Nonlinear Biomedical Signal Processing: Fuzzy Logic, Neural Networks, and New Algorithms
Nonlinear Biomedical Signal Processing: Fuzzy Logic, Neural Networks, and New Algorithms
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing (The Handbooks of Fuzzy Sets)
Pattern Recognition, Third Edition
Pattern Recognition, Third Edition
Advances in Fuzzy Clustering and its Applications
Advances in Fuzzy Clustering and its Applications
Fuzzy sets in pattern recognition and machine intelligence
Fuzzy Sets and Systems
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
Neurocomputing
Comparing partitions by means of fuzzy data mining tools
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
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The procedure of evaluating the results of a clustering algorithm is know under the term cluster validity. In general terms, cluster validity criteria can be classified in three categories: internal, external and relative. In this work we focus on the external criteria, which evaluate the results of a clustering algorithm based on a pre-specified structure S, that pertains to the data but which is independent of it. Usually Sis a crisp partition (i.e. the data labels), and the most common approach for external validation of fuzzy partitions is to apply measures defined for crisp partitions to fuzzy partitions, using crisp partitions derived (hardened) from them. In this paper we discuss fuzzy generalizations of two well known crisp external measures, which are able to assess the quality of a partition Uwithout the hardening of U. We also define a new external validity measure, that we call DNC index, useful for comparing a fuzzy Uto a crisp S. Numerical examples based on four real world data sets are given, demonstrating the higher reliability of the DNC index.