Hierarchical FCM in a stepwise discovery of structure in data
This paper is concerned with a stepwise mode of objective function-based fuzzy clustering. A revealed structure in data becomes refined in a successive manner by starting with the most dominant relationships and proceeding with its more detailed characterization. Technically, the proposed process develops a so-called hierarchy of clusters. Given the underlying clustering mechanism of the fuzzy C means (FCM), the produced architecture is referred to as a hierarchical FCM or hierarchical FCM tree (HFCM tree). We discuss the design of the tree demonstrating how its growth is guided by a certain mapping criterion. It is also shown how a structure at the higher level is effectively used to build clusters at the consecutive level by making use of the conditional FCM. Detailed investigations of computational complexity contrast a stepwise development of clusters with a single-step clustering completed for the equivalent number of clusters occurring in total at all final nodes of the HFCM tree. The analysis quantifies a significant reduction of the stepwise refinement of the clusters. Experimental studies include synthetic data as well as those coming from the machine learning repository.
hierarchical fcm refinement mapping criterion computational complexity clustering tree computing aspects data analysis fcm tree structure stepwise structure discovery problem decomposition