Fuzzy c-means clustering for data with tolerance using cosine correlation

This paper presents a new type of clustering algorithm by using cosine correlation and a tolerance vector. We aim to handle uncertain data with some range or missing values with the typical clustering algorithm of fuzzy c-means with cosine correlation (FCM-C). To handle such data, we introduce the concept of tolerance into the above FCM-C, and construct a new clustering algorithm. First, the tolerance vector is introduced into an optimization problem. Second, the optimization problem is solved and the algorithm is constructed based on the results. Finally, usefulness of the proposed algorithm is verified through some numerical examples.