Functional data mining with multiscalestatistical procedures

Multifractality;Wavelets;Hurst exponent;Fractional Brownian motion;Multifractional Brownian motion;Semi-supervised learning

Lee, Kichun ; Industrial and Systems Engineering

University:Georgia Institute of Technology

Department:Industrial and Systems Engineering

关键词: Multifractality;    Wavelets;    Hurst exponent;    Fractional Brownian motion;    Multifractional Brownian motion;    Semi-supervised learning;   

Others  :  https://smartech.gatech.edu/bitstream/1853/34716/1/lee_kichun__201008_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Hurst exponent and variance are two quantities that often characterize real-life, highfrequencyobservations. We develop the method for simultaneous estimation of a timechangingHurst exponent H(t) and constant scale (variance) parameter C in a multifractionalBrownian motion model in the presence of white noise based on the asymptotic behavior ofthe local variation of its sample paths. We also discuss the accuracy of the stable and simultaneousestimator compared with a few selected methods and the stability of computationsthat use adapted wavelet filters.Multifractals have become popular as flexible models in modeling real-life data of highfrequency. We developed a method of testing whether the data of high frequency is consistentwith monofractality using meaningful descriptors coming from a wavelet-generated multifractalspectrum. We discuss theoretical properties of the descriptors, their computationalimplementation, the use in data mining, and the effectiveness in the context of simulations,an application in turbulence, and analysis of coding/noncoding regions in DNA sequences.The wavelet thresholding is a simple and effective operation in wavelet domains that selectsthe subset of wavelet coefficients from a noised signal. We propose the selection of thissubset in a semi-supervised fashion, in which a neighbor structure and classification functionappropriate for wavelet domains are utilized. The decision to include an unlabeled coefficientin the model depends not only on its magnitude but also on the labeled and unlabeledcoefficients from its neighborhood. The theoretical properties of the method are discussedand its performance is demonstrated on simulated examples.