Time series experiments of cDNA microarrays have been commonly used in various biological studies and conducted under a lot of experimental factors. A popular approach of time series microarray analysis is to compare one gene with another in their expression profiles, and clustering expression sequences is a typical example. On the other hand, a practically important issue in gene expression is to identify the general timing difference that is caused by experimental factors. This type of difference can be extracted by comparing a set of time series expression profiles under a factor with those under another factor, and so it would be difficult to tackle this issue by using only a current approach for time series microarray analysis.