Multiscale Statistical Analysis of Self-Similar Processes with Applications in Geophysics and Health Informatics

Pupil;Wavelets;Self-similar process;Turbulence

Shi, Bin ; Industrial and Systems Engineering

University:Georgia Institute of Technology

Department:Industrial and Systems Engineering

关键词: Pupil;    Wavelets;    Self-similar process;    Turbulence;   

Others  :  https://smartech.gatech.edu/bitstream/1853/6887/1/Shi_Bin_200505_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

In this dissertation, we address the statistical analysis underthe multiscale framework for the self-similar process. Motivatedby the problems arising from geophysics and health informatics, wedevelop a set of statistical measures as discriminative summariesof the self-similar process. These measures include MultiscaleSchur Monotone (MSM) measures, Geometric Attributes ofMultifractal Spectrum(GAMFS), Quasi-Hurst exponents, MallatModel and Tsallis Maxent Model. These measures are usedasmethods to quantify the difference(or similarities) or as input(feature) vectors in the classification model. As the cornstone ofGAMFS, we study the estimation of multifractal spectrum and adopta Weighted Least Squares (WLS) schemes in the wavelet domain tominimize theheteroskedasticeffects , which is inherentbecause the sample variances ofthe wavelet coefficients depend on the scale. We also propose a Combined K-Nearest-Neighbor classifier (Comb-K-NN)to address the inhomogeneity of the class attributes,which is indicated by the large variations between subsets ofinput vectors. The Comb-K-NN classifier stabilizes the variationsin the sense of reducing the misclassification rates. Bayesianjustifications of Comb-K-NN classifier are provided. GAMFS, Quasi-Hurst exponents, Mallat Model and Tsallis MaxentModel are used in the study of assessing the effects ofatmospheric stability on the turbulence measurements in theinertial subrange. We also formulate the criteria for success inevaluating how atmospheric stability alters the MFS of a singleflow variable time series as a statistical classification model.We use the multifractal discriminate model as the solution of thisproblem. Also, high frequency pupil-diameter dynamic measurements,which are well documented as measures of mental workload, aresummarized using both GAMFS and MSM. These summaries are furtherused as the feature vector in the Comb-K-NN classifier. Theserious inhomogeneity among subjects in the same user group makesclassification difficult. These difficulties are overcome by usingComb-K-NN classifier.