Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are addressed by improving the fidelity to the study design. Principal axes and the components for variables are found through the arrangement of the training data set, and the centers of data are found according to the design. By using both the axes and the center, components for an observation that belong to various studies can be separately estimated. Both of the components for variables and observations are scaled to a unit length, which enables relationships to be seen between them. Results: Analyses in transcriptome studies showed an improvement in the separation of experimental groups and in robustness to bias and noise. Unknown samples were appropriately classified on predetermined axes. These axes well reflected the study design, and this facilitated the interpretation. Together, the introduced concepts resulted in improved generality and objectivity in the analytical results, with the ability to locate hidden structures in the data.
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