Optimization of clustering criteria by reformulation

Various hard, fuzzy and possibilistic clustering criteria (objective functions) are useful as bases for a variety of pattern recognition problems. At present, many of these criteria have customized individual optimization algorithms. Because of the specialized nature of these algorithms, experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time. This paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software. We prove that the original and reformulated versions of each criterion are fully equivalent. Finally, two numerical examples are given to illustrate reformulation