Fuzzy Shell Clustering Algorithms
The first two algorithms that are examined are suitable for hyperellipsoid-shaped clusters. The first of them [Dave 92a, Dave 92b] is called the adaptive fuzzy C-shells (AFCS) clustering algorithm, and the second one is known as the fuzzy C ellipsoidal shells (FCES) algorithm [Kris 95a].
The Adaptive Fuzzy C-Shells (AFCS) Algorithm
The AFCS uses the squared distance dnr between a point and a hyperellipsoidal (Eq. 14.49). Thus, Eq. (14.19) becomes(14.51)
It is clear that in this case the parameters used to identify a representative (an ellipse) are its center, cj, and the symmetric, positive definite matrix, ...
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