All clustering algorithms process unlabeled data and, consequently, su
ffer From two problems: (P1) choosing and validating the correct numbe
r of clusters and (P2) insuring that algorithmic labels correspond to
meaningful physical labels. Clustering algorithms such as hard and fuz
zy c-means, based on optimizing sums of squared errors objective funct
ions, suffer from a third problem: (P3) a tendency to recommend soluti
ons that equalize cluster populations. The semi-supervised c-means alg
orithms introduced in this paper attempt to overcome these three probl
ems for problem domains where a few data from each class can be labele
d. Segmentation of magnetic resonance images is a problem of this type
and we use it to illustrate the new algorithm. Our examples show that
the semi-supervised approach provides MRI segmentations that are supe
rior to ordinary fuzzy c-means and to the crisp k-nearest neighbor rul
e and further, that the new method ameliorates (P1)-(P3).