标题： 探索Lx-范数惩罚项在多变量曲线分辨率方法中解析LC/GC-MS数据的效果 显示英文标题

标题： Exploring the effects of Lx-norm penalty terms in multivariate curve resolution methods for resolving LC/GC-MS data

摘要： 复杂LC-MS或GC-MS数据的解析存在不同的问题，例如嵌入色谱峰的存在、连续背景以及不同组分在质量通道中的重叠。 这些问题导致使用多变量曲线分辨率(MCR)方法计算出的恢复轮廓出现旋转模糊性。 由于质谱本质上是稀疏的，最近提出了稀疏性作为分析LC-MS数据的MCR方法中的约束条件。 实现稀疏性约束有不同的方式，大多数方法依赖于基于恢复质谱的L0-、L1-和L2-范数的惩罚。 岭回归和最小绝对收缩与选择算子(Lasso)可以分别用于在MCR中实现L2-和L1-范数惩罚。 主要的问题是，在MCR方法中，哪个Lx-范数惩罚对于实现稀疏性约束更有价值。 为了回答这个问题，在这项工作中模拟了两组分和三组分的LC-MS数据，并用于案例研究。 使用网格搜索策略计算了可行解区域(AFS)。 计算零到二之间的x值在AFS中的Lx-范数值显示，优化曲面的梯度从x等于二逐渐增加到接近零的x值。 然而，当x等于零时，优化曲面类似于一个平台，这增加了陷入局部最小值的风险。 总的来说，本工作中的结果推荐使用L1-范数惩罚方法，如Lasso，用于在MCR-ALS算法中实现稀疏性约束，以找到更稀疏的解决方案并减少旋转模糊性的程度。 显示英文摘要

摘要： There are different problems for resolution of complex LC-MS or GC-MS data, such as the existence of embedded chromatographic peaks, continuum background and overlapping in mass channels for different components. These problems cause rotational ambiguity in recovered profiles calculated using multivariate curve resolution (MCR) methods. Since mass spectra are sparse in nature, sparsity has been proposed recently as a constraint in MCR methods for analyzing LC-MS data. There are different ways for implementation of the sparsity constraint, and majority of methods rely on imposing a penalty based on the L0-, L1- and L2-norms of recovered mass spectra. Ridge regression and least absolute shrinkage and selection operator (Lasso) can be used for implementation of L2- and L1-norm penalties in MCR, respectively. The main question is which Lx-norm penalty is more worthwhile for implementation of the sparsity constraint in MCR methods. In order to address this question, two and three component LC-MS data were simulated and used for the case study in this work. The areas of feasible solutions (AFS) were calculated using the grid search strategy. Calculating Lx-norms values in AFS for x between zero and two revealed that the gradient of optimization surface increased from x values equal to two to x values near zero. However, for x equal to zero, the optimization surface was similar to a plateau, which increased the risk of sticking in local minima. Generally, results in this work, recommend the use of L1-norm penalty methods like Lasso for implementation of sparsity constraint in MCR-ALS algorithm for finding more sparse solutions and reducing the extent of rotational ambiguity.