Partially supervised clustering for image segmentation

All clustering algorithms process unlabeled data and, consequently, suffer from two problems: (P1) choosing and validating the correct number of clusters; and (P2) insuring that algorithmic labels correspond to meaningful physical labels. Clustering algorithms such as hard and fuzzy c-Means, based on optimizing sums of squared errors objective functions, suffer from a third problem: (P3) a tendency to recommend solutions that equalize cluster populations. The semi-supervised c-Means algorithms introduced in this paper attempt to solve these three problems for problem domains where a few data from each class can be labeled. 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 superior to ordinary fuzzy c-Means and to the crisp k-nearest neighbor rule and further, that the new method ameliorates (P1)-(P3).