arXiv subjects

Hau-Tieng Wu

Publications and source records attributed to Hau-Tieng Wu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications

We introduce a novel ridge detection algorithm for time-frequency (TF) analysis, particularly tailored for intricate nonstationary time series encompassing multiple non-sinusoidal oscillatory components. The algorithm is rooted in the distinctive geometric patterns that emerge in the TF domain due to such non-sinusoidal oscillations. We term this method \textit{shape-adaptive mode decomposition-based multiple harmonic ridge detection} (\textsf{SAMD-MHRD}). A swift implementation is available when supplementary information is at hand. We demonstrate the practical utility of \textsf{SAMD-MHRD} through its application to a real-world challenge. We employ it to devise a cutting-edge walking activity detection algorithm, leveraging accelerometer signals from an inertial measurement unit across diverse body locations of a moving subject.

math.NA↗

arXiv2024

Data-Driven optimal shrinkage of singular values under high-dimensional noise with separable covariance structure with application

We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined {\em extended OptShrink} (eOptShrink) depends on the asymptotic behavior of singular values and singular vectors of the random matrix associated with the noisy data. Based on the developed theory, including the sticking property of non-outlier singular values and delocalization of the non-outlier singular vectors associated with weak signals with a convergence rate, and the spectral behavior of outlier singular values and vectors, we develop three estimators, each of these has its own interest. First, we design a novel rank estimator, based on which we provide an estimator for the spectral distribution of the pure noise matrix, and hence the optimal shrinker called eOptShrink. In this algorithm we do not need to estimate the separable covariance structure of the noise. A theoretical guarantee of these estimators with a convergence rate is given. On the application side, in addition to a series of numerical simulations with a comparison with various state-of-the-art optimal shrinkage algorithms, we apply eOptShrink to extract maternal and fetal electrocardiograms from the single channel trans-abdominal maternal electrocardiogram.

stat.AP↗

arXiv2024

Landmark Alternating Diffusion

Alternating Diffusion (AD) is a commonly applied diffusion-based sensor fusion algorithm. While it has been successfully applied to various problems, its computational burden remains a limitation. Inspired by the landmark diffusion idea considered in the Robust and Scalable Embedding via Landmark Diffusion (ROSELAND), we propose a variation of AD, called Landmark AD (LAD), which captures the essence of AD while offering superior computational efficiency. We provide a series of theoretical analyses of LAD under the manifold setup and apply it to the automatic sleep stage annotation problem with two electroencephalogram channels to demonstrate its application.

cs.LG↗

arXiv2024

Unsupervised Ensembling of Multiple Software Sensors with Phase Synchronization: A Robust Approach For Electrocardiogram-derived Respiration

Objective: We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one EDR signal that is of higher quality. Methods: We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality software sensors based on the respiratory signal quality index, aligned the highest-quality EDRs with a phase synchronization technique based on the graph connection Laplacian, and finally fused those aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR signal. The proposed algorithm was evaluated on two large-scale databases of whole-night polysomnograms. We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms. A sensitivity analysis was carried out for a total of five cases: fusion by taking the mean of EDR signals, and the four cases of EDR signal alignment without and with synchronization and without and with signal quality selection. Results: The sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated by the synchronized correlation (γ-score), optimal transport (OT) distance, and estimated average respiratory rate (EARR) score, all with statistical significance. The sensitivity analysis shows that the signal quality selection and EDR signal alignment are both critical for the performance, both with statistical significance. Conclusion: The sync-ensembled EDR provides robust respiratory information from electrocardiogram. Significance: Phase synchronization is not only theoretically rigorous but also practical to design a robust EDR.

eess.SP↗

arXiv2024

Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold

We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we leverage this insight to establish the existence of a minimizer for KL divergence.

stat.ML↗

arXiv2024

The Manifold Scattering Transform for High-Dimensional Point Cloud Data

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification tasks.

cs.LG↗

arXiv2024

Design a Metric Robust to Complicated High Dimensional Noise for Efficient Manifold Denoising

In this manuscript, we propose an efficient manifold denoiser based on landmark diffusion and optimal shrinkage under the complicated high dimensional noise and compact manifold setup. It is flexible to handle several setups, including the high ambient space dimension with a manifold embedding that occupies a subspace of high or low dimensions, and the noise could be colored and dependent. A systematic comparison with other existing algorithms on both simulated and real datasets is provided. This manuscript is mainly algorithmic and we report several existing tools and numerical results. Theoretical guarantees and more comparisons will be reported in the official paper of this manuscript.

stat.ML↗

arXiv2023

Unveil Sleep Spindles with Concentration of Frequency and Time

Objective: Sleep spindles contain crucial brain dynamics information. We introduce the novel non-linear time-frequency analysis tool 'Concentration of Frequency and Time' (ConceFT) to create an interpretable automated algorithm for sleep spindle annotation in EEG data and to measure spindle instantaneous frequencies (IFs). Methods: ConceFT effectively reduces stochastic EEG influence, enhancing spindle visibility in the time-frequency representation. Our automated spindle detection algorithm, ConceFT-Spindle (ConceFT-S), is compared to A7 (non-deep learning) and SUMO (deep learning) using Dream and MASS benchmark databases. We also quantify spindle IF dynamics. Results: ConceFT-S achieves F1 scores of 0.749 in Dream and 0.786 in MASS, which is equivalent to or surpass A7 and SUMO with statistical significance. We reveal that spindle IF is generally nonlinear. Conclusion: ConceFT offers an accurate, interpretable EEG-based sleep spindle detection algorithm and enables spindle IF quantification.

q-bio.NC↗

arXiv2023

Asymptotic analysis of synchrosqueezing transform -- toward statistical inference with nonlinear-type time-frequency analysis

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then, a central limit theorem result for SST is established. {As an example}, we provide a block bootstrap scheme based on the established SST theory to test if a given time series contains oscillatory components.

math.ST↗

arXiv2023

Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in sleep EEG data is used to illustrate the usefulness of the proposed methodology. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional non-stationary time series without variance lower bounds are established, which could be of independent interest.

stat.ME↗

arXiv2023

Arterial blood pressure waveform in liver transplant surgery possesses variability of morphology reflecting recipients' acuity and predicting short term outcomes

Background: We investigated clinical information underneath the beat-to-beat fluctuation of the arterial blood pressure (ABP) waveform morphology. We proposed the Dynamical Diffusion Map algorithm (DDMap) to quantify the variability of morphology. The underlying physiology could be the compensatory mechanisms involving complex interactions between various physiological mechanisms to regulate the cardiovascular system. As a liver transplant surgery contains distinct periods, we investigated its clinical behavior in different surgical steps. Methods: Our study used DDmap algorithm, based on unsupervised manifold learning, to obtain a quantitative index for the beat-to-beat variability of morphology. We examined the correlation between the variability of ABP morphology and disease acuity as indicated by Model for End-Stage Liver Disease (MELD) scores, the postoperative laboratory data, and 4 early allograft failure (EAF) scores. Results: Among the 85 enrolled patients, the variability of morphology obtained during the presurgical phase was best correlated with MELD-Na scores. The neohepatic phase variability of morphology was associated with EAF scores as well as postoperative bilirubin levels, international normalized ratio, aspartate aminotransferase levels, and platelet count. Furthermore, variability of morphology presents more associations with the above clinical conditions than the common BP measures and their BP variability indices. Conclusions: The variability of morphology obtained during the presurgical phase is indicative of patient acuity, whereas those during the neohepatic phase are indicative of short-term surgical outcomes.

q-bio.QM↗

arXiv2023

Topological Data Analysis Assisted Automated Sleep Stage Scoring Using Airflow Signals

Objective: Breathing pattern variability (BPV), as a universal physiological feature, encodes rich health information. We aim to show that, a high-quality automatic sleep stage scoring based on a proper quantification of BPV extracting from the single airflow signal can be achieved. Methods: Topological data analysis (TDA) is applied to characterize BPV from the intrinsically nonstationary airflow signal, where the extracted features are used to train an automatic sleep stage scoring model using the XGBoost learner. The noise and artifacts commonly present in the airflow signal are recycled to enhance the performance of the trained system. The state-of-the-art approach is implemented for a comparison. Results: When applied to 30 whole night polysomnogram signals with standard annotations, the leave-one-subject-out cross-validation shows that the proposed features (overall accuracy 78.8\%$\pm$8.7\% and Cohen's kappa 0.56$\pm 0.15$) outperforms those considered in the state-of-the-art work (overall accuracy 75.0\%$\pm$9.6\% and Cohen's kappa 0.50$\pm 0.15$) when applied to automatically score wake, rapid eyeball movement (REM) and non-REM (NREM). The TDA features are shown to contain complementary information to the traditional features commonly used in the literature via examining the feature importance. The respiratory quality index is found to be essential in the trained system. Conclusion: The proposed TDA-assisted automatic annotation system can accurately distinguish wake, REM and NREM from the airflow signal. Significance: Since only one single airflow channel is needed and BPV is universal, the result suggests that the TDA-assisted signal processing has potential to be applied to other biomedical signals and homecare problems other than the sleep stage annotation.

stat.AP↗

arXiv2023

An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$, so that the WSF jumps from one to another suddenly, the different WSFs and jumps encode useful information. We present an iterative warping and clustering algorithm to estimate $s_1,\ldots,s_K$ from a nonstationary oscillatory signal with time-varying amplitude and frequency, and hence the change points of the WSFs. The algorithm is a novel combination of time-frequency analysis, singular value decomposition entropy and vector spectral clustering. We demonstrate the efficiency of the proposed algorithm with simulated and real signals, including the voice signal, arterial blood pressure, electrocardiogram and accelerometer signal. Moreover, we provide a mathematical justification of the algorithm under the assumption that the amplitude and frequency of the signal are slowly time-varying and there are finite change points that model sudden changes from one wave-shape function to another one.

eess.SP↗

arXiv2023

Application of de-shape synchrosqueezing to estimate gait cadence from a single-sensor accelerometer placed in different body locations

Objective: Commercial and research-grade wearable devices have become increasingly popular over the past decade. Information extracted from devices using accelerometers is frequently summarized as ``number of steps" (commercial devices) or ``activity counts" (research-grade devices). Raw accelerometry data that can be easily extracted from accelerometers used in research, for instance ActiGraph GT3X+, are frequently discarded. Approach: Our primary goal is proposing an innovative use of the {\em de-shape synchrosqueezing transform} to analyze the raw accelerometry data recorded from a single sensor installed in different body locations, particularly the wrist, to extract {\em gait cadence} when a subject is walking. The proposed methodology is tested on data collected in a semi-controlled experiment with 32 participants walking on a one-kilometer predefined course. Walking was executed on a flat surface as well as on the stairs (up and down). Main Results: The cadences of walking on a flat surface, ascending stairs, and descending stairs, determined from the wrist sensor, are 1.98$\pm$0.15 Hz, 1.99$\pm$0.26 Hz, and 2.03$\pm$0.26 Hz respectively. The cadences are 1.98$\pm$0.14 Hz, 1.97$\pm$0.25 Hz, and 2.02$\pm$0.23 Hz, respectively if determined from the hip sensor, 1.98$\pm$0.14 Hz, 1.93$\pm$0.22 Hz and 2.06$\pm$0.24 Hz, respectively if determined from the left ankle sensor, and 1.98$\pm$0.14 Hz, 1.97$\pm$0.22 Hz, and 2.04$\pm$0.24 Hz, respectively if determined from the right ankle sensor. The difference is statistically significant indicating that the cadence is fastest while descending stairs and slowest when ascending stairs. Also, the standard deviation when the sensor is on the wrist is larger. These findings are in line with our expectations. Conclusion: We show that our proposed algorithm can extract the cadence with high accuracy, even when the sensor is placed on the wrist.

stat.AP↗

arXiv2022

Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud

We systematically study the spectrum of kernel-based graph Laplacian (GL) constructed from high-dimensional and noisy random point cloud in the nonnull setup. The problem is motived by studying the model when the clean signal is sampled from a manifold that is embedded in a low-dimensional Euclidean subspace, and corrupted by high-dimensional noise. We quantify how the signal and noise interact over different regions of signal-to-noise ratio (SNR), and report the resulting peculiar spectral behavior of GL. In addition, we explore the impact of chosen kernel bandwidth on the spectrum of GL over different regions of SNR, which lead to an adaptive choice of kernel bandwidth that coincides with the common practice in real data. This result paves the way to a theoretical understanding of how practitioners apply GL when the dataset is noisy.

math.ST↗

arXiv2022

Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries

We consider the eigenvalue problem $Ax = λx$ where $A \in \mathbb{R}^{n \times n}$ and the eigenvalue is also real $λ\in \mathbb{R}$. If we are given $A$, $λ$ and, additionally, the absolute value of the entries of $x$ (the vector $(|x_i|)_{i=1}^n$), is there a fast way to recover $x$? In particular, can this be done quicker than computing $x$ from scratch? This may be understood as a special case of the phase retrieval problem. We present a randomized algorithm which provably converges in expectation whenever $λ$ is a simple eigenvalue. The problem should become easier when $|λ|$ is large and we discuss another algorithm for that case as well.

math.FA↗

arXiv2022

Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application

Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the 2-dimensional time-frequency representation to a 3-dimensional representation, called time-frequency-chirp rate (TFC) representation, by adding one extra chirp rate parameter so that crossover frequencies are disentangled in higher dimension. The chirplet transform is an algorithm for this lifting idea, which leads to a TFC representation. However, in practice, we found that it has a strong ``blurring'' effect in the chirp rate axis, which limits its application in real-world data. Moreover, to our knowledge, we have limited mathematical understanding of the chirplet transform in the literature. Motivated by the need for the real-world data analysis, in this paper, we propose the synchrosqueezed chirplet transform (SCT) that enhances the TFC representation given by the chirplet transform. The resulting concentrated TFC representation has high contrast so that one can better distinguish different modes with crossover instantaneous frequencies. The basic idea is to use the phase information in the chirplet transform to determine a reassignment rule that sharpens the TFC representation determined by the chirplet transform. We also analyze the chirplet transform and provide theoretical guarantees of SCT.

math.NA↗

arXiv2022

Scalability and robustness of spectral embedding: landmark diffusion is all you need

While spectral embedding is a widely applied dimension reduction technique in various fields, so far it is still challenging to make it scalable to handle ``big data''. On the other hand, the robustness property is less explored and there exists only limited theoretical results. Motivated by the need of handling such data, recently we proposed a novel spectral embedding algorithm, which we coined Robust and Scalable Embedding via Landmark Diffusion (ROSELAND). In short, we measure the affinity between two points via a set of landmarks, which is composed of a small number of points, and ``diffuse'' on the dataset via the landmark set to achieve a spectral embedding. Roseland can be viewed as a generalization of the commonly applied spectral embedding algorithm, the diffusion map (DM), in the sense that it shares various properties of DM. In this paper, we show that Roseland is not only numerically scalable, but also preserves the geometric properties via its diffusion nature under the manifold setup; that is, we theoretically explore the asymptotic behavior of Roseland under the manifold setup, including handling the U-statistics-like quantities, and provide a $L^\infty$ spectral convergence with a rate. Moreover, we offer a high dimensional noise analysis and show that Roseland is robust to noise. We also compare Roseland with other existing algorithms with numerical simulations.

math.ST↗