Department of Chemistry, University of Isfahan, Isfahan, Iran.
Anal Chim Acta. 2013 Apr 15;772:16-25. doi: 10.1016/j.aca.2013.02.042. Epub 2013 Mar 6.
Multivariate curve resolution-particle swarm optimization (MCR-PSO) algorithm is proposed to exploit pure chromatographic and spectroscopic information from multi-component hyphenated chromatographic signals. This new MCR method is based on rotation of mathematically unique PCA solutions into the chemically meaningful MCR solutions. To obtain a proper rotation matrix, an objective function based on non-fulfillment of constraints is defined and is optimized using particle swarm optimization (PSO) algorithm. Initial values of rotation matrix are calculated using local rank analysis and heuristic evolving latent projection (HELP) method. The ability of MCR-PSO in resolving the chromatographic data is evaluated using simulated gas chromatography-mass spectrometry (GC-MS) and high-performance liquid chromatography-diode array detection (HPLC-DAD) data. To present a comprehensive study, different number of components and various levels of noise under proper constraints of non-negativity, unimodality and spectral normalization are considered. Calculation of the extent of rotational ambiguity in MCR solutions for different chromatographic systems using MCR-BANDS method showed that MCR-PSO solutions are always in the range of feasible solutions like true solutions. In addition, the performance of MCR-PSO is compared with other popular MCR methods of multivariate curve resolution-objective function minimization (MCR-FMIN) and multivariate curve resolution-alternating least squares (MCR-ALS). The results showed that MCR-PSO solutions are rather similar or better (in some cases) than other MCR methods in terms of statistical parameters. Finally MCR-PSO is successfully applied in the resolution of real GC-MS data. It should be pointed out that in addition to multivariate resolution of hyphenated chromatographic signals, MCR-PSO algorithm can be straightforwardly applied to other types of separation, spectroscopic and electrochemical data.
多元曲线分辨-粒子群优化（MCR-PSO）算法被提出用于从多组分键合色谱信号中挖掘纯色谱和光谱信息。这种新的 MCR 方法基于将数学上唯一的 PCA 解旋转到有化学意义的 MCR 解中。为了获得合适的旋转矩阵，定义了一个基于约束不满足的目标函数，并使用粒子群优化（PSO）算法对其进行优化。旋转矩阵的初始值使用局部秩分析和启发式演化潜在投影（HELP）方法计算。使用模拟气相色谱-质谱（GC-MS）和高效液相色谱-二极管阵列检测（HPLC-DAD）数据评估 MCR-PSO 在解析色谱数据方面的能力。为了进行全面的研究，在非负性、单峰性和光谱归一化等适当约束下，考虑了不同数量的成分和不同水平的噪声。使用 MCR-BANDS 方法计算不同色谱系统中 MCR 解的旋转模糊度程度表明，MCR-PSO 解始终在可行解范围内，如真实解。此外，将 MCR-PSO 的性能与其他流行的多元曲线分辨-目标函数最小化（MCR-FMIN）和多元曲线分辨-交替最小二乘法（MCR-ALS）的 MCR 方法进行了比较。结果表明，在统计参数方面，MCR-PSO 解与其他 MCR 方法相当或更好（在某些情况下）。最后，将 MCR-PSO 成功应用于实际 GC-MS 数据的解析。应当指出，除了对键合色谱信号进行多元分辨外，MCR-PSO 算法还可以直接应用于其他类型的分离、光谱和电化学数据。
