Alignment Of Time Series Research Articles

MPA: A multiple peak alignment algorithm to perform multiple comparisons of liquid‐phase proteomic profiles

Present proteomic studies increasingly address experimental strategies focused on multiple comparisons of proteomic profiles. To accomplish semiautomatic protein separations based on 2-D LC, the Beckman Coulter PF2D has been developed. Here, we present a novel general purpose tool called MPA (multiple peak alignment) able to perform multiple comparisons of proteomic profiles both in a pairwise guided fashion and in a fully automatic mode using a strategy based on dynamic programing and progressive alignment of time series. The tool is available at http://grup.cribi.unipd.it/people/stefano/mpa/.

Time-series alignment by non-negative multiple generalized canonical correlation analysis

BackgroundQuantitative analysis of differential protein expressions requires to align temporal elution measurements from liquid chromatography coupled to mass spectrometry (LC/MS). We propose multiple Canonical Correlation Analysis (mCCA) as a method to align the non-linearly distorted time scales of repeated LC/MS experiments in a robust way.ResultsMultiple canonical correlation analysis is able to map several time series to a consensus time scale. The alignment function is learned in a supervised fashion. We compare our approach with previously published methods for aligning mass spectrometry data on a large proteomics dataset. The proposed method significantly increases the number of proteins that are identified as being differentially expressed in different biological samples.ConclusionJointly aligning multiple liquid chromatography/mass spectrometry samples by mCCA substantially increases the detection rate of potential bio-markers which significantly improves the interpretability of LC/MS data.

Linear and nonlinear alignment of time series with applications to varve chronologies

AbstractThe problem of aligning time series arises naturally in a number of fields, but our investigation is motivated by the problem of extracting a paleoclimatic signal from glacial varve chronologies. Glacial varves are laminated sediments that record annual depositional cycles in certain lakes that are fed by glaciers. Varve thickness is determined by temperature and to a lesser extent by precipitation so that an accurate reconstruction of varve chronologies can be regarded as providing a potential long term proxy for paleoclimate. An important aspect of the varve problem is to align series from different locations. What makes the alignment problem particularly interesting is that in either series, one or more varves may be missing or a single varve might have been mistaken for a pair of varves.Traditionally, alignment problems have been treated using linear methods and concepts such as coherency and cross correlation. Since one of the pairs of varve series we look at is not well described by a linear model, in this paper we also employ nonlinear criteria that are derived from recent work on nonlinear identification and dependence modeling. More precisely, we use nonlinear least squares and measures of dependence such as the Kullback—Leibler measure and the Hellinger distance. Both local and global alignment are considered, and in particular we treat the situation where one or more observations may be missing from either series. Properties of the criteria are given and illustrated by simulation. We display examples where linear methods fail, but nonlinear criteria work. For the real data set of varves at our disposal, it will be seen that the nonlinear criteria perform as well as (or better than) the linear ones for the linearly related series, and that only the nonlinear criteria work for the two series that are not linearly related. Copyright © 2007 John Wiley & Sons, Ltd.

Projective filtering of time warped ECG beats

The paper proposes a modification of the nonlinear state-space projections (NSSP) method. Our approach, when applied to ECG signal processing, considerably improves the method's performance. One of the crucial operations in NSSP is the search for neighborhoods of the state-space trajectory points. The modification proposed is based on imposing a few restrictions on the time location of the neighborhood points. Dynamic time warping, a technique which allows for nonlinear alignment of time series or sequences of vectors, is applied as a straightforward solution to the task of neighborhoods determination with the restrictions imposed. The influence of nonlinear alignment on the distributions of the determined neighborhoods is presented, and the resulting method of ECG enhancement is investigated.

Scaling and time warping in time series querying

The last few years have seen an increasing understanding that Dynamic Time Warping (DTW), a technique that allows local flexibility in aligning time series, is superior to the ubiquitous Euclidean Distance for time series classification, clustering, and indexing. More recently, it has been shown that for some problems, Uniform Scaling (US), a technique that allows global scaling of time series, may just be as important for some problems. In this work, we note that for many real world problems, it is necessary to combine both DTW and US to achieve meaningful results. This is particularly true in domains where we must account for the natural variability of human action, including biometrics, query by humming, motion-capture/animation, and handwriting recognition. We introduce the first technique which can handle both DTW and US simultaneously, and demonstrate its utility and effectiveness on a wide range of problems in industry, medicine, and entertainment.

Gene Time Eχpression Warper: a tool for alignment, template matching and visualization of gene expression time series

An application tool for alignment, template matching and visualization of gene expression time series is presented. The core algorithm is based on dynamic time warping techniques used in the speech recognition field. These techniques allow for non-linear (elastic) alignment of temporal sequences of feature vectors and consequently enable detection of similar shapes with different phases. The Java program, examples and a tutorial are available at http://www.psb.ugent.be/cbd/papers/gentxwarper/

An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis

A three-dimensional image registration method for motion correction of functional magnetic resonance imaging (fMRI) time-series, based on independent component analysis (ICA), is described. We argue that movement during fMRI data acquisition results in a simultaneous increase in the joint entropy of the observed time-series and a decrease in the joint entropy of a nonlinear function of the derived spatially independent components calculated by ICA. We propose this entropy difference as a reliable criterion for motion correction and refer to a method that maximizes this as motion-corrected ICA (MCICA). Specifically, a given motion-corrupted volume may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion. In essence, MCICA consists of designing an adaptive spatial resampling filter which maintains maximum temporal independence among the recovered components. In contrast with conventional registration methods, MCICA does not require registration of motion-corrupted volumes to a single reference volume which can introduce artifacts because corrections are applied without accounting for variability due to the task-related activation. Simulations demonstrate that MCICA is robust to activation level, additive noise, random motion in the reference volumes and the exact number of independent components extracted. When the method was applied to real data with minimal estimated motion, the method had little effect and, hence, did not introduce spurious changes in the data. However, in a data series from a motor fMRI experiment with larger motion, preprocessing the data with the proposed method resulted in the emergence of activation in primary motor and supplementary motor cortices. Although mutual information (MI) was not explicitly optimized, the MI between all subsequent volumes and the first one was consistently increased for all volumes after preprocessing the data with MCICA. We suggest MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion.

Multipath Mitigation for Bridge Deformation Monitoring

GPS carrier phase multipath with varying amplitudes of up to several centimetres and periods of couple of minutes is a major error source, which affects the correct interpretation of bridge deformation. In this paper, a recursive adaptive filtering (AF) algorithm has been employed to mitigate multipath signature in the coordinate time series of GPS solutions. In order to maximise the suppression of the multipath signature, exact alignment of the input time series into the AF system is crucial. An algorithm using the cross-correlation coefficient of day-to-day GPS coordinate time series is presented to align GPS coordi-nates. To isolate multipath from the contaminated GPS coordinate time series, relative displacements cal-culated from the accelerations sensed simultaneously with GPS receiver by a triaxial accelerometer housed in a specially designed cage is used as the reference signal sequence within the AF system. Associated al-gorithm for the relative velocity and displacement calculation is also introduced in the paper. It demon-strates that it is possible to achieve millimetre positioning accuracy by the AF approach and an integrated sensor system of GPS receiver and triaxial accelerometer.

Performance assessment of an algorithm for the alignment of fMRI time series.

This paper reports on performance assessment of an algorithm developed to align functional Magnetic Resonance Image (fMRI) time series. The algorithm is based on the assumption that the human brain is subject to rigid-body motion and has been devised by pipelining fiducial markers and tensor based registration methodologies. Feature extraction is performed on each fMRI volume to determine tensors of inertia and gradient image of the brain. A head coordinate system is determined on the basis of three fiducial markers found automatically at the head boundary by means of the tensors and is used to compute a point-based rigid matching transformation. Intensity correction is performed with sub-voxel accuracy by trilinear interpolation. Performance of the algorithm was preliminarily assessed by fMR brain images in which controlled motion has been simulated. Further experimentation has been conducted with real fMRI time series. Rigid-body transformations were retrieved automatically and the value of motion parameters compared to those obtained with the Statistical Parametric Mapping (SPM99) and the Automatic Image Registration (AIR 3.08). Results indicate that the algorithm offers sub-voxel accuracy in performing both misalignment and intensity correction of fMRI time series.

Development and characterization of an automatic technique for the alignment of fMRI time series.

An automatic technique for the registration of fMRI time series has been developed, implemented and tested. The method assumes the human brain to be a rigid body and computes a head coordinate system on the basis of three reference points that lies on the directions corresponding to two of the principal axes of the volume at the intersections with the head boundary. Such directions are found computing the eigenvectors of the symmetric inertia matrix of the image. The inertia components were extracted weighting pixels' coordinates with their intensity values. The three reference points were found in the same position, relative to the head, in both the test and the reference images. The technique has been tested using T2*-weighted Magnetic Resonance (MR) images in which known rigid body transformations have been applied. The results obtained indicate that the method offers subvoxel accuracy in correcting misalignment among time points in fMRI time series.

A new statistical approach to the alignment of time series

Summary. Much research in the Earth Sciences is centred on the search for similarities in waveforms or amongst sets of observations. For example, in seismology and palaeomagnetism, this matching of records is used to align several series of observations against one another or to compare one set of observations against a master series. This paper gives a general mathematical and statistical formulation of the problem of transforming, linearly or otherwise, the time-scale or depth-scale of one series of data relative to another. Existing approaches to this problem, involving visual matching or the use of correlation coefficients, are shown to have several serious deficiencies, and a new statistical procedure, using least-squares cubic splines, is presented. The new method provides not only a best estimate of the ‘stretching function’ defining the relative alignment of the two series of observations, but also a statement, by means of confidence regions, of the precision of this transformation. The new procedure is illustrated by analyses of artificially generated data and of palaeomagnetic observations from two cores from Lake Vuokonjarvi, Finland. It may be applied in a wide variety of situations, wherever the observations satisfy the general underlying mathematical model.