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Vidakovic, Brani

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    Classification of High Frequency Pupillary Responses using Schur Monotone Descriptors in Multiscale Domains
    (Georgia Institute of Technology, 2004-09-21) Shi, Bin ; Moloney, Kevin P. ; Pan, Ye ; Emery, V. Kathlene ; Vidakovic, Brani ; Jacko, Julie A. ; Sainfort, François
    This paper addresses the problem of classifying users with different visual abilities based on their pupillary response data while performing computer-based tasks. Multiscale Schur Monotone (MSM) summaries of high frequency pupil diameter measurements are utilized as feature vectors (or input vectors) in this classification. Various MSM measures, such as Shannon, Picard, and Emlen entropies, the Gini coefficient and the Fishlow measure, are investigated to assess their discriminatory characteristics. A combination of classifiers, motivated by Bayesian paradigm, is proposed to minimize and stabilize the misclassification rate in training and test sets with the goal of improving classification accuracy. In addition, the issue of wavelet basis selection for optimal classification performance is discussed. The members of the Pollen wavelet library are included as competitors. The proposed methodology is validated with extensive simulation and applied to high-frequency pupil diameter measurements collected from 36 individuals with varying ocular abilities and pathologies. The expected misclassification rate of our procedure can be as low as 21% by appropriately choosing the Schur Monotone summary and using a properly selected wavelet basis.
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    Assessing the Effects of Atmospheric Stability on the Inertial Subrange of Surface Layer Turbulence using Local and Global Multiscale Approaches
    (Georgia Institute of Technology, 2004-06-19) Shi, Bin ; Vidakovic, Brani ; Albertson, John D. ; Katul, Gabriel
    The conceptual framework for modeling the inertial subrange is strongly influenced by the Richardson cascade, now the subject of various reinterpretations. One apparent departure from the Richardson cascade is attributed to boundary conditions influencing large-scale motion, which in turn, can directly interact with smaller scales thereby destroying the universal statistical scaling attributes of the inertial subrange. Investigating whether boundary conditions and inertial subrange eddies interact continues to be an active research problem in contemporary turbulence research. Using longitudinal (u), lateral (v), and vertical (w) velocities co-located with temperature (T) time series measurements collected in the atmospheric surface layer (ASL), we evaluate whether the inertial subrange is influenced by different stability regimes. The different stability regimes are proxies for different boundary conditions, as upper boundary condition force the mechanical shear and lower boundary condition force surface heating and buoyancy. The novelty of the present work lies in its combined use of global and local scaling properties (e.g. quasi-Hurst exponent, distributional properties of the wavelet coefficients, and Tsallis's thermostatic entropy measures) to assess whether atmospheric stability impacts both local and global inertial subrange scaling.
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    Quantifying the Effects of Atmospheric Stability on the Multifractal Spectrum of Turbulence
    (Georgia Institute of Technology, 2004) Shi, Bin ; Vidakovic, Brani ; Katul, Gabriel
    Over the past decade, several studies suggested possible analogy between price dynamics in the foreign exchange market and atmospheric turbulent flows. Such analogies suggest that applications in business and industry can directly benefit from detailed quantification of the scale-hierarchy existing in fully developed turbulent flows. Numerous studies have already demonstrated the multifractal properties of rough-wall boundary layer turbulence. How atmospheric stability (i.e. boundary conditions) alters the multifractal spectrum (MFS) of turbulent velocity and temperature fluctuations in the atmospheric surface layer remains to be investigated. A challenge of estimating the MFS from time series via traditional regression approaches is the heteroskedastic problem because the variance of the error term are shown to depend on scale. Using a combination of Discrete Wavelet Transforms (DWT) and a Weighted Least Squares (WLS) scheme, heteroskedastic effects are minimized and robust estimation of the scaling parameters needed to compute the MFS is derived. Next, to quantify the effects of atmospheric stability on the MFS, discriminative measures that utilize the left slope (rise), Hurst exponent (maxima), and broadness are employed. Distributional property of the estimators for these discriminative measures are investigated based on Monte Carlo simulations. These summary measures are applied to the MFS of velocity and temperature time series collected in the atmospheric surface layer for a wide range of atmospheric stability conditions. The criteria for success in evaluating how atmospheric stability alters the MFS of a single flow variable time series is formulated as a statistical classification model that properly infers the stability regime when these three discriminative measures are used as input vectors.
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    Multifractal Discrimination Model of High-Frequency Pupil-diameter Measurements
    (Georgia Institute of Technology, 2003-10-10) Shi, Bin ; Moloney, Kevin P. ; Emery, V. Kathlene ; Jacko, Julie A. ; Sainfort, François ; Vidakovic, Brani
    Multifractality present in high frequency pupil diameter measurements, usually connected with irregular scaling behavior and self-similarity, is modeled with statistical accuracy. A multifractal spectrum is used to discriminate pupil behavior measurements from four groups differing in ocular pathology. Broadness and the spectrum maximum, two measures characterizing the multifractal spectrum of observations, are proposed as the distinguishing features among the groups. Analysis based on descriptive statistics and kernel density estimation is provided to obtain the statistical description of the inherited mulitfractality. Model-free classification, together with the model combining technique, is adapted to build a reasonable classifier.