A novel bound constrained optimization method for three-way chemical data analysis with application to fluorescence excitation-emission matrix spectroscopy

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.