Developing the maximum likelihood estimation for component analysis: A state space approach

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Traditionally, scientists have used component analysis (CA) as descriptive tools in exploratory data analysis. Mathematically, a component is defined as a linear combination of the observed variables. The prototype of CA is principal component analysis. Other basic methods of CA include canonical correlation analysis and redundancy analysis. Over the past several decades, various generalizations of these basic component models were developed, including simultaneous component analysis, three-way component analysis, multiple-set canonical correlation analysis, and extended redundancy analysis, just to name a few.