A family of hierarchical clustering algorithms based on high-order dissimilarities

Traditional hierarchical techniques are used in many areas of research. However, they require the user to set the number of clusters or use some external criterion to find them. Also, they are unable to identify varying internal structures in classes, i.e. classes can be represented as unions of clusters. To overcome these issues, we propose a family of agglomerative hierarchical methods, which integrates a high-order dissimilarity measure, called dissimilarity increments, in traditional linkage algorithms. Dissimilarity increments are a measure over triplets of nearest neighbors. This family of algorithms is able to automatically find the number of clusters using a minimum description length criterion based on the dissimilarity increments distribution. Moreover, each algorithm of the proposed family is able to find classes as unions of clusters, leading to the identification of internal structures of classes. Experimental results show that any algorithm from the proposed family outperforms the traditional ones.