  With the membership function being strictly positive, the conventional fuzzy
c-means clustering method sometimes causes imbalanced influence when clusters
of vastly different sizes exist. That is, an outstandingly large cluster drags
to its center all the other clusters, however far they are separated. To solve
this problem, we propose a hybrid fuzzy-crisp clustering algorithm based on a
target function combining linear and quadratic terms of the membership
function. In this algorithm, the membership of a data point to a cluster is
automatically set to exactly zero if the data point is ``sufficiently'' far
from the cluster center. In this paper, we present a new algorithm for hybrid
fuzzy-crisp clustering along with its geometric interpretation. The algorithm
is tested on twenty simulated data generated and five real-world datasets from
the UCI repository and compared with conventional fuzzy and crisp clustering
methods. The proposed algorithm is demonstrated to outperform the conventional
methods on imbalanced datasets and can be competitive on more balanced
datasets.
