Negative matrix factorization analysis

The aim of factor analysis is to calculate a rotation matrix R which rotates the abstract factors (V) (principal components) into interpretable factors. The various algorithms for factor analysis differ in the criterion to calculate the rotation matrix R. Two classes of rotation methods can be distinguished (i) rotation procedures based on general criteria which are not specific for the domain of the data and (ii) rotation procedures which use specific properties of the factors (e.g. non-negativity). 

Paatero P, Tapper U (1994) Positive matrix factorization a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5 111-126 Park SK, O Neill MS, Stunder BJB et al (2007) Source location of air pollution and cardiac autonomic function trajectory cluster analysis for exposure assessment. J Expos Sci Environ Epidemiol 17 488 97... 

The linear relationship analysis results of heavy metals and the coefficient matrix are shown in Table 3.37, Cu-Cd and As-Cd showed a strong correlation. Cu and Cd take a diagonal position in the periodic table, and thus their chemical properties are similar and have comparable controlling factors. They displayed similar high content areas in the south of the Shandong Peninsula and in central SYS clay area, and their low content area in China s inshore area As and Cd showed a strong negative linear correlation, because As was a... 

When dealing with the analysis of low analyte levels in complex matrices, the resolution of the MS detector is a key parameter for consistent and reliable mass assignment [64,65]. Thus, the mass resolving power required to prevent false negative results in LC—MS residue screening methods depends on factors such as the anal)he concentration, type of matrix, and sample preparation [66]. 

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