In this talk, I will discuss a new clustering algorithm called D2-Clustering for objects which are characterized individually by a discrete distribution with finite but non-fixed support. This mathematical representation often arises in multimedia content analysis and can be viewed as a sparse representation of histogram-type feature vectors. The Kantorovich-Wasserstein metric is used as the distance between objects, which differs fundamentally from the Euclidean distance based on frequencies. The D2-Clustering algorithm groups objects by minimizing the total within-cluster squared distances, a criterion in the same spirit as k-means but applied to a significantly more complicated data type. The computational obstacle is overcome by a double loop iterative linear programming algorithm. To model objects with complex structures, I also propose Hypothetical Local Mapping (HLM) so that a mixture density function can be constructed based on pairwise distances. D2-Clustering and HLM are combined for applications to real-time image annotation.