Agglomerative Hierarchical Clustering for Data with Tolerance

This paper presents new clustering algorithms which are based on agglomerative hierarchical clustering (AHC) with centroid method. The algorithms can handle with data with tolerance of which the concept includes some errors, ranges, or missing values in data. First, the tolerance is introduced into optimization problems of clustering. Second, an objective function is introduced for calculating the centroid of cluster and the problem is solved using Kuhn-Tucker conditions. Next, new algorithms are constructed based on the solution of the problem. Finally, the effectiveness of the proposed algorithms in this paper is verified through some numeric examples for the artificial data.