Research On Similarity of Stochastic Non-stationary Time Series Data Based on Wavelet-Fractal

Traditional dimension reduction methods about similarity query introduce the smoothness to data series in some degree, but lead to the disappearance of the important features of time series about non-linearity and fractal. The matching method based on wavelet transformation measures the similarity by using the distance standard at some resolution level. But in the case of an unknown fractal dimension of non-stationary time series, the local error of similarity matching of series increases. The process of querying the similarity of curve figures will be affected to a certain degree. Stochastic non-stationary time series show the non-linear and fractal characters in the process of time-space kinetics evolution. The concept of series fractal time-varying dimension is presented. The original Fractal Brownian Motion model is reconstructed to be a stochastic process with local self-similarity. The Daubechies wavelet is used to deal with the local self-similarity process. An evaluation formula of the time-varying Hurst index is established. The algorithm of time-varying index is presented, and a new determinant standard of series similarity is also introduced. Similarity of the basic curve figures is queried and measured at some resolution ratio level, in the meantime, the fractal dimension in local similarity is matched. The effectiveness of the method is validated by means of the simulation example in the end. ∗ Supported by the National Natural Science Foundation of China under Grant Nos.69933010, 70371042 (国家自然科学基金); the China Post-Doctor Science Foundation under Grant No.2003033310 (中国博士后科学基金) ZHAO Hui was born in 1968. She is a post-doctor at the Department of Computer Information and Technology, Fudan University. Her research areas are data mining, database and the applications based on mobile agent. HOU Jian-Rong was born in 1965. He is a post-doctor at the School of Aetna Management, Shanghai Jiaotong University. His research areas are mathematical optimization, fractal, and wavelet analysis, with the applications in Web data mining. SHI Bai-Le was born in 1935. He is a professor and doctoral supervisor at the Department of Computer Information and Technology, Fudan University. His main research areas are database theory, data mining, digital library technology and optimization of stochastic system. 634 Journal of Software 软件学报 2004,15(5)