Hierarchical clustering on metric lattice

This work proposes a new clustering algorithm named 'fuzzy interval number hierarchical clustering' (FINHC) by converting original data into fuzzy interval number (FIN) firstly, then it proves F that denotes the collection of FINs is a lattice and introduces a novel metric distance based on the results from lattice theory, as well as combining them with hierarchical clustering. The relevant mathematical background about lattice theory and the specific algorithm which is used to construct FIN have been presented in this paper. Three evaluation indexes including compactness, recall and F1-measure are applied to evaluate the performance of FINHC, hierarchical clustering (HC) k-means, k-medoids, density-based spatial clustering of applications with noise (DBSCAN) in six experiments used UCI public datasets and one experiment used KEEL public dataset. The FINHC algorithm shows better clustering performance compared to other traditional clustering algorithms and the results are also discussed specifically.