Methodological study applying three-mode factor analysis to three-way chemical data sets

Abstract

Zeng, Yousheng and Hopke, P.K., 1990. Methodological study applying three-mode factor analysis to three-way chemical data sets. Chemometrics and Intelligent Laboratory Systems, 7: 237–250. A multivariate data analysis method, three-mode factor analysis (TMFA), has primarily been employed in the social sciences. Although it has not been extensively used in the natural sciences, TMFA provides the opportunity to examine data that are collected in form of a three-way matrix. With TMFA, one can simultaneously examine system variations in the three dimensions to determine the causal factors that control the system. This approach has been applied to the receptor modeling problem that attempts to relate ambient air quality to sources of pollution. By simulating an air pollution system, the relationships between the results of TMFA and the underlying physical model are investigated. In this way, the physical interpretation of the results of TMFA has been found. The model can be generalized to suit many three-way chemical data sets. It is also found that varimax rotation of the initially derived factors greatly improves their interpretability. The rotated solution can reflect the nature of the underlying physical system.