arXiv subjects

Hau-tieng Wu

Publications and source records attributed to Hau-tieng Wu.

At least 19 recordsLinked to original sources

arXiv2024

When Locally Linear Embedding Hits Boundary

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algorithm which is a potential approach to recover the Dirichlet Laplace-Beltrami operator.

math.ST↗

arXiv2023

Enhancing Missing Data Imputation of Non-stationary Signals with Harmonic Decomposition

Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibit non-stationary oscillatory behavior. In this paper, we introduce a novel algorithm, coined Harmonic Level Interpolation (HaLI), which enhances the performance of existing imputation algorithms for oscillatory time series. After running any chosen imputation algorithm, HaLI leverages the harmonic decomposition based on the adaptive nonharmonic model of the initial imputation to improve the imputation accuracy for oscillatory time series. Experimental assessments conducted on synthetic and real signals consistently highlight that HaLI enhances the performance of existing imputation algorithms. The algorithm is made publicly available as a readily employable Matlab code for other researchers to use.

eess.SP↗

arXiv2020

On the behavior of $1$-Laplacian Ratio Cuts on nearly rectangular domains

Given a connected set $Ω_0 \subset \mathbb{R}^2$, define a sequence of sets $(Ω_n)_{n=0}^{\infty}$ where $Ω_{n+1}$ is the subset of $Ω_n$ where the first eigenfunction of the (properly normalized) Neumann $p-$Laplacian $ -Δ^{(p)} ϕ= λ_1 |ϕ|^{p-2} ϕ$ is positive (or negative). For $p=1$, this is also referred to as the Ratio Cut of the domain. We conjecture that, unless $Ω_0$ is an isosceles right triangle, these sets converge to the set of rectangles with eccentricity bounded by 2 in the Gromov-Hausdorff distance as long as they have a certain distance to the boundary $\partial Ω_0$. We establish some aspects of this conjecture for $p=1$ where we prove that (1) the 1-Laplacian spectral cut of domains sufficiently close to rectangles of a given aspect ratio is a circular arc that is closer to flat than the original domain (leading eventually to quadrilaterals) and (2) quadrilaterals close to a rectangle of aspect ratio $2$ stay close to quadrilaterals and move closer to rectangles in a suitable metric. We also discuss some numerical aspects and pose many open questions.

math.SP↗

arXiv2019

A Novel Feature Representation for Single-Channel Heartbeat Classification based on Adaptive Fourier Decomposition

This paper proposes a novel approach for heartbeat classification from single-lead electrocardiogram (ECG) signals based on the novel adaptive Fourier decomposition (AFD). AFD is a recently developed signal processing tool that provides useful morphological features, referred to as AFD-derived instantaneous frequency (IF) features, that are different from those provided by traditional tools. A support vector machine (SVM) classifier is trained with the AFD-derived IF features, ECG landmark features, and RR interval features. To evaluate the performance of the trained classifier, the Association for the Advancement of Medical Instrumentation (AAMI) standard is applied to the publicly available benchmark databases, including MIT-BIH arrhythmia database and MIT-BIH supraventricular arrhythmia database, to classify heartbeats from single-lead ECG. The overall performance in terms of sensitivities and positive predictive values is comparable to the state-of-the-art automatic heartbeat classification algorithms based on two-leads ECG.

eess.SP↗

arXiv2019

Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification

We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information from two electroencephalograms (EEG). The diffusion geometry approach helps organize the nonlinear dynamical structure hidden in the EEG signal. The visualization is achieved by the nonlinear dimension reduction capability of the chosen diffusion geometry algorithms. For the automatic annotation purpose, the {support vector machine} is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC$^*$ {(SC = Sleep Cassette)} and ST$^*$ {(ST = Sleep Telemetry)}, with the leave-one-subject-out cross validation. When we have a single EEG channel (Fpz-Cz), the overall accuracy, macro F1 and Cohen's kappa achieve $82.72\%$,$75.91\%$ and $76.1\%$ respectively in Sleep-EDF SC$^*$ and $78.63\%$, $73.58\%$ and $69.48\%$ in Sleep-EDF ST$^*$. This performance is compatible {with} the state-of-the-art results. When we have two EEG channels (Fpz-Cz and Pz-Oz), the overall accuracy, macro F1 and Cohen's kappa achieve $84.44\%$,$78.25\%$ and $78.36\%$ respectively in Sleep-EDF SC$^*$ and $79.05\%$, $74.73\%$ and $70.31\%$ in Sleep-EDF ST$^*$. The results suggest the potential of the proposed algorithm in practical applications.

eess.SP↗

arXiv2019

On Zeroes of Random Polynomials and Applications to Unwinding

Let $μ$ be a probability measure in $\mathbb{C}$ with a continuous and compactly supported density function, let $z_1, \dots, z_n$ be independent random variables, $z_i \sim μ$, and consider the random polynomial $$ p_n(z) = \prod_{k=1}^{n}{(z - z_k)}.$$ We determine the asymptotic distribution of $\left\{z \in \mathbb{C}: p_n(z) = p_n(0)\right\}$. In particular, if $μ$ is radial around the origin, then those solutions are also distributed according to $μ$ as $n \rightarrow \infty$. Generally, the distribution of the solutions will reproduce parts of $μ$ and condense another part on curves. We use these insights to study the behavior of the Blaschke unwinding series on random data.

math.PR↗

arXiv2019

Recycling cardiogenic artifacts in impedance pneumography

Purpose: Biomedical sensors often exhibit cardiogenic artifacts which, while distorting the signal of interest, carry useful hemodynamic information. We propose an algorithm to remove and extract hemodynamic information from these cardiogenic artifacts. Methods: We apply a nonlinear time-frequency analysis technique, the de-shape synchrosqueezing transform (dsSST), to adaptively isolate the high- and low-frequency components of a single-channel signal. We demonstrate this technique's effectiveness by removing and deriving hemodynamic information from the cardiogenic artifact in an impedance pneumography (IP). Results: The instantaneous heart rate is extracted, and the cardiac and respiratory signals are reconstructed. Conclusions: The dsSST is suitable for generating useful hemodynamic information from the cardiogenic artifact in a single-channel IP. We propose that the usefulness of the dsSST as a recycling tool extends to other biomedical sensors exhibiting cardiogenic artifacts.

physics.data-an↗

arXiv2019

Fetus: the radar of maternal stress, a cohort study

Objective: We hypothesized that prenatal stress (PS) exerts lasting impact on fetal heart rate (fHR). We sought to validate the presence of such PS signature in fHR by measuring coupling between maternal HR (mHR) and fHR. Study design: Prospective observational cohort study in stressed group (SG) mothers with controls matched for gestational age during screening at third trimester using Cohen Perceived Stress Scale (PSS) questionnaire with PSS-10 equal or above 19 classified as SG. Women with PSS-10 less than 19 served as control group (CG). Setting: Klinikum rechts der Isar of the Technical University of Munich. Population: Singleton 3rd trimester pregnant women. Methods: Transabdominal fetal electrocardiograms (fECG) were recorded. We deployed a signal processing algorithm termed bivariate phase-rectified signal averaging (BPRSA) to quantify coupling between mHR and fHR resulting in a fetal stress index (FSI). Maternal hair cortisol was measured at birth. Differences were assumed to be significant for p value less than 0.05. Main Outcome Measures: Differences for FSI between both groups. Results: We screened 1500 women enrolling 538 of which 16.5 % showed a PSS-10 score equal or above 19 at 34+0 weeks. Fifty five women eventually comprised the SG and n=55 served as CG. Median PSS was 22.0 (IQR 21.0-24.0) in the SG and 9.0 (6.0-12.0) in the CG, respectively. Maternal hair cortisol was higher in SG than CG at 86.6 (48.0-169.2) versus 53.0 (34.4-105.9) pg/mg. At 36+5 weeks, FSI was significantly higher in fetuses of stressed mothers when compared to controls [0.43 (0.18-0.85) versus 0.00 (-0.49-0.18)]. Conclusion: Our findings show a persistent effect of PS affecting fetuses in the last trimester.

q-bio.QM↗

arXiv2019

Differentiation of skin incision and laparoscopic trocar insertion via quantifying transient bradycardia measured by electrocardiogram

Background. Most surgical procedures involve structures deeper than the skin. However, the difference in surgical noxious stimulation between skin incision and laparoscopic trocar insertion is unknown. By analyzing instantaneous heart rate (IHR) calculated from the electrocardiogram, in particular the transient bradycardia in response to surgical stimuli, this study investigates surgical noxious stimuli arising from skin incision and laparoscopic trocar insertion. Methods. Thirty-five patients undergoing laparoscopic cholecystectomy were enrolled in this prospective observational study. Sequential surgical steps including umbilical skin incision (11 mm), umbilical trocar insertion (11 mm), xiphoid skin incision (5 mm), xiphoid trocar insertion (5 mm), subcostal skin incision (3 mm), and subcostal trocar insertion (3 mm) were investigated. IHR was derived from electrocardiography and calculated by the modern time-varying power spectrum. Similar to the classical heart rate variability analysis, the time-varying low frequency power (tvLF), time-varying high frequency power (tvHF), and tvLF-to-tvHF ratio (tvLHR) were calculated. Prediction probability (PK) analysis and global pointwise F-test were used to compare the performance between indices and the heart rate readings from the patient monitor. Results. Analysis of IHR showed that surgical stimulus elicits a transient bradycardia, followed by the increase of heart rate. Transient bradycardia is more significant in trocar insertion than skin incision. The IHR change quantifies differential responses to different surgical intensity. Serial PK analysis demonstrates de-sensitization in skin incision, but not in laparoscopic trocar insertion. Conclusions. Quantitative indices present the transient bradycardia introduced by noxious stimulation. The results indicate different effects between skin incision and trocar insertion.

q-bio.QM↗

arXiv2018

Diffusion geometry approach to efficiently remove electrical stimulation artifacts in intracranial electroencephalography

Cortical oscillations, electrophysiological activity patterns, associated with cognitive functions and impaired in many psychiatric disorders can be observed in intracranial electroencephalography (iEEG). Direct cortical stimulation (DCS) may directly target these oscillations and may serve as therapeutic approaches to restore functional impairments. However, the presence of electrical stimulation artifacts in neurophysiological data limits the analysis of the effects of stimulation. Currently available methods suffer in performance in the presence of nonstationarity inherent in biological data. Our algorithm, Shape Adaptive Nonlocal Artifact Removal (SANAR) is based on unsupervised manifold learning. By estimating the Euclidean median of k nearest neighbors of each artifact in a nonlocal fashion, we obtain a faithful representation of the artifact which is then subtracted. This approach overcomes the challenges presented by nonstationarity. SANAR is effective in removing stimulation artifacts in the time domain while preserving the spectral content of the endogenous neurophysiological signal. We demonstrate the performance in a simulated dataset as well as in human iEEG data. Using two quantitative measures, that capture how much of information from endogenous activity is retained, we demonstrate that SANAR's performance exceeds that of one of the widely used approaches, independent component analysis, in the time domain as well as the frequency domain. This approach allows for the analysis of iEEG data, single channel or multiple channels, during DCS, a crucial step in advancing our understanding of the effects of periodic stimulation and developing new therapies.

physics.med-ph↗

arXiv2018

Sleep-wake classification via quantifying heart rate variability by convolutional neural network

Fluctuations in heart rate are intimately tied to changes in the physiological state of the organism. We examine and exploit this relationship by classifying a human subject's wake/sleep status using his instantaneous heart rate (IHR) series. We use a convolutional neural network (CNN) to build features from the IHR series extracted from a whole-night electrocardiogram (ECG) and predict every 30 seconds whether the subject is awake or asleep. Our training database consists of 56 normal subjects, and we consider three different databases for validation; one is private, and two are public with different races and apnea severities. On our private database of 27 subjects, our accuracy, sensitivity, specificity, and AUC values for predicting the wake stage are 83.1%, 52.4%, 89.4%, and 0.83, respectively. Validation performance is similar on our two public databases. When we use the photoplethysmography instead of the ECG to obtain the IHR series, the performance is also comparable. A robustness check is carried out to confirm the obtained performance statistics. This result advocates for an effective and scalable method for recognizing changes in physiological state using non-invasive heart rate monitoring. The CNN model adaptively quantifies IHR fluctuation as well as its location in time and is suitable for differentiating between the wake and sleep stages.

stat.AP↗

arXiv2018

Analyzing transient-evoked otoacoustic emissions by concentration of frequency and time

The linear part of transient evoked (TE) otoacoustic emission (OAE) is thought to be generated via coherent reflection near the characteristic place of constituent wave components. Because of the tonotopic organization of the cochlea, high frequency emissions return earlier than low frequencies; however, due to the random nature of coherent reflection, the instantaneous frequency (IF) and amplitude envelope of TEOAEs both fluctuate. Multiple reflection components and synchronized spontaneous emissions can further make it difficult to extract the IF by linear transforms. In this paper, we propose to model TEOAEs as a sum of {\em intrinsic mode-type functions} and analyze it by a {nonlinear-type time-frequency analysis} technique called concentration of frequency and time (ConceFT). When tested with synthetic OAE signals {with possibly multiple oscillatory components}, the present method is able to produce clearly visualized traces of individual components on the time-frequency plane. Further, when the signal is noisy, the proposed method is compared with existing linear and bilinear methods in its accuracy for estimating the fluctuating IF. Results suggest that ConceFT outperforms the best of these methods in terms of optimal transport distance, reducing the error by 10 to {21\%} when the signal to noise ratio is 10 dB or below.

eess.SP↗

arXiv2018

A Novel Blaschke Unwinding Adaptive Fourier Decomposition based Signal Compression Algorithm with Application on ECG Signals

This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD). The Blaschke unwinding AFD is a newly developed signal decomposition theory. It utilizes the Nevanlinna factorization and the maximal selection principle in each decomposition step, and achieves a faster convergence rate with higher fidelity. The proposed compression algorithm is applied to the electrocardiogram signal. To assess the performance of the proposed compression algorithm, in addition to the generic assessment criteria, we consider the less discussed criteria related to the clinical needs -- for the heart rate variability analysis purpose, how accurate the R peak information is preserved is evaluated. The experiments are conducted on the MIT-BIH arrhythmia benchmark database. The results show that the proposed algorithm performs better than other state-of-the-art approaches. Meanwhile, it also well preserves the R peak information.

eess.SP↗

arXiv2017

Non-invasive biomarkers of fetal brain development reflecting prenatal stress: an integrative multi-scale multi-species perspective on data collection and analysis

Prenatal stress (PS) impacts early postnatal behavioural and cognitive development. This process of 'fetal programming' is mediated by the effects of the prenatal experience on the developing hypothalamic-pituitary-adrenal (HPA) axis and autonomic nervous system (ANS). The HPA axis is a dynamic system regulating homeostasis, especially the stress response, and is highly sensitive to adverse early life experiences. We review the evidence for the effects of PS on fetal programming of the HPA axis and the ANS. We derive a multi-scale multi-species approach to devising preclinical and clinical studies to identify early non-invasively available pre- and postnatal biomarkers of these programming effects. Such approach would identify adverse postnatal brain developmental trajectories, a prerequisite for designing therapeutic interventions. The multiple scales include the biomarkers reflecting changes in the brain epigenome, metabolome, microbiome and the ANS activity gauged via an array of advanced non-invasively obtainable properties of fetal heart rate fluctuations. The proposed framework has the potential to reveal mechanistic links between maternal stress during pregnancy and changes across these physiological scales. Such biomarkers may hence be useful as early and non-invasive predictors of neurodevelopmental trajectories influenced by the PS. We conclude that studies into PS effects must be conducted on multiple scales derived from concerted observations in multiple animal models and human cohorts performed in an interactive and iterative manner and deploying machine learning for data synthesis, identification and validation of the best non-invasive biomarkers.

q-bio.QM↗

arXiv2017

Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian

Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle. As a result, we can construct a distance in this class which leads to a pre-compactness theorem on the class under consideration.

math.DG↗

arXiv2017

Latent common manifold learning with alternating diffusion: analysis and applications

The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion. A method based on alternating diffusion is presented and analyzed; we provide theoretical analysis of the method under the latent common manifold model. To exemplify the power of the proposed framework, experimental results in several applications are reported.

physics.data-an↗

arXiv2017

Entropy-based Time-Varying Window Width Selection for Nonlinear type Time-Frequency Analysis

We propose a time-varying optimal window width (TVOWW) selection scheme to optimize the performance of several nonlinear-type time-frequency analyses, including the reassignment method, and the synchrosqueezing transform (SST) and its variations. A window rendering the most concentrated distribution in the time-frequency representation (TFR) is regarded as the optimal window. The TVOWW selection scheme is particularly useful for signals that comprise fast-varying instantaneous frequencies and small spectral gaps. To demonstrate the efficacy of the method, in addition to analyzing a synthetic signal, we study an atomic time-varying dipole moment driven by two-color mid-infrared laser fields in attosecond physics.

physics.data-an↗

arXiv2017

Efficient fetal-maternal ECG signal separation from two channel maternal abdominal ECG via diffusion-based channel selection

There is a need for affordable, widely deployable maternal-fetal ECG monitors to improve maternal and fetal health during pregnancy and delivery. Based on the diffusion-based channel selection, here we present the mathematical formalism and clinical validation of an algorithm capable of accurate separation of maternal and fetal ECG from a two channel signal acquired over maternal abdomen.

physics.med-ph↗