Burst Detection And Analysis In Time Series

Time series analysis is an important research of data mining, and burst detectionand analysis, which is an inherent problem for time series, has been a hot researchproblem in data mining domain. Burst in time series means abnormal frequency ornumber of data emerges during the current period of time diverging from last period oftime or baseline. Burst detection is also a popular analysis technique of time series thatcan detect or monitor burstiness automatically, so it has been widely used in manyapplications such as finance, disaster and medical research, weather and hydrologyresearch, internet traffic management, science computing and so on. Today there arebroad efforts from research community that more and more burst models and detectionmethods based on different burst definitions have been proposed for differentapplications, producing very different results. Actually, there are several important anddifficult problems in burst research, such as burst detection on time series with noise,long time-span property, or real-time requirement that attract attention extremely, aswell as parameter-free detection methods and evaluation of result accuracy. Meanwhile,burst detection of multiple time series and new applications bring new challenges ofburst research.Based on the above problems, we analyze the advantages and disadvantages ofexisting models. This paper argues the concepts of burst direction—positive andnegative direction, and the form of burst—beginning, smoothing, and end phases withtwo types of beginning and end phases—gradual and sudden shapes. And then burst oftime series is formally defined based on new hypotheses and a novel burst model andtwo detection methods are proposed for fixed-length and real-time applicationsrespectively. Since it is a challenge of getting accurate bursts of real-life applications forevaluation of the burst detection, we propose three measurements for quantitativeanalysis of results and performances. We perform two experiments to evaluate theperformance of fix-length and real-time detection methods. The first experiment useevent sequences (textual data) from Wikipedia and pixel sequences (numerical data)from three gray pictures comparing our fixed-length method with three recognized burstdetection methods. The second experiment, designed mainly for evaluation of updatingstrategies of our real-time method, also utilize two datasets. One is the data of the samepictures used in first experiment and the other is hydrology data of an American river.Burst definition in this paper explicitly explains the shapes and positions ofbeginning and end of burst, and direction and intensity of burst, based on a newhypothesis, i.e. burst is a relative wave with respect to global and local changingaverage. We believe that the problem of whether a certain interval is a burst is differentfrom the problem of whether the intensity of this interval is strong or not. According to the experiments and formal analysis, our parameter-free, linear-time burst detectionapproach can be efficiently applied to detect reasonable burstiness on datasets withnoise, long time-span, real-time or sparse problems. Our method get pretty goodperformances on different datasets with low time cost, so we believe it can be furtherutilized to the time series or data streams from other applications.