Empirical mode decomposition of field potentials from macaque V4 in visual spatial attention

Empirical mode decomposition (EMD) has recently been introduced as a local and fully data-driven technique for the analysis of non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. In this article we consider the application of EMD to the analysis of neuronal activity in visual cortical area V4 of a macaque monkey performing a visual spatial attention task. We show that, by virtue of EMD, field potentials can be resolved into a sum of intrinsic components with different degrees of oscillatory content. Low-frequency components in single-trial recordings contribute to the average visual evoked potential (AVEP), whereas high-frequency components do not, but are identified as gamma-band (30–90 Hz) oscillations. The magnitude of time-varying gamma activity is shown to be enhanced when the monkey attends to a visual stimulus as compared to when it is not attending to the same stimulus. Comparison with Fourier analysis shows that EMD may offer better temporal and frequency resolution. These results support the idea that the magnitude of gamma activity reflects the modulation of V4 neurons by visual spatial attention. EMD, coupled with instantaneous frequency analysis, is demonstrated to be a useful technique for the analysis of neurobiological time-series.     

Analysis of time-course microarray data: Comparison of common tools

High-throughput time-series data have a special value for studying the dynamism of biological systems. However, the interpretation of such complex data can be challenging. The aim of this study was to compare common algorithms recently developed for the detection of differentially expressed genes in time-course microarray data. Using different measures such as sensitivity, specificity, predictive values, and related signaling pathways, we found that limma, timecourse, and gprege have reasonably good performance for the analysis of datasets in which only test group is followed over time. However, limma has the additional advantage of being able to report significance cut off, making it a more practical tool. In addition, limma and TTCA can be satisfactorily used for datasets with time-series data for all experimental groups. These findings may assist investigators to select appropriate tools for the detection of differentially expressed genes as an initial step in the interpretation of time-course big data.     

Empirical Mode Decomposition and Wavelet Transform Based ECG Data Compression Scheme

ObjectiveIn health-care systems, compression is an essential tool to solve the storage and transmission problems. In this regard, this paper reports a new electrocardiogram (ECG) data compression scheme which employs sifting function based empirical mode decomposition (EMD) and discrete wavelet transform.MethodEMD based on sifting function is utilized to get the first intrinsic mode function (IMF). After EMD, the first IMF and four significant sifting functions are combined together. This combination is free from many irrelevant components of the signal. Discrete wavelet transform (DWT) with mother wavelet ‘bior4.4’ is applied to this combination. The transform coefficients obtained after DWT are passed through dead-zone quantization. It discards small transform coefficients lying around zero. Further, integer conversion of coefficients and run-length encoding are utilized to achieve a compressed form of ECG data.ResultsCompression performance of the proposed scheme is evaluated using 48 ECG records of the MIT-BIH arrhythmia database. In the comparison of compression results, it is observed that the proposed method exhibits better performance than many recent ECG compressors. A mean opinion score test is also conducted to evaluate the true quality of the reconstructed ECG signals.ConclusionThe proposed scheme offers better compression performance with preserving the key features of the signal very well.     

Differential gene expression detection and sample classification using penalized linear regression models

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.     

A temporal precedence based clustering method for gene expression microarray data

Background  

Time-course microarray experiments can produce useful data which can help in understanding the underlying dynamics of the system. Clustering is an important stage in microarray data analysis where the data is grouped together according to certain characteristics. The majority of clustering techniques are based on distance or visual similarity measures which may not be suitable for clustering of temporal microarray data where the sequential nature of time is important. We present a Granger causality based technique to cluster temporal microarray gene expression data, which measures the interdependence between two time-series by statistically testing if one time-series can be used for forecasting the other time-series or not.     

Identification of oscillatory genes in somitogenesis from functional genomic analysis of a human mesenchymal stem cell model

During somitogenesis, oscillatory expression of genes in the notch and wnt signaling pathways plays a key role in regulating segmentation. These oscillations in expression levels are elements of a species-specific developmental mechanism. To date, the periodicity and components of the human clock remain unstudied. Here we show that a human mesenchymal stem/stromal cell (MSC) model can be induced to display oscillatory gene expression. We observed that the known cycling gene HES1 oscillated with a 5 h period consistent with available data on the rate of somitogenesis in humans. We also observed cycling of Hes1 expression in mouse C2C12 myoblasts with a period of 2 h, consistent with previous in vitro and embryonic studies. Furthermore, we used microarray and quantitative PCR (Q-PCR) analysis to identify additional genes that display oscillatory expression both in vitro and in mouse embryos. We confirmed oscillatory expression of the notch pathway gene Maml3 and the wnt pathway gene Nkd2 by whole mount in situ hybridization analysis and Q-PCR. Expression patterns of these genes were disrupted in Wnt3a(tm1Amc) mutants but not in Dll3(pu) mutants. Our results demonstrate that human and mouse in vitro models can recapitulate oscillatory expression observed in embryo and that a number of genes in multiple developmental pathways display dynamic expression in vitro.     

Local Properties of Vigilance States: EMD Analysis of EEG Signals during Sleep-Waking States of Freely Moving Rats

Understanding the inherent dynamics of the EEG associated to sleep-waking can provide insights into its basic neural regulation. By characterizing the local properties of the EEG using power spectrum, empirical mode decomposition (EMD) and Hilbert-spectral analysis, we can examine the dynamics over a range of time-scales. We analyzed rat EEG during wake, NREMS and REMS using these methods. The average instantaneous phase, power spectral density (PSD) of intrinsic mode functions (IMFs) and the energy content in various frequency bands show characteristic changes in each of the vigilance states. The 2nd and 7th IMFs show changes in PSD for wake and REMS, suggesting that those modes may carry wake- and REMS-associated cognitive, conscious and behavior-specific information of an individual even though the EEG may appear similar. The energy content in θ₂ (6Hz-9Hz) band of the 1st IMF for REMS is larger than that of wake. The decrease in the phase function of IMFs from wake to REMS to NREMS indicates decrease of the mean frequency in these states, respectively. The rate of information processing in waking state is more in the time scale described by the first three IMFs than in REMS state. However, for IMF5-IMF7, the rate is more for REMS than that for wake. We obtained Hilbert-Huang spectral entropy, which is a suitable measure of information processing in each of these state-specific EEG. It is possible to evaluate the complex dynamics of the EEG in each of the vigilance states by applying measures based on EMD and Hilbert-transform. Our results suggest that the EMD based nonlinear measures of the EEG can provide useful estimates of the information possessed by various oscillations associated with the vigilance states. Further, the EMD-based spectral measures may have implications in understanding anatamo-physiological correlates of sleep-waking behavior and clinical diagnosis of sleep-pathology.     

基于EMD的左右手运动想象脑电信号分析研究

基于经验模态分解（EMD）理论,提出一种左右手运动想象脑电信号分析方法。首先利用时间窗对脑电信号数据进行划分,对每段数据通过经验模态分解法将其分解为一组固有模态函数IMF,提取主要信号所在的IMF层去除信号中的噪声。对含有主要信号的几层IMF进行Hilbert变换,得到瞬时频率与对应的瞬时幅值。再提取左右手想象的特定频段mu节律和beta节律的能量信号作为特征,分别利用支持向量机（SVM）和Fisher进行了分类比较。对EMD和小波包在去噪和特征提取进行了比较。结果表明,EMD是一种很有效的去噪方法,经过EMD分解后提取的能量信号在区分左右手想象上更具有优势,识别率高。     

Expression profiling analysis for genes related to meat quality and carcass traits during postnatal development of backfat in two pig breeds

The competitive equilibrium of fatty acid biosynthesis and oxidation in vivo determines porcine sub-cutaneous fat thickness(SFT) and intramuscular fat(IMF) content.Obese and lean-type pig breeds show obvious differences in adipose deposition;however, the molecular mechanism underlying this phenotypic variation remains unclear.We used pathway-focused oligo microarray studies to examine the expression changes of 140 genes associated with meat quality and carcass traits in backfat at five growth stages(1―5 months) of Landrace(a leaner, Western breed) and Taihu pigs(a fatty, indigenous, Chinese breed).Variance analysis(ANOVA) revealed that differences in the expression of 25 genes in Landrace pigs were significant(FDR adjusted permutation, P<0.05) among 5 growth stages.Gene class test(GCT) indicated that a gene-group was very significant between 2 pig breeds across 5 growth stages(PErmineJ<0.01), which consisted of 23 genes encoding enzymes and regulatory proteins associ-ated with lipid and steroid metabolism.These findings suggest that the distinct differences in fat deposition ability between Landrace and Taihu pigs may closely correlate with the expression changes of these genes.Clustering analysis revealed a very high level of significance(FDR adjusted, P<0.01) for 2 gene expression patterns in Landrace pigs and a high level of significance(FDR adjusted, P<0.05) for 2 gene expression patterns in Taihu pigs.Also, expression patterns of genes were more diversified in Taihu pigs than those in Landrace pigs, which suggests that the regulatory mechanism of micro-effect polygenes in adipocytes may be more complex in Taihu pigs than in Landrace pigs.Based on a dy-namic Bayesian network(DBN) model, gene regulatory networks(GRNs) were reconstructed from time-series data for each pig breed.These two GRNs initially revealed the distinct differences in physiological and biochemical aspects of adipose metabolism between the two pig breeds;from these results, some potential key genes could be identified.Quantitative, real-time RT-PCR(QRT-PCR) was used to verify the microarray data for five modulated genes, and a good correlation between the two measures of expression was observed for both 2 pig breeds at different growth stages(R=0.874±0.071).These results highlight some possible candidate genes for porcine fat characteristics and provide some data on which to base further study of the molecular basis of adipose metabolism.     

Adjustments and measures of differential expression for microarray data

MOTIVATION: Existing analyses of microarray data often incorporate an obscure data normalization procedure applied prior to data analysis. For example, ratios of microarray channels intensities are normalized to have common mean over the set of genes. We made an attempt to understand the meaning of such procedures from the modeling point of view, and to formulate the model assumptions that underlie them. Given a considerable diversity of data adjustment procedures, the question of their performance, comparison and ranking for various microarray experiments was of interest. RESULTS: A two-step statistical procedure is proposed: data transformation (adjustment for slide-specific effect) followed by a statistical test applied to transformed data. Various methods of analysis for differential expression are compared using simulations and real data on colon cancer cell lines. We found that robust categorical adjustments outperform the ones based on a precisely defined stochastic model, including some commonly used procedures.     

Information quantification of empirical mode decomposition and applications to field potentials

The empirical mode decomposition (EMD) method can adaptively decompose a non-stationary time series into a number of amplitude or frequency modulated functions known as intrinsic mode functions. This paper combines the EMD method with information analysis and presents a framework of information-preserving EMD. The enhanced EMD method has been exploited in the analysis of neural recordings. It decomposes a signal and extracts only the most informative oscillations contained in the non-stationary signal. Information analysis has shown that the extracted components retain the information content of the signal. More importantly, a limited number of components reveal the main oscillations presented in the signal and their instantaneous frequencies, which are not often obvious from the original signal. This information-coupled EMD method has been tested on several field potential datasets for the analysis of stimulus coding in visual cortex, from single and multiple channels, and for finding information connectivity among channels. The results demonstrate the usefulness of the method in extracting relevant responses from the recorded signals. An investigation is also conducted on utilizing the Hilbert phase for cases where phase information can further improve information analysis and stimulus discrimination. The components of the proposed method have been integrated into a toolbox and the initial implementation is also described.     

Modeling nonlinearity in dilution design microarray data

MOTIVATION: Dilution design (Mixed tissue RNA) has been utilized by some researchers to evaluate and assess the performance of multiple microarray platforms. Current microarray data analysis approaches assume that the quantified signal intensities are linearly related to the expression of the corresponding genes in the sample. However, there are sources of nonlinearity in microarray expression measurements. Such nonlinearity study in the expressions of the RNA mixtures provides a new way to analyze gene expression data, and we argue that the nonlinearity can reveal novel information for microarray data analysis. Therefore, we proposed a statistical model, called proportion model, which is based on the linear regression analysis. To approximately quantify the nonlinearity in the dilution design, a new calibration, beta ratio (BR) was derived from the proportion model. Furthermore, a new adjusted fold change (adj-FC) was proposed to predict the true FC without nonlinearity, in particular for large FC. RESULTS: We applied our method to one microarray dilution dataset. The experimental results indicated that, to some extent, there are global biases comparing with the linear assumption for the significant genes. Further analysis of those highly expressed genes with significant nonlinearity revealed some promising results, e.g. 'poison' effect was discovered for some genes in RNA mixtures. The adj-FCs of those genes with 'poison' effect, indicate that the nonlinearity can be also caused by the inherent feature of the genes besides signal noise and technical variation. Moreover, when percentage of overlapping genes (POG) was used as a cross-platform consistency measure, adj-FC outperformed simple fold change to show that Affymetrix and Illumina platforms are consistent. AVAILABILITY: The R codes which implements all described methods, and some Supplementary material, are freely available from http://www.utdallas.edu/~ying.liu/BetaRatio.htm     

Analysis of trends and variability of toxic concentrations in the Niagara River using the Hilbert-Huang transform method

This study introduces a more recent data analysis method, Hilbert Huang Transform method (HHT), to describe contaminant concentration data of a non-stationary and non-linear nature. In order to improve the modeling of the contaminant concentrations, it is proposed to first process the data using the Empirical mode decomposition (EMD) method from HHT to obtain a collection of intrinsic mode functions (IMFs) which can then be modeled separately using either autoregressive moving average (ARMA) models expanded with a seasonal term, or linear regression analysis, depending on the nature of the IMF. Three priority contaminants measured at Niagara-on-the-Lakes are selected for this study. It is found that the trend of fluoranthene concentrations from April of 1986 to March of 1997 is decreasing and then beginning to increase; the 1,2,4-trichlorobenzene concentrations are decreasing; while the dieldrin concentrations are decreasing. With HHT, appropriate time series models can be identified and constructed for the studied contaminant concentrations to better illustrate the variability of each IMF (and thus the contaminant concentrations) for the studied period. For all data sets modeled in this study, pre-processing the data with HHT allowed for higher R² values, correlation coefficients and lower sum of squared errors when compared to modeling without HHT. It is thus confirmed that pre-processing the data with HHT and modeling with time series analysis will provide a more effective means of the studied data sets when identifying and analyzing the trends and variability of studied contaminant concentrations in the Niagara River.     

Temporal associations between weather and headache: analysis by empirical mode decomposition

Background

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 derived from a large-scale epidemiological survey of headache in the Greater Taipei area.

Methodology/Principal Findings

The study sample consisted of 52 randomly selected headache patients. The weather time-series parameters were detrended by the EMD method into a set of embedded oscillatory components, i.e. intrinsic mode functions (IMFs). Multiple linear regression models with forward stepwise methods were used to analyze the temporal associations between weather and headaches. We found no associations between the raw time series of weather variables and headache incidence. For decomposed intrinsic weather IMFs, temperature, sunshine duration, humidity, pressure, and maximal wind speed were associated with headache incidence during the cold period, whereas only maximal wind speed was associated during the warm period. In analyses examining all significant weather variables, IMFs derived from temperature and sunshine duration data accounted for up to 33.3% of the variance in headache incidence during the cold period. The association of headache incidence and weather IMFs in the cold period coincided with the cold fronts.

Conclusions/Significance

Using EMD analysis, we found a significant association between headache and intrinsic weather components, which was not detected by direct comparisons of raw weather data. Contributing weather parameters may vary in different geographic regions and different seasons.     

Microarray learning with ABC

Standard clustering algorithms when applied to DNA microarray data often tend to produce erroneous clusters. A major contributor to this divergence is the feature characteristic of microarray data sets that the number of predictors (genes) in such data far exceeds the number of samples by many orders of magnitude, with only a small percentage of predictors being truly informative with regards to the clustering while the rest merely add noise. An additional complication is that the predictors exhibit an unknown complex correlational configuration embedded in a small subspace of the entire predictor space. Under these conditions, standard clustering algorithms fail to find the true clusters even when applied in tandem with some sort of gene filtering or dimension reduction to reduce the number of predictors. We propose, as an alternative, a novel method for unsupervised classification of DNA microarray data. The method, which is based on the idea of aggregating results obtained from an ensemble of randomly resampled data (where both samples and genes are resampled), introduces a way of tilting the procedure so that the ensemble includes minimal representation from less important areas of the gene predictor space. The method produces a measure of dissimilarity between each pair of samples that can be used in conjunction with (a) a method like Ward's procedure to generate a cluster analysis and (b) multidimensional scaling to generate useful visualizations of the data. We call the dissimilarity measures ABC dissimilarities since they are obtained by aggregating bundles of clusters. An extensive comparison of several clustering methods using actual DNA microarray data convincingly demonstrates that classification using ABC dissimilarities offers significantly superior performance.     

Missing value imputation for microRNA expression data by using a GO-based similarity measure

Missing values are commonly present in microarray data profiles. Instead of discarding genes or samples with incomplete expression level, missing values need to be properly imputed for accurate data analysis. The imputation methods can be roughly categorized as expression level-based and domain knowledge-based. The first type of methods only rely on expression data without the help of external data sources, while the second type incorporates available domain knowledge into expression data to improve imputation accuracy. In recent years, microRNA (miRNA) microarray has been largely developed and used for identifying miRNA biomarkers in complex human disease studies. Similar to mRNA profiles, miRNA expression profiles with missing values can be treated with the existing imputation methods. However, the domain knowledge-based methods are hard to be applied due to the lack of direct functional annotation for miRNAs. With the rapid accumulation of miRNA microarray data, it is increasingly needed to develop domain knowledge-based imputation algorithms specific to miRNA expression profiles to improve the quality of miRNA data analysis. We connect miRNAs with domain knowledge of Gene Ontology (GO) via their target genes, and define miRNA functional similarity based on the semantic similarity of GO terms in GO graphs. A new measure combining miRNA functional similarity and expression similarity is used in the imputation of missing values. The new measure is tested on two miRNA microarray datasets from breast cancer research and achieves improved performance compared with the expression-based method on both datasets. The experimental results demonstrate that the biological domain knowledge can benefit the estimation of missing values in miRNA profiles as well as mRNA profiles. Especially, functional similarity defined by GO terms annotated for the target genes of miRNAs can be useful complementary information for the expression-based method to improve the imputation accuracy of miRNA array data. Our method and data are available to the public upon request.     

A novel model-free approach for reconstruction of time-delayed gene regulatory networks

Many important biological processes (e.g. cellular differentiation during development, aging, disease etiology etc.) are very unlikely controlled by a single gene instead by the underlying complex regulatory interactions between thousands of genes within …