Abstract
Clustering is one of data analysis methods and divides data into some groups. Although it needs the number of groups, there are cases that we don't know the appropriate number of groups. In order to know it, the indexes called cluster validity measures have been proposed. By the way, a datum is generally represented as one point, while we often find that it includes some uncertainties e.g., errors, ranges or some missing value of attributes. The concept of tolerance has been proposed as the representation of them and adapted to cluster validity measures for data with tolerance. However, we think these can't evaluate cluster partitions enough, because tolerances in themselves aren't evaluated.
In this paper, we introduce new cluster validity measures for data with tolerance and show their performances through numerical examples.
