Interpretation of Principal Components

• Main Author: Dabdoub, Marwan A.
• Format: Others
• Published: DigitalCommons@USU 1978
• Subjects: principal components; interpretation; Applied Statistics; Statistics and Probability
• Online Access: https://digitalcommons.usu.edu/etd/6950; https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=8051&context=etd

The principal component analysis can be carried out two ways. First the R-mode: R = K'K and the second is the Q-mode: Q = K K' where K is a data matrix centered by column or by row. The most commonly used method is the R-mode. It has been suggested that principal components computed from either the R-mode or the Q-mode may have the same interpretation. If this is true, then interpretation of the principal components could be put on a much more intuitive level in many applications. This will occur whenever one type of principal component is more intuitively related to the physical or natural system being studied than the other. The relationship between the principal components of the R-mode and the Q-mode have been investigated with the result that they show a perfect correlation between them. The conclusion that the principal components of the R-mode or the Q-mode have the same interpretation is established. An example is given to illustrate this work. The resulting interpretation is found to be the same as that obtained by Donald L. Phillips (1977) using different methods.