Browsing by Author "Wu, HT"

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    Analysis of click-evoked otoacoustic emissions by concentration of frequency and time: Preliminary results from normal hearing and Ménière's disease ears
    (AIP Conference Proceedings, 2018-05-31) Liu, TC; Wu, HT; Chen, YH; Chen, YH; Fang, TY; Wang, PC; Liu, YW
    © 2018 Author(s). The presence of click-evoked (CE) otoacoustic emissions (OAEs) has been clinically accepted as an indicator of normal cochlear processing of sounds. For treatment and diagnostic purposes, however, clinicians do not typically pay attention to the detailed spectrum and waveform of CEOAEs. A possible reason is due to the lack of noise-robust signal processing tools to estimate physiologically meaningful time-frequency properties of CEOAEs, such as the latency of spectral components. In this on-going study, we applied a modern tool called concentration of frequency and time (ConceFT, [1]) to analyze CEOAE waveforms. Randomly combined orthogonal functions are used as windowing functions for time-frequency analysis. The resulting spectrograms are subject to nonlinear time-frequency reassignment so as to enhance the concentration of time-varying sinusoidal components. The results after reassignment could be further averaged across the random choice of windows. CEOAE waveforms are acquired by a linear averaging paradigm, and longitudinal data are currently being collected from patients with Ménière's disease (MD) and a control group of normal hearing subjects. When CEOAE is present, the ConceFT plots show traces of decreasing but fluctuating instantaneous frequency against time. For comparison purposes, same processing methods are also applied to analyze CEOAE data from cochlear mechanics simulation.
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    On the spectral property of kernel-based sensor fusion algorithms of high dimensional data
    Ding, X; Wu, HT
    In this paper, we apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two sequences of random vectors $\mathcal{X}:=\{\xb_i\}_{i=1}^n$ and $\mathcal{Y}:=\{\yb_i\}_{i=1}^n$ under the null hypothesis. The matrix of interest is a product of the kernel matrices associated with $\mathcal{X}$ and $\mathcal{Y}$, which may not be diagonalizable in general. We prove that in the regime where dimensions of both random vectors are comparable to the sample size, if NCCA and AD are conducted using a smooth kernel function, then the first few nontrivial eigenvalues will converge to real deterministic values provided $\mathcal{X}$ and $\mathcal{Y}$ are independent Gaussian random vectors. We propose an eigenvalue-ratio test based on the real parts of the eigenvalues of the product matrix to test if $\mathcal{X}$ and $\mathcal{Y}$ are independent and do not share common information. Simulation study verifies the usefulness of such statistic.
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    On Zeroes of Random Polynomials and an Application to Unwinding
    (International Mathematics Research Notices) Steinerberger, S; Wu, HT