Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series

Knowledge-based matrix factorization temporally resolves the cellular responses to IL-6 stimulation

<p>Abstract</p> <p>Background</p> <p>External stimulations of cells by hormones, cytokines or growth factors activate signal transduction pathways that subsequently induce a re-arrangement of cellular gene expression. The analysis of such changes is complicated, as they consist of multi-layered temporal responses. While classical analyses based on clustering or gene set enrichment only partly reveal this information, matrix factorization techniques are well suited for a detailed temporal analysis. In signal processing, factorization techniques incorporating data properties like spatial and temporal correlation structure have shown to be robust and computationally efficient. However, such correlation-based methods have so far not be applied in bioinformatics, because large scale biological data rarely imply a natural order that allows the definition of a delayed correlation function.</p> <p>Results</p> <p>We therefore develop the concept of graph-decorrelation. We encode prior knowledge like transcriptional regulation, protein interactions or metabolic pathways in a weighted directed graph. By linking features along this underlying graph, we introduce a partial ordering of the features (e.g. genes) and are thus able to define a graph-delayed correlation function. Using this framework as constraint to the matrix factorization task allows us to set up the fast and robust graph-decorrelation algorithm (GraDe). To analyze alterations in the gene response in <it>IL-6 </it>stimulated primary mouse hepatocytes, we performed a time-course microarray experiment and applied GraDe. In contrast to standard techniques, the extracted time-resolved gene expression profiles showed that <it>IL-6 </it>activates genes involved in cell cycle progression and cell division. Genes linked to metabolic and apoptotic processes are down-regulated indicating that <it>IL-6 </it>mediated priming renders hepatocytes more responsive towards cell proliferation and reduces expenditures for the energy metabolism.</p> <p>Conclusions</p> <p>GraDe provides a novel framework for the decomposition of large-scale 'omics' data. We were able to show that including prior knowledge into the separation task leads to a much more structured and detailed separation of the time-dependent responses upon <it>IL-6 </it>stimulation compared to standard methods. A Matlab implementation of the GraDe algorithm is freely available at <url>http://cmb.helmholtz-muenchen.de/grade</url>.</p

A review of second-order blind identification methods

Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed.This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Dat

Second-order blind source separation based on multi-dimensional autocovariances

SOBI is a blind source separation algorithm based on time decorrelation. It uses multiple time autocovariance matrices, and performs joint diagonalization thus being more robust than previous time decorrelation algorithms such as AMUSE. We propose an extensioncalled mdSOBI by using multidimensional autocovariances, which can be calculated for data sets with multidimensional parameterizations such as images or fMRI scans. mdSOBI has the advantage of using the spatial data in all directions, whereas SOBI only uses a single direction. These findings are confirmed by simulations and an application to fMRI analysis, where mdSOBI outperforms SOBI considerably

Simultaneous pulse rate estimation for two individuals that share a sensor-laden bed

Master of ScienceDepartment of Electrical and Computer EngineeringSteven WarrenSleep monitoring has received increased attention in recent years given an improved understanding of the impact of sleep quality on overall well-being. A Kansas State University team has developed a sensor-based bed that can unobtrusively track sleep quality for an individual by analyzing their ballistocardiograms (BCGs) while they lay on the bed, foregoing the need to visit a sleep clinic to quantify their sleep quality. A BCG is a signal that represents cardiac forces that have spread from the heart to the rest of the body – forces that result in part from the injection of blood into the vascular system. The sensor bed software can extract BCG-based health parameters such as heart rate and respiration rate from data acquired continuously throughout the night. Such a toolset creates a new challenge, namely that many people sleep on a shared bed. In such cases, a given sensor bed would acquire mixed BCGs that contain information for both people. This thesis documents efforts to create an algorithm to extract individual health parameters from mixed parent BCGs obtained from bed sensors that reside on a shared bed. The first component of the two-part algorithm performs ‘blind source separation:’ a technique originally designed for mixed audio applications that attempts to optimally separate two individual BCGs contained in an original mixed signal. The second component of the algorithm utilizes a frequency-domain, peak-scoring method to identify the most likely fundamental BCG harmonic for each separated signal – a harmonic that corresponds to the pulse rate for that individual. The peak-scoring approach allows the algorithm to overcome challenges associated with different time-domain BCG waveform shapes, the presence of signal artifact, and the loss of BCG characteristic features that occurs during the separation stage. These challenges can be problematic for time-domain pulse rate algorithms, but the repetitive waveform patterns can be exploited in the frequency-spectrum. The peak-scoring algorithm was verified by comparing pulse rates determined from single-subject BCGs (obtained in various sleeping positions) against pulse rates determined from simultaneously collected electrocardiograms. The separation and peak-scoring components were combined together, and this overall technique was applied to over 20 sets of paired BCG data, with variations in sensor placement, sensor type and mattress type. Early results indicate the ability of the algorithm to determine pulse rates from mixed BCGs with acceptable levels of success but with areas for improvement

A comparative DC-EEG study about learned helplessness

Erlernte Hilflosigkeit tritt auf wenn ein Individuum keine Erwartung mehr hat Kontrolle ausüben zu können und dadurch passiv wird. Der Frage wie Hilflosigkeit mit neuronalen Prozessen zusammen hängt sind bisher nur wenige Studien nachgegangen. EEG-Studien (Bauer et al., 2002; Fretska et al., 1999) zeigten dass hilflose Personen signifikant positive Veränderungen der langsamen kortikalen Potentiale während der Hilflosigkeitsinduktion aufwiesen im Vergleich zur Kontrollbedingung. Darüber hinaus gab es Hinweise darauf dass Frauen eher zu Hilflosigkeit neigen und auch auf neuronaler Ebene signifikante Veränderungen zeigen im Vergleich zu den Männern die eher weniger emotional reagierten. Die Analyse der neuronalen Quellenlokalisation mit LORETA wies auf eine erniedrigte Aktivität des anterioren cingulären cortex (ACC) während der Hilflosigkeitsinduktion hin. Die vorliegende Studie untersuchte angelehnt an Bauer et al. (2003) langsame kortikale Potentiale bei Personen die hilflos wurden und Personen die nicht hilflos wurden. Hilflosigkeit wurde mit Hilfe von unlösbaren Zahlenreihenaufgaben induziert und die Hilflosigkeitsklassifikation wurde anhand eines Scores aus dem Hilflosigkeitsfragebogen (Bauer et al., 2003) ermittelt. Insgesamt wurden 57,1 % der Teilnehmer hilflos. Obwohl etwas mehr Frauen (63,2 %) als Männer (52,2%) hilflos wurden, war dieser Effekt nicht signifikant. Hilflose zeigten Veränderungen ihrer langsamen kortikalen Potentiale in Richtung Positivität während der Phase der Hilflosigkeitsinduktion im Vergleich zu nicht hilflosen Personen. Dieser Trend stellte sich als statistisch nicht signifikant heraus. Jedoch ergaben sich Geschlechtsunterschiede in der Hinsicht, dass Frauen signifikant positivere langsame kortikale Potenziale während der Bearbeitung unlösbarer Aufgaben zeigten. Diese Ergebnisse stimmen mit den Studien von Fretska et al. (1999) und Bauer et al. (2003) überein. Für die gesamte Stichprobe hat sich gezeigt dass langsame kortikale Potenziale am positivsten in den Elektroden frontal-rechts waren. Die Analyse der neuronalen Quellenlokalisation mit sLORETA brachte keine signifikanten Unterschiede zwischen den einzelnen Gruppen (hilflos und nicht hilflos, Männer und Frauen) und konnte somit das Ergebnis von Bauer et al. (2003) nicht bestätigen.Learned helplessness emerges when individuals do not have any expectancy of control any more and therefore become passive. So far only a few studies have dealt with the question how learned helplessness is associated with neuronal processes. EEG studies (Bauer et al., 2002; Fretska et al., 1999) showed that helpless subjects had significant positive going slow cortical potential shifts (SCP-shifts) during helplessness induction compared to the control phase. Furthermore, the studies indicated that women became more helpless or more often helpless than men. Moreover, analysis of neuronal source localization with LORETA demonstrated a significant decrease in activity of the anterior cingulate cortex (ACC) during helplessness. Based on the study of Bauer et al. (2003), the present study investigated SCPs in 42 subjects (23 females). Helplessness was induced by unolvable numerical series and was assessed via a score from the helplessness questionnaire (Bauer et al., 2003). Data analysis revealed that overall 57.1 % of the participants became helpless. Although slightly more women became helpless (63.2%) than men (52.2%), this effect was not significant. Helpless subjects showed positive going SCP shifts during the helplessness induction compared to non-helpless subjects. However these trends were only limited to posterior regions and were statistically not significant. Female participants though, showed significant positive going SCP shifts in the unsolvable condition (helplessness induction) which is consistent with the findings of Fretska et al. (1999) and Bauer et al. (2003). For the whole sample, SCPs appeared to be most positive in frontal-right electrodes. The neuronal source localization analysis with sLORETA did not reveal any significant differences between the groups (helpless and non helpless subjects, male and female) and could not confirm the findings of Bauer et al. (2003)