Abstract
In general, data contain the uncertainty of the error, range, and the loss, etc, and thus, the data are handled as intervals on the pattern space.
The concept of tolerance in this paper enables these data to be handled as a point on the pattern space by using tolerance vectors.
The advantage is that we can handle uncertain data in the framework of optimization without introducing any particular measures between intervals.
In recent years, this concept is positively introduced into clustering methods and the effectiveness is confirmed. However, we can not find the application of the concept into multivariate analysis methods except regression models in spite of its effectiveness.
Therefore, in this paper, we propose a new algorithm of principal component analysis for uncertain data by introducing the concept of the tolerance. Moreover, we verify the effectiveness through some numerical examples.
