Interval clustering using fuzzy and rough set theory

In many data mining applications, use of interval sets to represent clusters can be more appropriate than crisp representations. Interval set representation of a cluster consists of a lower bound and an upper bound. Objects in lower bound are definitely part of the cluster, and only belong to that cluster. Objects in the upper bound are possibly part of that cluster and potentially belong to another cluster. The interval sets make it possible to describe ambiguity in categorizing some of the objects. The interval clusters can be unsupervised counterparts of supervised rough sets. This paper describes two unsupervised algorithms for obtaining interval clusters. First algorithm is an extension of K-means based on properties of rough sets. The second algorithm is an extension of fuzzy C-means clustering. The paper describes conditions under which the fuzzy C-means clustering can lead to interval sets that obey some of the properties of rough sets. An experimental comparison of interval clusters from both the approaches is also provided.