On principal component analysis for data with tolerance

In many cases, data are handled as intervals on the pattern space because the data generally contain the uncertainty of error, loss and so on. The concept of tolerance in this paper enables us to handle these data as a point on the pattern space. 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, there are few applications of the concept into multivariate analysis methods except regression models in spite of its effectiveness. Therefore, we propose a new algorithm of principal component analysis for uncertain data by introducing the concept of the tolerance in this paper. Moreover, we verify the effectiveness through some numerical examples.