Multivariate Time Series Decomposition into Oscillation Components

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings

Modern neurophysiological recordings are performed using multichannel sensor arrays that are able to record activity in an increasingly high number of channels numbering in the 100s to 1000s. Often, underlying lower-dimensional patterns of activity are responsible for the observed dynamics, but these representations are difficult to reliably identify using existing methods that attempt to summarize multivariate relationships in a post hoc manner from univariate analyses or using current blind source separation methods. While such methods can reveal appealing patterns of activity, determining the number of components to include, assessing their statistical significance, and interpreting them requires extensive manual intervention and subjective judgment in practice. These difficulties with component selection and interpretation occur in large part because these methods lack a generative model for the underlying spatio-temporal dynamics. Here, we describe a novel component analysis method anchored by a generative model where each source is described by a bio-physically inspired state-space representation. The parameters governing this representation readily capture the oscillatory temporal dynamics of the components, so we refer to it as oscillation component analysis. These parameters - the oscillatory properties, the component mixing weights at the sensors, and the number of oscillations - all are inferred in a data-driven fashion within a Bayesian framework employing an instance of the expectation maximization algorithm. We analyze high-dimensional electroencephalography and magnetoencephalography recordings from human studies to illustrate the potential utility of this method for neuroscience data.

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings

Modern neurophysiological recordings are performed using multichannel sensor arrays that are able to record activity in an increasingly high number of channels numbering in the 100's to 1000's. Often, underlying lower-dimensional patterns of activity are responsible for the observed dynamics, but these representations are difficult to reliably identify using existing methods that attempt to summarize multivariate relationships in a post-hoc manner from univariate analyses, or using current blind source separation methods. While such methods can reveal appealing patterns of activity, determining the number of components to include, assessing their statistical significance, and interpreting them requires extensive manual intervention and subjective judgement in practice. These difficulties with component selection and interpretation occur in large part because these methods lack a generative model for the underlying spatio-temporal dynamics. Here we describe a novel component analysis method anchored by a generative model where each source is described by a bio-physically inspired state space representation. The parameters governing this representation readily capture the oscillatory temporal dynamics of the components, so we refer to it as Oscillation Component Analysis (OCA). These parameters - the oscillatory properties, the component mixing weights at the sensors, and the number of oscillations - all are inferred in a data-driven fashion within a Bayesian framework employing an instance of the expectation maximization algorithm. We analyze high-dimensional electroencephalography and magnetoencephalography recordings from human studies to illustrate the potential utility of this method for neuroscience data.

State space methods for phase amplitude coupling analysis

Phase amplitude coupling (PAC) is thought to play a fundamental role in the dynamic coordination of brain circuits and systems. There are however growing concerns that existing methods for PAC analysis are prone to error and misinterpretation. Improper frequency band selection can render true PAC undetectable, while non-linearities or abrupt changes in the signal can produce spurious PAC. Current methods require large amounts of data and lack formal statistical inference tools. We describe here a novel approach for PAC analysis that substantially addresses these problems. We use a state space model to estimate the component oscillations, avoiding problems with frequency band selection, nonlinearities, and sharp signal transitions. We represent cross-frequency coupling in parametric and time-varying forms to further improve statistical efficiency and estimate the posterior distribution of the coupling parameters to derive their credible intervals. We demonstrate the method using simulated data, rat local field potentials (LFP) data, and human EEG data.

Spatiotemporal hysteresis distribution and decomposition of solar activities and climatic oscillation during 1900-2020

Solar radiation is the external driving force of the Earth's climate system. In different spatial and temporal scales, meteorological elements have different responses and lag periods to solar activity (SA), climatic oscillation (CO), geographic factors (GF) and other influencing factors. However, such studies are not abundant and in-depth in the world. To further understand the "solar-climate-water resource" system, this study considers China as the study area and investigates the monthly data of temperature (T) and precipitation (P) during 1900-2020 that were obtained from 3836 grid stations. The strong interaction and lag distribution between T or P with SA and CO were studied and influence weights of SA, CO, and geographical factors (GF) of each grid station were calculated. A multivariate hysteretic decomposition model was established to simulate and quantitatively decompose the periodic lag considering the factors of the earth's revolution. It is found that the strong interaction/lag periods obtained in a long-time scale can be decomposed into several periods shorter than the SA period. The distribution of strong interaction/lag periods is nested with topography and echoes with cities. The underlying surface conditions and urbanization are also important factors affecting the T and P lag. There are two distinct dividing lines in the lag period and influencing factor pattern of T and P. The T dividing line moves through valleys where water or mountain ranges meet, where the gap facilitates monsoon movement across regions, while the P dividing line is a zone of dramatic terrain, where tall mountains block water vapor transport. In the lag trend of T, the northern region of China has the longest lag period, and the lag period of surrounding regions tends to converge to the northern region. The lag period caused by SN in southwest China is larger than that in northwest China, while the lag effect of CO is opposite in the above two regions. The lag trend of P also has the above characteristics, but the difference is that the lag period in central China is the longest.

Oscillator decomposition of infant fNIRS data

The functional near-infrared spectroscopy (fNIRS) can detect hemodynamic responses in the brain and the data consist of bivariate time series of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) on each channel. In this study, we investigate oscillatory changes in infant fNIRS signals by using the oscillator decompisition method (OSC-DECOMP), which is a statistical method for extracting oscillators from time series data based on Gaussian linear state space models. OSC-DECOMP provides a natural decomposition of fNIRS data into oscillation components in a data-driven manner and does not require the arbitrary selection of band-pass filters. We analyzed 18-ch fNIRS data (3 minutes) acquired from 21 sleeping 3-month-old infants. Five to seven oscillators were extracted on most channels, and their frequency distribution had three peaks in the vicinity of 0.01-0.1 Hz, 1.6-2.4 Hz and 3.6-4.4 Hz. The first peak was considered to reflect hemodynamic changes in response to the brain activity, and the phase difference between oxy-Hb and deoxy-Hb for the associated oscillators was at approximately 230 degrees. The second peak was attributed to cardiac pulse waves and mirroring noise. Although these oscillators have close frequencies, OSC-DECOMP can separate them through estimating their different projection patterns on oxy-Hb and deoxy-Hb. The third peak was regarded as the harmonic of the second peak. By comparing the Akaike Information Criterion (AIC) of two state space models, we determined that the time series of oxy-Hb and deoxy-Hb on each channel originate from common oscillatory activity. We also utilized the result of OSC-DECOMP to investigate the frequency-specific functional connectivity. Whereas the brain oscillator exhibited functional connectivity, the pulse waves and mirroring noise oscillators showed spatially homogeneous and independent changes. OSC-DECOMP is a promising tool for data-driven extraction of oscillation components from biological time series data.

Time-series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattended listening, and frequency-modulated tones classification

BACKGROUND

The nonstationarity of EEG/MEG signals is important for understanding the functioning of the human brain. From our previous research we know that short, 250-500-ms MEG signals are variance-nonstationary. The covariance of a stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time.

NEW METHOD

We analyse data from 148-channel MEG, which represent rest state, unattended listening, and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain and for the dominant frequencies of 8-12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity, and gaussianity, and propose ARMA-modelling for their description.

RESULTS

The analysed time series have weak-stationarity properties independently of the functional state of the brain and channel localization. Only a small percentage of them, mostly related to the cognitive task, reveal nonstationarity. The obtained mathematical models show that the spectral density of the analysed signals depends on only two to three previous trials.

COMPARISON WITH EXISTING METHODS

The presented method has limitations related to FFT resolution and univariate models, but it is computationally simple and allows obtaining a low-complex stochastic model of the EEG/MEG spectrum variability.

CONCLUSIONS

Although physiological short-time MEG signals are in principle nonstationary in time, their power spectrum at the dominant (alpha) frequencies varies as a weakly stationary process. The proposed methodology has possible applications in prediction of EEG/MEG spectral properties in theoretical and clinical neuroscience.

Unsupervised Heart Sound Decomposition and State Estimation with Generative Oscillation Models

This paper proposes a new generative probabilistic model for phonocardiograms (PCGs) that can simultaneously capture oscillatory factors and state transitions in cardiac cycles. Conventionally, PCGs have been modeled in two main aspects. One is a state space model that represents recurrent and frequently appearing state transitions. Another is a factor model that expresses the PCG as a non-stationary signal consisting of multiple oscillations. To model these perspectives in a unified framework, we combine an oscillation decomposition with a state space model. The proposed model can decompose the PCG into cardiac state dependent oscillations by reflecting the mechanism of cardiac sounds generation in an unsupervised manner. In the experiments, our model achieved better accuracy in the state estimation task compared to the empirical mode decomposition method. In addition, our model detected S2 onsets more accurately than the supervised segmentation method when distributions among PCG signals were different.

Multitaper Infinite Hidden Markov Model for EEG

Electroencephalographam (EEG) monitoring of neural activity is widely used for identifying underlying brain states. For inference of brain states, researchers have often used Hidden Markov Models (HMM) with a fixed number of hidden states and an observation model linking the temporal dynamics embedded in EEG to the hidden states. The use of fixed states may be limiting, in that 1) pre-defined states might not capture the heterogeneous neural dynamics across individuals and 2) the oscillatory dynamics of the neural activity are not directly modeled. To this end, we use a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), which discovers the set of hidden states that best describes the EEG data, without a-priori specification of state number. In addition, we introduce an observation model based on classical asymptotic results of frequency domain properties of stationary time series, along with the description of the conditional distributions for Gibbs sampler inference. We then combine this with multitaper spectral estimation to reduce the variance of the spectral estimates. By applying our method to simulated data inspired by sleep EEG, we arrive at two main results: 1) the algorithm faithfully recovers the spectral characteristics of the true states, as well as the right number of states and 2) the incorporation of the multitaper framework produces a more stable estimate than traditional periodogram spectral estimates.