Research Of Time Series Representation Based On Value-radius Complex Function

Time series data mining has attracted more and more domestic and foreignscholars and experts. Because many 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 beingdisturbed 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’ methods, 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 describe 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 paper, 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-tail 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 information.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 thesis confirms by the experiment thatcomparing to the other widely-used time series representation methods this paper’smethod basing on value-radius complex function has an obvious advantage in aspectof not only time series classification effectiveness but also classification stability,.