Abstract There is a great deal of interests in multivariate approaches which may offer a necessary, and often sufficient, data analysis technique in many fields such as analytical chemistry, biology and environmental chemistry. However, few of these multivariate approaches have paid attention to the nonnegativity constraint in the decomposition process. In this paper, a novel bound constrained optimization method was proposed for three-way chemical data analysis. In this method, nonnegative matrix factorization was introduced to replace the traditional trilinear decomposition to provide the constraints on the nonnegative boundary on excitation-emission matrix spectra data. And the least-squares problem was transformed into a bound constrained optimization problem which can be solved by projected gradient methods. The alternating least squares were applied during each optimization iteration to obtain the individual components. Analysis of simulated three-way arrays indicated that the proposed method has a better performance than parallel factor analysis and alternating trilinear decomposition methods in nonnegativity. Experiments of real excitation-emission matrix spectra data also show that the proposed method is robust with the background interferences in practical applications.

中文翻译：

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一种应用于荧光激发发射矩阵光谱的三向化学数据分析的新绑定约束优化方法

摘要 多变量方法引起了人们极大的兴趣，这些方法可以在分析化学、生物学和环境化学等许多领域提供必要且通常是充分的数据分析技术。然而，这些多元方法很少关注分解过程中的非负性约束。在本文中，提出了一种用于三向化学数据分析的新的有界约束优化方法。在该方法中，引入非负矩阵分解来代替传统的三线性分解，以提供对激发-发射矩阵光谱数据的非负边界的约束。并将最小二乘问题转化为有界约束优化问题，可以通过投影梯度方法解决。在每次优化迭代期间应用交替最小二乘法以获得单个组件。对模拟三路阵列的分析表明，该方法在非负性方面比并行因子分析和交替三线性分解方法具有更好的性能。实际激发发射矩阵光谱数据的实验也表明，该方法在实际应用中对背景干扰具有鲁棒性。