Improved fuzzy clustering for pattern recognition with applications to image segmentation
Amine M. Bensaid · 1995
When pattern recognition algorithms are applied to image segmentation, the goal is to solve a classification problem. However, they don't directly optimize classification quality. As a result, they are susceptible to two problems: (P1) the criterion they optimize may not be a good estimator of true classification quality, and (P2) they often admit many (suboptimal) solutions, therefore, they require some means of choosing between solutions. In addition, when all data are unlabeled and a clustering approach is taken, two further problems are encountered: (P3) choosing and validating the correct number of clusters, and (P4) insuring that algorithmic labels correspond to meaningful physical labels. Moreover, clustering algorithms such as hard and fuzzy c-means, based on optimizing sums-of-squared-errors objective functions, suffer from a fifth problem: (P5) a tendency to recommend solutions that equalize cluster populations. On the other hand, when a supervised learning approach is adopted, classification results are at the mercy of training data; different training sets lead to different solutions. Furthermore, for image segmentation, it is often highly impractical or very expensive to collect enough good training data. Two algorithms are introduced to address these problems. The first is a partially- or semi-supervised c-means algorithm, referred to as ssFCM. It attempts to solve these problems for domains where only few data from each class can be labeled. It offers a way for a clustering algorithm to take advantage of training data to mitigate P1-P5, while still avoiding critical dependence on imperfect training data. ssFCM is also useful in cases where training examples are not available for every class. The second algorithm does not make use of labeled data. It consists of using cluster validity information to guide a (re)clustering process towards better solutions; it is called validity-guided (re)clustering (VGC). It starts with a partition generated by a clustering algorithm. Then it iteratively alters the partition by applying simultaneous split-and-merge operations to the clusters. Partition modifications that result in improved partition validity are upheld. VGC and ssFCM are tested on both synthetic and real-world data. Synthetic data sets are used to analyze the behavior of VGC and ssFCM in presence of one or more of problems P1-P5. The two algorithms are also used to segment magnetic resonance images (MRIs) of the brain. Evaluations by radiologists show that the performance of VGC and ssFCM in the MRI application compares favorably with that of the fuzzy c-means and k-nearest-neighbors algorithms.