONVALUE-RADIUS COMPLEX FUNCTIONA Dissertation Submitted toNanjing University of Finance and Economics
2、For the Academic Degree of Master of EngineeringBYYang JiwenSupervised byAssociate Professor Wu GangSchool of Information and EngineeringNanjing University of Finance and EconomicsJanuary 2013学位论文独创性声明本论文是我个人在导师指导下进行的研究工作及取得的研究成果。论文中除了特别加以标注和致谢的地方外，不包含其他人或其它机构已经发表或撰写过的研究成果。其他同志对本研究的启发和所做的贡献均已在论文中作了明
3、确的声明并表示了谢意。作者签名：日期：学位论文使用授权声明本人完全了解南京财经大学有关保留、使用学位论文的规定，即：学校有权保留送交论文的复印件，允许论文被查阅和借阅；学校可以公布论文的全部或部分内容，可以采用影印、缩印或其它复制手段保存论文。保密的论文在解密后遵守此规定。作者签名：导师签名：日期：摘要时间序列数据挖掘已经受到越来越多的国内外学者和专家的关注，因为时间序列中潜在隐藏着有用的规律和信息，人们希望能获取这些信息来预测未来以及进一步了解事物发展。然而时间序列具有海量复杂、短期波动频繁、易受噪声干扰等特点，使得直接在原始数据上进行挖掘不但效率低下，而且往往也难以获得满意的结果。因此需要
4、对时间序列进行重新表达，以更好的进行数据挖掘算法。本文是在总结前人方法的基础上，提出了一种基于值半径复函数的时间序列表示方法。该表示方法首先将时间序列表示成值半径复函数，然后用该函数的傅里叶变换系数构成描述时间序列的特征向量，那么在相似检索时，只需计算两个时间序列各自特征向量的欧氏距离就可以度量两个时间序列的相似性。该方法的关键就在于值半径复函数的构造。本文是将时间序列数据值作为复函数的实部，将每个序列点的带正负号的半径作为复函数的虚部，而半径定义为该点到左右某个窗口大小的两点连线的垂直距离。另外还对具有特殊性的首尾几个点和波峰波谷点给予了特别处理。本文提出的这个表示方法是希望通过值半径复函数
5、的实部保存时间序列的全局信息，而虚部包含了局部特征信息。因此值半径复函数能很好的保留时间序列的有效信息，而且通过傅里叶变换能极大的压缩数据，同时也便于欧氏距离的度量。本文的第四章还用实验验证了与其他几个使用较广泛的表示方法相比，值半径复函数表示方法不管在时间序列分类效果还是分类稳定性方面，都具有明显的优势。关键词： 时间序列；值半径复函数；峰谷检测；离散傅里叶变换；IABSTRACTTime series data mining has attracted more and more domestic and foreignscholars and experts. Because many
6、useful rules and information are potentiallyhiddened in the time series, people hope to obtain these information in order to predictthe future and further understand the development of things. However, the time seriesdatas are very massive, complex, short-term frequently fluctuant and easily beingdi
7、sturbed by the noise, which makes that directly mining on the original data is notonly inefficient, but also is always difficult to obtain satisfactory result. So it isnecessary to represent the time series in order to better going on the data miningalgorithm. After summarizing the predecessors meth
8、ods, this thesis proposes a newtime series representation method which is basing on the value-radius complexfunction. First of all, in the method time series is represented as the value-radiuscomplex function, then the Fourier transform coefficients of the function is used forfeature vectors to desc
9、ribe the time series.Therefore,when doing the two time seriessimilarity retrieval, we only need to calculate Euclidean distance of their featurevectors. The key of this thesis is how to create the value-radius complex function.Complex function contains the real part and the imaginary part. In this p
10、aper, thevalue of the time series data is considered as the real part of complex functions, andthe imaginary part is the radius of each sequence point. The radius is defined as thevertical distance the point to the line being made up of two points of certain windowsize. In addition, several head-tai
11、l points and peak-valley points are given specialtreatment.The purpose of the representation method presented by this paper is to hope thatthe real part of value-radius complex function can preservate the global information oftime series, and the imaginary part can contain the local feature informat
12、ion.Therefore the value-radius complex functions can be a very good function whichpreserves the effective information of time series, and the fourier transform cangreatly compress the data, at the same time it is convenient for the Euclidean distancemetric. Moreover, the fourth chapter in this thesi
13、s confirms by the experiment thatcomparing to the other widely-used time series representation methods this papersmethod basing on value-radius complex function has an obvious advantage in aspectof not only time series classification effectiveness but also classification stability,.IIKEY WORDS:Time series; Value-radius complex function; Peak and valleydetection; Discrete Fourier transform;III
