A parallel model of independent component analysis constrained by a 5-parameter reference curve and its solution by multi-target particle swarm optimization

Abstract

The separation technologies of 3D chromatograms have been researched for a long time to obtain spectra and chromatogram peaks for individual compounds. However, before applying most of the current methods, the number of compounds must be known in advance. Independent Component Analysis (ICA) is applied to separate 3D chromatograms without knowing the compounds' number in advance, but the existence of the noise component in the results makes it complex for computation. In this paper, a parallel model of Independent Component Analysis constrained by a 5-parameter Reference Curve (pICA5pRC) is proposed based on the ICA model. Introducing a priori knowledge from chromatogram peaks, the pICA5pRC model transformed the 3D chromatogram separation problem to a 5 parameters optimization issue. An algorithm named multi-target particle swarm optimization (mPSO) has been developed to solve the pICA5pRC model. Through simulations, the performance and explanation of our method were described. Through experiments, the practicability of our method is validated. The results show that: (1) our method could separate 3D chromatograms efficiently even with severe overlap without knowing the compounds' number in advance; (2) our method extracted chromatogram peaks from the dataset directly without noise components; (3) our method could be applied to the practical HPLC-DAD dataset.

Separation model of Generalized Reference Curve Measurement for HPLC-DAD and it solution by multi-target Bare Bones Particle Swarm Optimization

“…Our method had advantage over MCR-ALS at stability and practicability. The GRCM model is simpler and quicker than our previous method in literature [3].…”

“…The reference curve used in the experiment is the five-parameter function proposed in literature [3]. The results are shown in Table II and Figure 4.…”

“…The structure of parameters p θ and the estimator used to calculate spectra are the same as that in literature [3], which is not repeated here. In the first stage, four times of initialization with P parameters are implemented to generate 4 P × parameters totally.…”

“…2, the GRCM model is consisted of the Reference Curves (RCs) ( ) R θ , X , the Reference Curve Measurement (RCM) model, the Predicted Curves (PC) Y , and the Measurement Operator (MO) MO i . The ( ) R θ are the same as that used in literature [3].…”

“…Then, the High Performance Liquid Chromatography with Diode Array Detector (HPLC-DAD) data set is applied prevalently, whose principle can be descripted by following equation [3].…”