Beyond FCM: Graph-theoretic post-processing algorithms for learning and representing the data structure

Authors:
Nikolaos A. Laskaris;Stefanos P. Zafeiriou
Affiliations:
Artificial Intelligence and Information Analysis Laboratory, Department of Informatics, Aristotle University, Biology Building, BOX 451, GR-54124 Thessaloniki, Greece;Artificial Intelligence and Information Analysis Laboratory, Department of Informatics, Aristotle University, Biology Building, BOX 451, GR-54124 Thessaloniki, Greece
Venue:
Pattern Recognition
Year:
2008

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Abstract

We show that when fuzzy C-means (FCM) algorithm is used in an over-partitioning mode, the resulting membership values can be further utilized for building a connectivity graph that represents the relative distribution of the computed centroids. Standard graph-theoretic procedures and recent algorithms from manifold learning theory are subsequently applied to this graph. This facilitates the accomplishment of a great variety of data-analysis tasks. The definition of optimal cluster number C"o, the detection of intrinsic geometrical constraints within the data, and the faithful low-dimensional representation of the original structure are all performed efficiently, by working with just a down-sampled version (comprised of the centroids) of the data. Our approach is extensively demonstrated using synthetic data and actual brain signals.