Norden Huang

• Doctor of Philosophy
• Head of Department at National Central University

It has been shown that, for full information spectral representation of any time series signal, a spectral form of high-dimensional manifold, known as Holo-Hilbert Spectral Analysis (HHSA), is necessary. The higher-dimensional manifold comes from the additional information of the envelopes of the carriers from a second layer of empirical mode decom...

Background: The Flanker task measures visuospatial attention and assesses the attentional network by distinguishing pathways for enhancing information at attended regions and suppressing information at unattended ones (Kopp et al., 1996). In Parkinson's disease (PD), the attentional network is impaired due to dysfunctional fronto-subcortical circui...

Electrophysiological working memory (WM) research shows brain areas communicate via macroscopic oscillations across frequency bands, generating nonlinear amplitude modulation (AM) in the signal. Traditionally, AM is expressed as the coupling strength between the signal and a prespecified modulator at a lower frequency. Therefore, the idea of AM and...

Aims Our aim was to differentiate patients with mild cognitive impairment (MCI) and Alzheimer’s disease (AD) from cognitively normal (CN) individuals and predict the progression from MCI to AD within a 3-year longitudinal follow-up. A newly developed Holo-Hilbert Spectral Analysis (HHSA) was applied to resting state EEG (rsEEG), and features were e...

Anxiety and mindfulness are two inversely linked traits shown to be involved in various physiological domains. The current study used resting state electroencephalography (EEG) to explore differences between people with low mindfulness-high anxiety (LMHA) (n = 29) and high mindfulness-low anxiety (HMLA) (n = 27). The resting EEG was collected for a...

Electroencephalography (EEG) can reveal the abnormalities of dopaminergic subcortico-cortical circuits in patients with Parkinson’s disease (PD). However, conventional time-frequency analysis of EEG signals cannot fully reveal the non-linear processes of neural activities and interactions. A novel Holo-Hilbert Spectral Analysis (HHSA) was applied t...

Electrophysiological working memory (WM) research has shown that distinct brain areas communicate through macroscopic oscillatory activities across multiple frequency bands. Such cross-frequency interactions generate nonlinear amplitude modulations (AM) in the observed signal. Traditionally, the AM of a signal is expressed as coupling strength betw...

For epidemics such as COVID-19, with a significant population having asymptomatic, untested infection, model predictions are often not compatible with data reported only for the cases confirmed by laboratory tests. Additionally, most compartmental models have instantaneous recovery from infection, contrary to observation. Tuning such models with ob...

Non-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical change...

Patterns in external sensory stimuli can rapidly entrain neuronally generated oscillations observed in electrophysiological data. Here, we manipulated the temporal dynamics of visual stimuli with cross-frequency coupling (CFC) characteristics to generate steady-state visual evoked potentials (SSVEPs). Although CFC plays a pivotal role in neural com...

Non-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical change...

Visual working memory (VWM) relies on sustained neural activities that code information via various oscillatory frequencies. Previous studies, however, have emphasized time-frequency power changes, while overlooking the possibility that rhythmic amplitude variations can also code frequency-specific VWM information in a completely different dimensio...

The spread of an epidemic should be a phenomenon governed by the natural growth law: More infected beget more infections. This basic rule would be useful especially when an outbreak is caused by a novel virus with its basic characteristics full of unknowns so much that there would be too many uncertainties that would be impossible for anyone to run...

New COVID-19 epicenters have sprung up in Europe and US as the epidemic in China wanes. Many mechanistic models’ past predictions for China were widely off the mark (1, 2), and still vary widely for the new epicenters, due to uncertain disease characteristics. The epidemic ended in Wuhan, and later in South Korea, with less than 1% of their populat...

The response latency of steady-state visually evoked potentials (SSVEPs) is a sensitive measurement for investigating visual functioning of the human brain, specifically in visual development and for clinical evaluation. This latency can be measured from the slope of phase versus frequency of responses by using multiple frequencies of stimuli. In a...

Natural sensory signals have nonlinear structures dynamically composed of the carrier frequencies and the variation of the amplitude (i.e., envelope). How the human brain processes the envelope information is still poorly understood, largely due to the conventional analysis failing to quantify it directly. Here, we used a recently developed method,...

Data presented are related to the research article entitled “Using Holo-Hilbert spectral analysis to quantify the modulation of Dansgaard-Oeschger events by obliquity” (J. Deng et al., 2018). The datasets in Deng et al. (2018) are analyzed on the foundation of ensemble empirical mode decomposition (EEMD) (Z.H. Wu and N.E. Huang, 2009), and reveal m...

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may overlook the simultaneous and reciprocal nature of causal interactions observed in real world phenomena. Here, we present a causal decomposition approach that is not based on prediction, but based on the in...

Astronomical forcing (obliquity and precession) has been thought to modulate Dansgaard-Oeschger (DO) events, yet the detailed quantification of such modulations has not been examined. In this study, we apply the novel Holo-Hilbert Spectral Analysis (HHSA) to five polar ice core records, quantifying astronomical forcing's time-varying amplitude modu...

The intrinsic composition and functional relevance of resting-state blood oxygen level–dependent signals are fundamental in research using functional magnetic resonance imaging (fMRI). Using the Hilbert–Huang Transform to estimate high-resolution time-frequency spectra, we investigated the instantaneous frequency and amplitude modulation of resting...

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may overlook the simultaneous and reciprocal nature of causal interactions observed in real world phenomena. Here, we present a causal decomposition approach that is not based on prediction, but based on the in...

Empirical mode decomposition (EMD) is an adaptive filter bank for processing nonlinear and non-stationary signals, such as electroencephalographic (EEG) signals. EMD works well to decompose a time series into a set of intrinsic mode functions with specific frequency bands. An IMF therefore represents an intrinsic component on its correspondingly in...

Objectives: This prospective study compared the efficacy of atrial substrate modification guided by a nonlinear phase mapping technique with that of conventional substrate ablation. Background: The optimal ablation strategy for persistent atrial fibrillation (AF) was unknown. Methods: In phase 1 study, we applied a cellular automation techniqu...

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulati...

In many applications in science, engineering and mathematics, it is useful to understand functions depending on time and/or space from many different points of view. Accordingly, a wide range of transformations and analysis tools have been developed over time. Fourier series and the Fourier transform, first proposed almost 200 years ago, provided o...

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spa...

The complex fluctuations in heart rate variability (HRV) reflect cardiac autonomic modulation and are an indicator of congestive heart failure (CHF). This paper proposes a novel nonlinear approach to HRV investigation, the multi dynamic trend analysis (MDTA) method, based on the empirical mode decomposition algorithm of the Hilbert–Huang transform...

Researches to date on the association between headache and weather have yielded inconsistent results. Only a limited number of studies have examined the clinical significance of self-reported weather sensitivity. This study aimed to identify the difference in the association of headache with temperature between migraine patients with and without te...

Analyzing data from real world is a challenge; we have to face the limitations imposed by reality: nonstationarity, nonlinearity. The traditional methods cannot fully accommodate these restrictions. To alleviate this difficulty, various assumptions and approximations have often been invoked to process and analyze data. Unfortunately, methods based...

Schizophrenia is characterized by heterogeneous pathophysiology. Using multiscale entropy (MSE) analysis, which enables capturing complex dynamics of time series, we characterized MSE patterns of blood-oxygen-level-dependent (BOLD) signals across different time scales and determined whether BOLD activity in patients with schizophrenia exhibits incr...

For multi-dimensional temporal-spatial data, EEMD is applied to time series of each spatial location to obtain IMF-like components of different time scales. All the ith IMF-like components of all the time series of all spatial locations are arranged to obtain ith temporal-spatial multi-dimensional IMF-like component. For two-dimensional spatial dat...

The apolipoprotein E (APOE) gene is associated with structural and functional brain changes. We have used multiscale entropy (MSE) analysis to detect changes in the complexity of resting blood oxygen level-dependent (BOLD) signals associated with aging and cognitive function. In this study, we further hypothesized that the APOE genotype may affect...

One of the preliminary tasks when analyzing a dataset is to determine whether it or its components contain useful information. The task is essentially a binary hypothesis testing problem in which a null hypothesis of pure noise is often pre-proposed. To test against the null hypothesis, the characteristics of noise need to be understood first, and...

This paper discusses some mat hematical issues related to empirical mode decom-position (EMD). A B-spline EMD algorithm is introduced and developed for the convenience of mathematical studies. The numerical analysis using both simulated and practical signals and application examples from vibration analysis indicate that the B-spline algorithm has a...

The theoretical solution for a Multiple-Degree-Of-Freedom (MDOF) structure is composed of a combination of several individual modes. When we demonstrate the actual response directly on the time-frequency spectrum, the energy distribution is usually concentrated at some range of frequencies, with the temporal variations of each band clearly shown. T...

A degree of nonlinearity based on intra-wave frequency modulation is proposed here with the value substantially between 0 and 1. The degree of nonlinearity is used for obtaining the state rather than a system. The data required for defining the degree of nonlinearity is the state of the motion or the observed data. For a complicate state with more...

With the development of high-density intercity railway networks, substantial investments are now required, in terms of labor and machinery, in order to be able to conduct safety inspections. This results in high operational costs. High-capacity and high-speed operations have resulted in levels of damage and deterioration of railway system component...

In the empirical mode decomposition (EMD) for the Hilbert-Huang transform (HHT), a nonlinear and non-stationary signal is adaptively decomposed by an HHT into a series of intrinsic mode functions (IMFs) with the lowest one as the trend. At each step of the EMD, the low-frequency component is mainly determined by the average of the upper envelope (c...

Projection of future sea level change relies on the understanding of present sea-level trend and how it has varied in the past. Here we investigate the global-mean sea level (GMSL) change during 1993–2012 using Empirical Mode Decomposition, in an attempt to distinguish the trend over this period from the interannual variability. It is found that th...

Antitachycardia pacing (ATP), a quick, painless and effective therapy available in implantable cardioverter-defibrillators (ICDs), can terminate most, but not all, sustained ventricular tachycardias (VTs). This study investigated the possible ventricular electrogram (EGM) factors for predicting the effectiveness of ATP therapy from ICD recordings....

It has been claimed that any expression of a(t) cosθ(t) with a(t) as the instantaneous amplitude and cosθ(t) as the carrier varying along with the phase θ(t) could not be uniquely defined. However, based on the fact that a(t) cosθ(t) with all its variational forms have the same numerical value at any given time, we propose the existence of a unique...

-Identification of critical atrial substrates in nonparoxysmal atrial fibrillation (AF) patients failing to respond to pulmonary vein isolation (PVI) is important. This study investigated the signal characteristics, substrate nature, and ablation results of rotors during AF. -In total 53 patients (age=55±8), 31 with persistent AF and 22 with long-l...

A noise-assisted approach in conjunction with multivariate empirical mode decomposition (MEMD) algorithm is proposed for the computation of empirical mode decomposition (EMD), in order to produce localized frequency estimates at the accuracy level of instantaneous frequency. Despite many advantages of EMD, such as its data driven nature, a compact...

Signal detection from noisy data by rejecting a noise null hypothesis depends critically on a priori assumptions regarding the background noise and the associated statistical methods. Rejecting one kind of noise null hypothesis cannot rule out the possibility that the detected oscillations are generated from the stochastic processes of another kind...

The safety of steel towers strongly influences the reliability of power supply in transmission lines. The dynamic characteristics, non-linear behavior, and ultimate capacity of 345 kV steel transmission towers are mainly studied in this article. The approach in this article is based on the ensemble empirical mode decomposition method, the down-samp...

A compact empirical mode decomposition (CEMD) is presented to reduce mode mixing, end effect, and detrend uncertainty in analysis of time series (with N data points). This new approach consists of two parts: (a) highest-frequency sampling (HFS) to generate pseudo extrema for effective identification of upper and lower envelopes, and (b) a set of 2N...

Bipolar disorder seasonality has been documented previously, though information on the effect of demographic and clinical variables on seasonal patterns is scant. This study examined effects of age, sex, index admission, and predominant polarity on bipolar disorder seasonality in a nationwide population. An inpatient cohort admitted to hospital exc...

Nonlinear Analysis of Atrial Fibrillation. Introduction: Currently, the identification of complex fractionated atrial electrograms (CFEs) in the substrate modification is mostly based on cycle length-derived algorithms. The characteristics of the fibrillation electrogram morphology and their consistency over time are not clear. The aim of this stud...

A reappraisal of wave theory from the beginning to the present day is made here. On the surface, the great progress in both theory and applications seems to be so successful that there would be no great challenge in wave studies anymore. On deeper examination, we found problems in many aspects of wave studies starting from the definition of frequen...

This study proposes a new more precise and detailed method to examine the performance of IPCC AR4 models in simulation of nonlinear variability of global ocean heat content (OHC) on the annual time scale during 1950–1999. The method is based on the intercomparison of modulated annual cycle (MAC) of OHC and its instantaneous frequency (IF), derived...

The requirements for inspection and management of track irregularity have to be more rigorous due to safety and serviceability concerns as the increment of the train speed of high-speed train. The wavelength of track irregularity significantly affects running safety and riding comfort. To improve inspection, operation, efficiency, and address, the...

Purpose: The impact of media reporting on copycat suicides has been well established in various cases of celebrity suicide. However, knowledge is limited about the spatial and temporal relationship between suicide death and media reporting over a long period of time. This study investigated the association of suicide deaths with suicide news in lo...

Quantitative electroencephalographs (qEEG) provide a potential method to objectively quantify the cortical activations in Alzheimer's disease (AD), but they are too insensitive to probe the alteration of EEG in the early AD. The sample entropy (SaEn) attempts to quantify the complex information embedded in EEG non-linearly, which fits in that EEG o...

Background: The characteristics of atrial electrograms associated with atrial fibrillation (AF) termination are controversial. We investigated the electrogram characteristics that indicate procedural AF termination during continuous complex fractionated electrogram ablation. Methods and results: Fifty-two consecutive patients with persistent AF...

We propose the application of ICA-EEMD to secure communication systems. ICA-EEMD is employed to retrieve the message data encrypted by a mixture of Gaussian white noise and chaotic noise. The results showed that ICA-EEMD can effectively extract the two original message data.

Image presents the basic physical features of an object. Geometry, on the other hand, provides us a powerful way to quantify the information reflected by images or their shapes. Traditional geometry however finds limitation in describing the differences between highly irregular objects，which requires us to find new approaches to measure an object a...

nformation security has become a major issue in recent years, as new ways of information exchange arise due to the rapid development of computing, communication and internet technologies. We propose the image communication systems to secure the information by using a steganographic system and empirical mode decomposition method. The concealed messa...

The Earth has warmed at an unprecedented pace in the decades of the 1980s and 1990s (IPCC in Climate change 2007: the scientific basis, Cambridge University Press, Cambridge, 2007). In Wu et al. (Proc Natl Acad Sci USA 104:14889–14894, 2007) we showed that the rapidity of the warming in the late twentieth century was a result of concurrence of a se...

The trends and intrinsic frequencies in the time series of the number of Tropical Cyclones (TCs), hurricanes and typhoons, and Categories 4 and 5 hurricanes and typhoons in the Atlantic and Pacific Ocean domains, and the yearly integral of hurricane wind energy, represented by the Power Density Index (PDI), in the Atlantic and Eastern North Pacific...

The existing methods of data analysis, either the probability theory or the spectral analysis, are all developed by mathematicians or based on their rigorous mathematical rules. For analyzing data from the real physical world, we have to face the reality of nonstationarity and nonlinearity in the processes. The traditional analysis methods are base...

In this paper, we propose and evaluate two parallel implementations of Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD) for multi-core (CPU) and many-core (GPU) architectures. Relative to a sequential C implementation, our double precision GPU implementation, using the CUDA programming model, achieves up to 48.6x speedup on NVIDIA Te...

In this paper, we present some general considerations about data analysis from the perspective of a physical scientist and advocate the physical, instead of mathematical, analysis of data. These considerations have been accompanying our development of novel adaptive, local analysis methods, especially the empirical mode decomposition and its major...

As the original definition on Hilbert spectrum was given in terms of total energy and amplitude, there is a mismatch between the Hilbert spectrum and the traditional Fourier spectrum, which is defined in terms of energy density. Rigorous definitions of Hilbert energy and amplitude spectra are given in terms of energy and amplitude density in the ti...

Research has implicated environmental risk factors, such as meteorological variables, in suicide. However, studies have not investigated air pollution, known to induce acute medical conditions and increase mortality, in suicide. This study comprehensively assesses the temporal relationship between suicide and air pollution, weather, and unemploymen...

Although Internet has become an important source for affected people seeking suicide information, the connection between Internet searches for suicide information and suicidal death remains largely unknown. This study aims to evaluate the association between suicide and Internet searches trends for 37 suicide-related terms representing major known...

Patients frequently report that weather changes trigger headache or worsen existing headache symptoms. Recently, the method of empirical mode decomposition (EMD) has been used to delineate temporal relationships in certain diseases, and we applied this technique to identify intrinsic weather components associated with headache incidence data derive...

List of 54 geographic areas with search trend data of depression. (0.11 MB DOC)

List of equivalent words representing the search term “depression” in non-English languages. (0.05 MB DOC)

Power spectrum of search interest time series for depression within the United States. The spectrum was derived from Hilbert transform. The most energetic intrinsic mode function (IMF) is the fifth IMF, which corresponds to seasonal oscillations of search interests over time. Of note, the fifth IMF shows a stable frequency modulation at around one...

Cross-correlation coefficient between seasonal IMF of local search trend and that of temperature as well as solar radiation. (0.01 MB PDF)

Empirical mode decomposition of search interest time series for depression within the United States, Jan 1 2004 through Jun 30 2009. (2.27 MB TIF)

Raw dataset of search trends of depression. (0.04 MB ZIP)

Seasonal depression has generated considerable clinical interest in recent years. Despite a common belief that people in higher latitudes are more vulnerable to low mood during the winter, it has never been demonstrated that human's moods are subject to seasonal change on a global scale. The aim of this study was to investigate large-scale seasonal...

Atmospheric and oceanic climate factors and conditions play a crucial role in modulating seasonal/annual tropical cyclone activity in the North Atlantic Ocean Basin. In the following, correlations between North Atlantic tropical cyclone activity including frequency of occurrence and pathways are explored, with special emphasis on hurricanes. The va...

The empirical mode decomposition (EMD) based time-frequency analysis has been used in many scientific and engineering fields. The mathematical expression of EMD in the time-frequency-energy domain appears to be a generalization of the Fourier transform (FT), which leads to the speculation that the latter may be a special case of the former. On the...

We proposed a new model validation method through ensemble empirical mode decomposition (EEMD) and scale separate correlation. EEMD is used to analyze the nonlinear and nonstationary ozone concentration data and the data simulated from the Taiwan Air Quality Model (TAQM). Our approach consists of shifting an ensemble of white noise-added signal and...

Hilbert-Huang Transformation (HHT) is designed especially for analyzing data from nonlinear and nonstationary processes. It consists of the Empirical Mode Decomposition (EMD) to generate Intrinsic Mode Function (IMF) components, from which the instan-taneous frequency can be computed for the time-frequency Hilbert spectral Analysis. Currently, EMD,...

Motivation Mass spectrometry is a high throughput, fast, and accurate method of protein analysis. Using the peaks detected in spectra, we can compare a normal group with a disease group. However, the spectrum is complicated by scale shifting and is also full of noise. Such shifting makes the spectra non-stationary and need to align before compariso...

Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) and a trend function through sifting processes. For lack of a firm mathematical foundation, the implementation of EMD is still empirical and ad hoc. In this paper, we prove mathe...

The phenomenon of mode-mixing caused by intermittence signals is an annoying problem in Empirical Mode Decomposition (EMD) method. The noise assisted method of Ensemble EMD (EEMD) has not only effectively resolved this problem but also generated a new one, which tolerates the residue noise in the signal reconstruction. Of course, the relative magni...

A Time-Dependent Intrinsic Correlation (TDIC) method is introduced. This new approach includes both auto- and cross-correlation analysis designed especially to analyze, capture and track the local correlations between nonlinear and nonstationary time series pairs. The approach is based on Empirical Mode Decomposition (EMD) to decompose the nonlinea...

This paper revises Sedgley's model of innovation-driven endogenous growth and applies it to the case of Taiwan. The methods of empirical mode decomposition (EMD) and constrained vector error correction (VEC model or VECM) are used in the process. The EMD is used to filter out very short term fluctuations in growth, while the VECM is used to detect...

The human heartbeat interval is determined by complex nerve control and environmental inputs. As a result, the heartbeat interval for a human is a complex time series, as shown by previous studies. Most of the analysis algorithms proposed for characterizing the profile of heartbeat time series, such as detrended fluctuation analysis and multi-scale...

The human heartbeat interval reflects a complicated composition with different underlying modulations and the reactions against environmental inputs. As a result, the human heartbeat interval is a complex time series and its complexity can be scaled using various physical quantifications, such as the property of long-term correlation in detrended f...

The empirical mode decomposition (EMD) is the core of the Hilbert–Huang transform (HHT). In HHT, the EMD is responsible for decomposing a signal into intrinsic mode functions (IMFs) for calculating the instantaneous frequency and eventually the Hilbert spectrum. The EMD method as originally proposed, however, has an annoying mode mixing problem cau...

The Nakagami parameter associated with the Nakagami distribution estimated from ultrasonic backscattered signals reflects the scatterer concentration in a tissue. A nonfocused transducer does not allow tissue characterization based on the Nakagami parameter. This paper proposes a new method called the noise-assisted Nakagami parameter based on empi...