A comparison of two algorithms for warping of analytical signals

The alignment of analytical signals is an important preprocessing step when further analysis (e.g. PCA) requires the same lengths of all of them. Two techniques for alignment of profiles, namely dynamic time warping (DTW) and correlation optimized warping (COW) were tested and compared. The attention was focused on chromatographic and spectroscopic profiles. Simulated and two sets of real data were studied in this study.     

Hotelling trace criterion as a figure of merit for the optimization of chromatogram alignment

We present a methodology for optimization of chromatogram alignment using a class separability measure called the Hotelling trace criterion (HTC). This metric is a multi‐class distance measure that accounts for within‐class and between‐class variation. We chose the correlation optimized warping algorithm as our alignment method and used the HTC to judge the effectiveness of the alignment based on algorithm parameters called segment length and max warp. Biodiesel feedstock samples representing classes of soy, canola, tallow, waste grease, and hybrid were used in our experiments. Fatty acid methyl esters in each biodiesel were separated using gas chromatography‐mass spectroscopy. The entire data set was baseline corrected, aligned, normalized, and mean‐centered prior to principal components (PCs) analysis. The aligned, baseline corrected data sets were used to compute a figure of merit called warping effect, while the PC‐transformed data sets were used to evaluate the HTC. The segment length and max warp parameters that maximized the warping effect and/or HTC were then determined. Scores plots of pairs of PCs, along with 95% confidence ellipses, were created and analyzed. The results demonstrated that the parameters derived from maximizing the HTC more effectively aligned the data, as evidenced by better clustering of the biodiesels in the scores plots. This behavior was robust to the number of PCs used in the computation of the HTC. We conclude that the HTC is an objective measure of alignment quality that allows for optimal class separability and can be applied to optimize other methods of chromatogram alignment. Copyright © 2015 John Wiley & Sons, Ltd.     

A comparison of three algorithms for chromatograms alignment

In this paper the performance of three alignment algorithms, correlation optimized warping, parametric time warping and semi-parametric time warping, is compared on real chromatograms. Among these, parametric time warping is the simplest and fastest; generally less than 1s is required to align two chromatograms. It does not require the optimization of input parameters and allows the alignment of peak shifts in only one direction, or non-complex peak shifts in both directions. With correlation optimized warping and semi-parametric time warping complex peak shifts in both directions can be corrected but at the expense of the optimization of two input parameters. Semi-parametric time warping requires the selection of the proper number of B-splines in the warping function and, if necessary, the optimization of the penalty parameter. Often the default values can be used to obtain aligned signals. The optimization of the input parameters for correlation optimized warping (section length, slack) is not easy and time-consuming. Moreover, dependent on the input parameters, the computation time of the correlation optimized warping algorithm can be twice as long as for semi-parametric time warping for which computation times up to 23 s are required. However, the performance of both algorithms is equally good considering the improvement of the precision of the peak retention times and correlation coefficients between the chromatograms, after alignment. For the data aligned in this study, the average retention time precision and the lowest correlation before warping were 14 and 0.17, and were improved to three and 0.83, and six and 0.87 after warping, with correlation optimized warping and semi-parametric time warping, respectively.     

Longest distance shifting: A simple and efficient approach for the alignment of shifted chromatographic peaks

The preprocessing of chromatograms, such as the alignment of retention time shifts, is often a crucial step in the proper data analysis chain. Here, an efficient approach to align shifted chromatographic signals, longest distance shifting, is presented and highlighted. The performance of this novel strategy was demonstrated by using both simulated chromatograms that covered the different kinds of retention time shifts and the real experimental chromatograms of Pudilan Xiaoyan Tablets obtained by high‐performance liquid chromatography with photodiode array detection. The averaged correlation coefficient for experimental chromatograms were in the range of 0.9517–0.9840 and the peak factor was 0.9989. As a comparison, all the chromatograms have also been aligned using correlation optimized warping and Interval Correlation Optimized Shifting algorithms. The obtained results indicate that the longest distance shifting algorithm is simpler, faster and more effective, and will be potentially suitable for the alignment of other types of signals.     

icoshift: An effective tool for the alignment of chromatographic data

The Interval Correlation Optimised Shifting algorithm (icoshift) has recently been introduced for the alignment of nuclear magnetic resonance spectra. The method is based on an insertion/deletion model to shift intervals of spectra/chromatograms and relies on an efficient Fast Fourier Transform based computation core that allows the alignment of large data sets in a few seconds on a standard personal computer. The potential of this programme for the alignment of chromatographic data is outlined with focus on the model used for the correction function. The efficacy of the algorithm is demonstrated on a chromatographic data set with 45 chromatograms of 64,000 data points. Computation time is significantly reduced compared to the Correlation Optimised Warping (COW) algorithm, which is widely used for the alignment of chromatographic signals. Moreover, icoshift proved to perform better than COW in terms of quality of the alignment (viz. of simplicity and peak factor), but without the need for computationally expensive optimisations of the warping meta-parameters required by COW. Principal component analysis (PCA) is used to show how a significant reduction on data complexity was achieved, improving the ability to highlight chemical differences amongst the samples.     

Evaluation of novel sample identification approach based on chromatographic fingerprint set correlation homogeneity analysis

Instead of usual rationale for chromatographic fingerprint based sample identification which relies upon visual inspection or principal component analysis of raw or aligned chromatograms novel nonparametric statistical measure of fingerprint set homogeneity is proposed. Randomization test is applied for significance analysis of fingerprint set homogeneity while average maximum crosscorrelation is used as a merit function. Chromatogram sets generated by random selection from standard and unknown sample chromatogram collections are compared with respect to merit function values with set of chromatograms that represents standard and/or unknown sample. In that instance fingerprint homogeneity significance is represented by the fraction of random chromatogram sets that have higher merit values than the standard and/or unknown sample sets. A set of peptide maps corresponding to different haemoglobin variants has been selected for evaluation of proposed test. This approach is compared to chromatogram alignment based on correlation optimized warping coupled with principal component or cluster analysis. Proposed method is simple i.e. straightforward sample identification procedure which reliability has been evaluated here. Impact of this approach on peptide mapping validation and system suitability analysis is discussed.     

High-speed peak matching algorithm for retention time alignment of gas chromatographic data for chemometric analysis

A rapid retention time alignment algorithm was developed as a preprocessing utility to be used prior to chemometric analysis of large datasets of diesel fuel profiles obtained using gas chromatography (GC). Retention time variation from chromatogram-to-chromatogram has been a significant impediment against the use of chemometric techniques in the analysis of chromatographic data due to the inability of current chemometric techniques to correctly model information that shifts from variable to variable within a dataset. The alignment algorithm developed is shown to increase the efficacy of pattern recognition methods applied to diesel fuel chromatograms by retaining chemical selectivity while reducing chromatogram-to-chromatogram retention time variations and to do so on a time scale that makes analysis of large sets of chromatographic data practical. Two sets of diesel fuel gas chromatograms were studied using the novel alignment algorithm followed by principal component analysis (PCA). In the first study, retention times for corresponding chromatographic peaks in 60 chromatograms varied by as much as 300 ms between chromatograms before alignment. In the second study of 42 chromatograms, the retention time shifting exhibited was on the order of 10 s between corresponding chromatographic peaks, and required a coarse retention time correction prior to alignment with the algorithm. In both cases, an increase in retention time precision afforded by the algorithm was clearly visible in plots of overlaid chromatograms before and then after applying the retention time alignment algorithm. Using the alignment algorithm, the standard deviation for corresponding peak retention times following alignment was 17 ms throughout a given chromatogram, corresponding to a relative standard deviation of 0.003% at an average retention time of 8 min. This level of retention time precision is a 5-fold improvement over the retention time precision initially provided by a state-of-the-art GC instrument equipped with electronic pressure control and was critical to the performance of the chemometric analysis. This increase in retention time precision does not come at the expense of chemical selectivity, since the PCA results suggest that essentially all of the chemical selectivity is preserved. Cluster resolution between dissimilar groups of diesel fuel chromatograms in a two-dimensional scores space generated with PCA is shown to substantially increase after alignment. The alignment method is robust against missing or extra peaks relative to a target chromatogram used in the alignment, and operates at high speed, requiring roughly 1 s of computation time per GC chromatogram.     

Multi‐scale Gaussian/Haar wavelet strategies coupled with sub‐window factor analysis for an accurate alignment in nontargeted metabolic profiling to enhance herbal origin discrimination capability

Metabolic dataset can provide an overview of different herbal origin, which is conducted by some statistical procedures. Such results often deviate to a certain degree, due to peaks shifts in chromatographic signals. In order to solve this problem, an improved algorithm of combining sub‐window factor analysis with the mass spectrum information is proposed. The algorithm uses a peak detection approach derived either from multi‐scale Gaussian function or Haar wavelet to locate the peaks with different application scope; the candidate drift points at each peak are estimated by Fast Fourier transform cross correlation; Specifically, the best drift points at each candidate peaks are confirmed by sub‐window factor analysis and mass spectrum information in nontargeted metabolic profiling. Finally, the peak regions were aligned against a reference chromatogram, and the non‐peak regions were used linear interpolation. The chromatographic signals of 30 Bupleurum samples were aligned as an illustration of this algorithm, and they could be well distinguished using some statistical procedures. The result demonstrates that the presented method is stronger than other mass‐spectra based algorithms, when facing the alignment of some co‐eluted peaks.     

Real-time target selection optimization to enhance alignment of gas chromatograms

An improved method for real-time selection of the target for the alignment of gas chromatographic data is described. Further outlined is a simple method to determine the accuracy of the alignment procedure. The target selection method proposed uses a moving window of aligned chromatograms to generate a target, herein referred to as the window target method (WTM). The WTM was initially tested using a series of 100 simulated chromatograms, and additionally evaluated using a series of 55 diesel fuel gas chromatograms obtained with four fuel samples. The WTM was evaluated via a comparison to a related method (the nearest neighbor method (NNM)). The results using the WTM with simulated chromatograms showed a significant improvement in the correlation coefficient and the accuracy of alignment when compared to the alignments performed using the NNM. A significant improvement in real-time alignment accuracy, as assessed by a correlation coefficient metric, was achieved with the WTM (starting at ∼1.0 and declining to only ∼0.985 for the 100th sample), relative to the NNM (starting at ∼1.0 and declining to ∼0.4 for the 100th sample) for the simulated chromatogram study. The results determined when using the WTM with the diesel fuels also showed an improvement in correlation coefficient and accuracy of the within-class alignments as compared to the results obtained from the NNM. In practice, the WTM could be applied to the real-time analysis of process and feedstock industrial streams to enable real-time decision making from the more precisely aligned chromatographic data.     

复杂色谱信号自动解析中的化学计量学方法

色谱及其联用技术日趋完善,并向自动化、高通量和快速的方向发展。化学计量学利用"数学分离"手段,可以实现色谱信号的自动化解析,已成为现代色谱分析中非常活跃的研究领域。但以往的化学计量学方法并不能完全有效地实现复杂色谱信号自动化解析。为此,自动化色谱解析算法成为科研工作者关心的重点,众多新型的自动化解析算法被提出。针对复杂一维色谱数据以及联用仪器得到的二维和更高维数据的自动化分析,化学计量学研究主要集中在自动色谱峰识别、背景以及基线漂移校正、色谱谱峰漂移校正以及重叠色谱峰的解析。该文对近十年来发展的复杂体系色谱信号自动化解析中化学计量学方法的原理与应用进行了总结与评述,比较了各类方法的优势与不足。在此基础上,针对当前色谱自动化分析过程中的难题对未来该领域的研究方向进行了展望。     

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.     

Retention time alignment of LC/MS data by a divide-and-conquer algorithm

Liquid chromatography-mass spectrometry (LC/MS) has become the method of choice for characterizing complex mixtures. These analyses often involve quantitative comparison of components in multiple samples. To achieve automated sample comparison, the components of interest must be detected and identified, and their retention times aligned and peak areas calculated. This article describes a simple pairwise iterative retention time alignment algorithm, based on the divide-and-conquer approach, for alignment of ion features detected in LC/MS experiments. In this iterative algorithm, ion features in the sample run are first aligned with features in the reference run by applying a single constant shift of retention time. The sample chromatogram is then divided into two shorter chromatograms, which are aligned to the reference chromatogram the same way. Each shorter chromatogram is further divided into even shorter chromatograms. This process continues until each chromatogram is sufficiently narrow so that ion features within it have a similar retention time shift. In six pairwise LC/MS alignment examples containing a total of 6507 confirmed true corresponding feature pairs with retention time shifts up to five peak widths, the algorithm successfully aligned these features with an error rate of 0.2%. The alignment algorithm is demonstrated to be fast, robust, fully automatic, and superior to other algorithms. After alignment and gap-filling of detected ion features, their abundances can be tabulated for direct comparison between samples.     

Unsupervised parameter optimization for automated retention time alignment of severely shifted gas chromatographic data using the piecewise alignment algorithm

Simulated chromatographic separations were used to study the performance of piecewise retention time alignment and to demonstrate automated unsupervised (without a training set) parameter optimization. The average correlation coefficient between the target chromatogram and all remaining chromatograms in the data set was used to optimize the alignment parameters. This approach frees the user from providing class information and makes the alignment algorithm applicable to classifying completely unknown data sets. The average peak in the raw simulated data set was shifted up to two peak-widths-at-base (average relative shift=2.0) and after alignment the average relative shift was improved to 0.3. Piecewise alignment was applied to severely shifted GC separations of gasolines and reformate distillation fraction samples. The average relative shifts in the raw gasolines and reformates data were 4.7 and 1.5, respectively, but after alignment improved to 0.5 and 0.4, respectively. The effect of piecewise alignment on peak heights and peak areas is also reported. The average relative difference in peak height was -0.20%. The average absolute relative difference in area was 0.15%.     

A new algorithm of piecewise automated beam search for peak alignment of chromatographic fingerprints

The alignment of chromatographic signals is an important preprocessing step before further multivariate analysis. This paper presents a method, automated peak alignment by beam search (Auto-PABS), to solve the problem of peak shift in chemical chromatographic fingerprints by piecewise shifting and linearly interpolating. It is characterized by searching an adaptive range for the values of shifting and linearly interpolating of each segment. This search range is estimated by the calculation of fast Fourier transform cross correlation between the sample segment and its corresponding reference segment. Thus, arbitrary peak alignment is avoided when the real peak shifts are unknown in a large data set. Since the maximum of search range is close to the real shift, more accurate beam search is adopted to accomplish the optimization process. Simulated data and herbal medicine fingerprints of HPLC and GC are selected for evaluation. The output matrix of aligned chromatographic profiles is used directly for principal components analysis, yielding satisfactory results on real samples.     

Rapid Determination of Amino Acids in Ginseng by High Performance Liquid Chromatography and Chemometric Resolution

Ginseng is one of the most important traditional Chinese medicines and functional foods.A method for the fast determination of amino acids in ginseng samples using high performance liquid chromatography（HPLC） was developed,in which strong isocratic elution was employed for simplifying the separation and speeding up the analysis.All amino acids were eluted within 3 min with the chromatogram composed of overlapped peaks from the interferences.Then,non-negative immune algorithm（NNIA） was adopted to resolve the chromatographic signals of the components from the chromatogram measured.The results show that the signals of the amino acids can be correctly extracted by NNIA and the signal extracted can be used for the quantitative analysis.The method was validated via determining six amino acids of four different samples of ginseng.The recoveries of the spiked samples are in a range of 96.6％-106.3％.     

Total ion chromatographic fingerprints combined with chemometrics and mass defect filter to predict antitumor components of Picrasma quassioids

A method of total ion chromatogram combined with chemometrics and mass defect filter was established for the prediction of active ingredients in Picrasma quassioides samples. The total ion chromatogram data of 28 batches were pretreated with wavelet transformation and correlation optimized warping to correct baseline drifts and retention time shifts. Then partial least squares regression was applied to construct a regression model to bridge the total ion chromatogram fingerprints and the antitumor activity of P. quassioides. Finally, the regression coefficients were used to predict the active peaks in total ion chromatogram fingerprints. In this strategy, mass defect filter was employed to classify and characterize the active peaks from a chemical point of view. A total of 17 constituents were predicted as the potential active compounds, 16 of which were identified as alkaloids by this developed approach. The results showed that the established method was not only simple and easy to operate, but also suitable to predict ultraviolet undetectable compounds and provide chemical information for the prediction of active compounds in herbs.     

Alignment and clustering strategies for GC×GC–MS features using a cylindrical mapping

Comprehensive two-dimensional gas chromatography coupled to mass spectrometry is a powerful tool to analyze complex samples. For application of the technique in studies like biomarker discovery in which large sets of complex samples have to be analyzed, extensive preprocessing is needed to align the data obtained in several injections (analyses). We developed new alignment and clustering algorithms for this type of data. New in the current procedures is the consistent way in which the phenomenon referred to as wrap-around is treated. The data analysis problems associated with this phenomenon are solved by treating the 2D display as the surface of a three-dimensional cylinder. Based on this transformation we developed a new similarity metric for features as a function of both the cylindrical distance (reflecting similarity in chromatographic behavior) and of the mass spectral correlation (reflecting similarity in chemical structure). The concepts are used in warping and clustering, and include a protection against greedy warping.     

自动化色谱谱图解析——谱峰的自动识别与快速解析

结合基于高阶导数的谱峰识别方法和面积重现法,建立了一种完全自动化的对色谱曲线进行分割、识别与快速解析的方法。其中,DW(Durbin-Watson)测试的引入和区分信号与噪声判据的采用减少了在色谱解析过程中的人为干预,降低了对操作人员专业知识和经验的要求,为实现色谱解析的自动化奠定了基础。通过对模拟色谱和实验色谱的比较,验证了该方法是一个很有用的工具,可以为色谱分析工作提供有力的帮助。     

Peak alignment using wavelet pattern matching and differential evolution

Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).     

Spurenbestimmung von Vergaser- und Dieselkraftstoffen im Wasser mittels Capillar-Gas-Chromatographie/automatischer Mustererkennung

Summary A method for trace analysis determination of carburetor and diesel fuels in water is described. The isolation and concentration of fuel traces is carried out by microextraction with n-hexane using a suitable micro-separator. After their separation by capillary gas chromatography fuels provide typically structured chromatographic patterns and, therefore, a chromatogram (sample pattern) of the extract is generated. The sample pattern is searched for fuel patterns by comparing the chromatogram with reference chromatograms of these fuels in a library. An automatic pattern recognition algorithm is applied, using elements of the fuzzy set theory. As preliminary interpretation the computer delivers a list of identification proposals which have to be assessed and submitted to a final interpretation by the analyst.