  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.
