arXiv subjects

Hernando Ombao

Publications and source records attributed to Hernando Ombao.

At least 109 records · Page 6Linked to original sources

arXiv2018

Evolutionary State-Space Model and Its Application to Time-Frequency Analysis of Local Field Potentials

We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of components (e.g., AR(2) process) with oscillatory activity at pre-defined frequency bands. To account for the potential non-stationarity of these components (since the brain responses could vary throughout the entire experiment), the parameters are allowed to vary over epochs. Compared with classical approaches such as independent component analysis and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates non-stationarity. For inference purpose, we propose a novel computational algorithm based upon using Kalman smoother, maximum likelihood and blocked resampling. The E-SSM model is applied to simulation studies and an application to a multi-epoch local field potentials (LFP) signal data collected from a non-spatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power for different components across different phases in the experiment and identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of different electrodes does change over the course of an experiment in practice, treating these epoch recordings as realizations of an identical process could lead to misleading results. In summary, the proposed method underscores the importance of capturing the evolution in brain responses over the study period.

stat.ME↗

arXiv2018

Modeling Brain Connectivity with Graphical Models on Frequency Domain

Multichannel electroencephalograms (EEGs) have been widely used to study cortical connectivity during acquisition of motor skills. In this paper, we introduce copula Gaussian graphical models on spectral domain to characterize dependence in oscillatory activity between channels. To obtain a simple and robust representation of brain connectivity that can explain the most variation in the observed signals, we propose a framework based on maximizing penalized likelihood with Lasso regularization to search for the sparse precision matrix. To address the optimization problem, graphical Lasso, Ledoit-Wolf and sparse estimation of a covariance matrix (SPCOV) algorithms were modified and implemented. Simulations show the benefit of using the proposed algorithms in terms of robustness and small estimation errors. Furthermore, analysis of the EEG data in a motor skill task conducted using algorithms of modified graphical LASSO and Ledoit-Wolf, reveal a sparse pattern of brain connectivity among cortices which is consistent with the results from other work in the literature.

stat.AP↗

arXiv2018

Modeling Dependence via Copula of Functionals of Fourier Coefficients

The goal of this paper is to develop a measure for characterizing complex dependence between stationary time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter both from elliptical and Archimedean families. Our approach is to analyze changes in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary theoretical background, the multivariate models and an illustration of our methodology on these local field potential data. Simulations with non-linear dependent data show information that were missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex non-linear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats.

stat.ME↗

arXiv2018

Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials

This paper intends to develop tools for characterizing non-linear spectral dependence between spontaneous brain signals. We use parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation behind this work is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded at various channels. We address the following major questions. First, we ask whether one can detect any changepoint in the regime of a brain channel for a given frequency band based on a difference between the cumulative distribution functions modeled for each epoch (small window of time). Our proposed approach is an iterative algorithm which compares each successive bivariate copulas on all the epochs range, using a bivariate Kolmogorov-Smirnov statistic. Second, we ask whether stroke can alter the dependence structure of brain signals; and examine whether changes in dependence are present only in some channels or generalized across channels. These questions are addressed by comparing Vine-copulas models fitted for each epoch. We provide the necessary framework and show the effectiveness of our methods through the results for the local field potential data analysis of a rat.

stat.AP↗

arXiv2018

A Markov-Switching Model Approach to Heart Sound Segmentation and Classification

Objective: This paper considers challenges in developing algorithms for accurate segmentation and classification of heart sound (HS) signals. Methods: We propose an approach based on Markov switching autoregressive model (MSAR) to segmenting the HS into four fundamental components each with distinct second-order structure. The identified boundaries are then utilized for automated classification of pathological HS using the continuous density hidden Markov model (CD-HMM). The MSAR formulated in a state-space form is able to capture simultaneously both the continuous hidden dynamics in HS, and the regime switching in the dynamics using a discrete Markov chain. This overcomes the limitation of HMM which uses a single-layer of discrete states. We introduce three schemes for model estimation: (1.) switching Kalman filter (SKF); (2.) refined SKF; (3.) fusion of SKF and the duration-dependent Viterbi algorithm (SKF-Viterbi). Results: The proposed methods are evaluated on Physionet/CinC Challenge 2016 database. The SKF-Viterbi significantly outperforms SKF by improvement of segmentation accuracy from 71% to 84.2%. The use of CD-HMM as a classifier and Mel-frequency cepstral coefficients (MFCCs) as features can characterize not only the normal and abnormal morphologies of HS signals but also morphologies considered as unclassifiable (denoted as X-Factor). It gives classification rates with best gross F1 score of 90.19 (without X-Factor) and 82.7 (with X-Factor) for abnormal beats. Conclusion: The proposed MSAR approach for automatic localization and detection of pathological HS shows a noticeable performance on large HS dataset. Significance: It has potential applications in heart monitoring systems to assist cardiologists for pre-screening of heart pathologies.

eess.SP↗

arXiv2018

Topological Brain Network Distances

Existing brain network distances are often based on matrix norms. The element-wise differences in the existing matrix norms may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A major disadvantage to element-wise distance calculations is that it could be severely affected even by a small number of extreme edge weights. Thus it is necessary to develop network distances that recognize topology. In this paper, we provide a survey of bottleneck, Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances that are adapted for brain networks, and compare them against matrix-norm based network distances. Bottleneck and GH-distances are often used in persistent homology. However, they were rarely utilized to measure similarity between brain networks. KS-distance is recently introduced to measure the similarity between networks across different filtration values. The performance analysis was conducted using the random network simulations with the ground truths. Using a twin imaging study, which provides biological ground truth, we demonstrate that the KS distance has the ability to determine heritability.

stat.AP↗

arXiv2018

Regularized matrix data clustering and its application to image analysis

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation.

stat.ME↗

arXiv2018

Intrinsic data depth for Hermitian positive definite matrices

Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian positive definite matrices by exploiting the geometric structure of the space as a Riemannian manifold. The depth functions allow one to naturally characterize most central or outlying matrices, but also provide a practical framework for inference in the context of samples of positive definite matrices. First, the desired properties of an intrinsic data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally fast pointwise and integrated data depth functions that satisfy each of these requirements and investigate several robustness and efficiency aspects. As an application, we construct depth-based confidence regions for the intrinsic mean of a sample of positive definite matrices, which is applied to the exploratory analysis of a collection of covariance matrices associated to a multicenter research trial.

stat.ME↗

arXiv2017

Modeling high dimensional multichannel brain signals

Our goal is to model and measure functional and effective (directional) connectivity in multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The difficulties from analyzing these data mainly come from two aspects: first, there are major statistical and computational challenges for modeling and analyzing high dimensional multichannel brain signals; second, there is no set of universally-agreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO+LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). Then we employ some measures of connectivity but put an emphasis on partial directed coherence (PDC) which can capture the directional connectivity between channels. PDC is a frequency-specific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the network. The proposed modeling approach provided key insights into potential functional relationships among simultaneously recorded sites during performance of a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types.

stat.AP↗

arXiv2017

Coherence-based Time Series Clustering for Brain Connectivity Visualization

We develop the hierarchical cluster coherence (HCC) method for brain signals, a procedure for characterizing connectivity in a network by clustering nodes or groups of channels that display high level of coordination as measured by "cluster-coherence". While the most common approach to measuring dependence between clusters is through pairs of single time series, our method proposes cluster coherence which measures dependence between whole clusters rather than between single elements. Thus it takes into account both the dependence between clusters and within channels in a cluster. Using our method, the identified clusters contain time series that exhibit high cross-dependence in the spectral domain. That is, these clusters correspond to connected brain regions with synchronized oscillatory activity. In the simulation studies, we show that the proposed HCC outperforms commonly used clustering algorithms, such as average coherence and minimum coherence based methods. To study clustering in a network of multichannel electroencephalograms (EEG) during an epileptic seizure, we applied the HCC method and identified connectivity in alpha (8-12) Hertz and beta (16-30) Hertz bands at different phases of the recording: before an epileptic seizure, during the early and middle phases of the seizure episode. To increase the potential impact of this work in neuroscience, we also developed the HCC-Vis, an R-Shiny app (RStudio), which can be downloaded from this https://carolinaeuan.shinyapps.io/hcc-vis/.

stat.AP↗

arXiv2017

Statistical Challenges in Modeling Big Brain Signals

Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible solutions, and highlight future research directions.

stat.ME↗

arXiv2017

Multi-Scale Factor Analysis of High-Dimensional Brain Signals

In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the massive spatio-temporal data defined over the complex networks into a finite set of regional clusters. To achieve further dimension reduction, we represent the signals in each cluster by a small number of latent factors. The correlation matrix for all nodes in the network are approximated by lower-dimensional sub-structures derived from the cluster-specific factors. To estimate regional connectivity between numerous nodes (within each cluster), we apply principal components analysis (PCA) to produce factors which are derived as the optimal reconstruction of the observed signals under the squared loss. Then, we estimate global connectivity (between clusters or sub-networks) based on the factors across regions using the RV-coefficient as the cross-dependence measure. This gives a reliable and computationally efficient multi-scale analysis of both regional and global dependencies of the large networks. The proposed novel approach is applied to estimate brain connectivity networks using functional magnetic resonance imaging (fMRI) data. Results on resting-state fMRI reveal interesting modular and hierarchical organization of human brain networks during rest.

stat.AP↗

arXiv2017

Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models

Recent studies on analyzing dynamic brain connectivity rely on sliding-window analysis or time-varying coefficient models which are unable to capture both smooth and abrupt changes simultaneously. Emerging evidence suggests state-related changes in brain connectivity where dependence structure alternates between a finite number of latent states or regimes. Another challenge is inference of full-brain networks with large number of nodes. We employ a Markov-switching dynamic factor model in which the state-driven time-varying connectivity regimes of high-dimensional fMRI data are characterized by lower-dimensional common latent factors, following a regime-switching process. It enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We consider the switching VAR to quantity the dynamic effective connectivity. We propose a three-step estimation procedure: (1) extracting the factors using principal component analysis (PCA) and (2) identifying dynamic connectivity states using the factor-based switching vector autoregressive (VAR) models in a state-space formulation using Kalman filter and expectation-maximization (EM) algorithm, and (3) constructing the high-dimensional connectivity metrics for each state based on subspace estimates. Simulation results show that our proposed estimator outperforms the K-means clustering of time-windowed coefficients, providing more accurate estimation of regime dynamics and connectivity metrics in high-dimensional settings. Applications to analyzing resting-state fMRI data identify dynamic changes in brain states during rest, and reveal distinct directed connectivity patterns and modular organization in resting-state networks across different states.

stat.AP↗

arXiv2016

Exploratory Analysis of High Dimensional Time Series with Applications to Multichannel Electroencephalograms

In this paper, we address the the major hurdle of high dimensionality in EEG analysis by extracting the optimal lower dimensional representations. Using our approach, connectivity between regions in a high-dimensional brain network is characterized through the connectivity between region-specific factors. The proposed approach is motivated by our observation that electroencephalograms (EEGs) from channels within each region exhibit a high degree of multicollinearity and synchrony. These observations suggest that it would be sensible to extract summary factors for each region. We consider the general approach for deriving summary factors which are solutions to the criterion of squared error reconstruction. In this work, we focus on two special cases of linear auto encoder and decoder. In the first approach, the factors are characterized as instantaneous linear mixing of the observed high dimensional time series. In the second approach, the factors signals are linear filtered versions of the original signal which is more general than an instantaneous mixing. This exploratory analysis is the starting point to the multi-scale factor analysis model where the concatenated factors from all regions are represented by vector auto-regressive model that captures the connectivity in high dimensional signals. We performed evaluations on the two approaches via simulations under different conditions. The simulation results provide insights on the performance and application scope of the methods. We also performed exploratory analysis of EEG recorded over several epochs during resting state. Finally, we implemented these exploratory methods in a Matlab toolbox XHiDiTS available from https://goo.gl/uXc8ei .

stat.AP↗

arXiv2016

The Hierarchical Spectral Merger algorithm: A New Time Series Clustering Procedure

We present a new method for time series clustering which we call the Hierarchical Spectral Merger (HSM) method. This procedure is based on the spectral theory of time series and identifies series that share similar oscillations or waveforms. The extent of similarity between a pair of time series is measured using the total variation distance between their estimated spectral densities. At each step of the algorithm, every time two clusters merge, a new spectral density is estimated using the whole information present in both clusters, which is representative of all the series in the new cluster. The method is implemented in an R package HSMClust. We present two applications of the HSM method, one to data coming from wave-height measurements in oceanography and the other to electroencefalogram (EEG) data.

stat.CO↗

arXiv2016

A Multi-Resolution Spatio-Temporal Model for Brain Activation and Connectivity in fMRI Data

Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. For the sake of feasibility, standard models typically reduce dimensionality by modeling covariance among regions of interest (ROIs) -- coarser or larger spatial units -- rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect activation patterns in the brain and hence produce misleading results. To overcome these problems, we introduce a multi-resolution spatio-temporal model and a computationally efficient methodology to estimate cognitive control related activation and whole-brain connectivity. The proposed model allows for testing voxel-specific activation while accounting for non-stationary local spatial dependence within anatomically defined ROIs, as well as regional dependence (between-ROIs). Furthermore, the model allows for detection of interpretable connectivity patterns among ROIs using the graphical Least Absolute Shrinkage Selection Operator (LASSO). The model is used in a motor-task fMRI study to investigate brain activation and connectivity patterns aimed at identifying associations between these patterns and regaining motor functionality following a stroke.

stat.AP↗

arXiv2015

Spectral Synchronicity in Brain Signals

Brain activity following stimulus presentation and during resting state are often the result of highly coordinated responses of large numbers of neurons both locally and globally. Coordinated activity of neurons can give rise to oscillations which are captured by electroencephalograms (EEG). In this paper, we examine EEGs as this is the primary data being used by our collaborators who are studying coordination of neuronal response during the execution of tasks such as learning, and memory formation, retention and retrieval. In this paper, we develop the spectral merger clustering (SMC) method that identifies synchronized brain regions during resting state in a sense that these regions share similar oscillations or waveforms. The SMC method, produces clusters of EEGs which serve as a proxy for segmenting the brain cortical surface since the EEGs capture neuronal activity over a locally distributed region on the cortical surface. The extent of desynchronicity between a pair of EEGs is measured using the total variation distance (TVD) which gives the largest possible difference between the spectral densities of the pair of EEGs. We considered the spectral merger algorithm for clustering EEGs, which updates the spectral estimate of the cluster from a weighted average of the spectral estimate obtained from each EEG in the cluster. Numerical experiments suggest that the SMC method performs very well in producing the correct clusters. When applied to resting state EEG data, the method showed how some regions, though not contiguously connected on the cortical surface, are spectrally synchronized during resting state. Moreover, the method demonstrates that brain organization, as expressed in cluster formation, evolves over resting state.

stat.AP↗

arXiv2014

An Introduction to Applications of Wavelet Benchmarking with Seasonal Adjustment

Prior to adjustment, accounting conditions between national accounts data sets are frequently violated. Benchmarking is the procedure used by economic agencies to make such data sets consistent. It typically involves adjusting a high frequency time series (e.g. quarterly data) so it becomes consistent with a lower frequency version (e.g. annual data). Various methods have been developed to approach this problem of inconsistency between data sets. This paper introduces a new statistical procedure; namely wavelet benchmarking. Wavelet properties allow high and low frequency processes to be jointly analysed and we show that benchmarking can be formulated and approached succinctly in the wavelet domain. Furthermore the time and frequency localisation properties of wavelets are ideal for handling more complicated benchmarking problems. The versatility of the procedure is demonstrated using simulation studies where we provide evidence showing it substantially outperforms currently used methods. Finally, we apply this novel method of wavelet benchmarking to official Office of National Statistics (ONS) data.

stat.AP↗