Hierarchical FCM in a stepwise discovery of structure in data |
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Authors: | A Pedrycz M Reformat |
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Affiliation: | (1) Department of Electrical & Computer Engineering, University of Alberta, Edmonton, T6G 2V4, Canada |
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Abstract: | 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. |
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Keywords: | Hierarchical FCM Mapping criterion Clustering tree Computing aspects Data analysis FCM tree structure Stepwise structure discovery Computational complexity Problem decomposition Refinement |
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