Clustering fuzzy sets with application to image database categorization

Clustering is considered as one of the most important tools to organize and analyze large multimedia databases. Most existing clustering techniques assume that the clusters have well-defined shapes (spherical or ellipsoidal). Thus, they are not suitable for image database categorization where images are usually mapped to high-dimensional feature vectors, and it is hard to even guess the shape of the clusters in the feature space. In this paper, we assume that the high dimensional object signature can be modeled by a fuzzy set and we introduce an algorithm to cluster these sets. First, we define a measure to assess the dissimilarity between two fuzzy sets. Then, we integrate this measure into our synchronization-based clustering approach. The resulting algorithm, called SyMP_FD is robust to noise and outliers, determines the number of clusters in an unsupervised manner, and identifies clusters of arbitrary shapes. The robustness of SyMP_FD is an intrinsic property of the synchronization mechanism. To identify clusters of various shapes, SyMP_FD models each cluster by an ensemble of fuzzy sets. Clusters with simple shapes would be modeled by few sets while clusters with more complex shapes would require a larger number of sets. The performance of the proposed algorithm is illustrated by using it to categorize a collection of images, where each image is described by a fuzzy set representing its color distribution.