Many clustering algorithms have been proposed to partition a set of static data points into groups. In this paper, we consider an evolutionary clustering problem where the input data points may move, disappeare, and emerge. Generally, these changes should result in a smooth evolution of the clusters. Mining this naturally smooth evolution is valuable for providing an aggregated view of the numerous individual behaviors. We solve this novel and generalized form of clustering problem by converting it into a Bayesian learning problem. Analogous to that the EM clustering algorithm clusters static data points by learning a Gaussian mixture model, our method mines the evolution of clusters from dynamic data points by learning a hidden semi-Markov model (HSMM). By utilizing characteristics of the evolutionary clustering problem, we derive a new unsupervised learning algorithm which is much more efficient than the algorithms used to learn traditional variable-duration HSMMs. Because the HSMM models the probabilistic relationship between the dynamic data set and corresponding evolving clusters, we can interpret the learned parameters as the evolving clusters intuitively using the Viterbi filtering technique. Because learning an HSMM is in fact learning an optimal Viterbi filter, the learned cluster evolutions are smooth and fit well with the data. We demonstrate the effectiveness of this method by experiments on both synthetic data and real data.

Presents a matrix-based technique for reconstructing solids with quadric surfaces from three orthographic views. First, the relationship between a conic and its orthographic projections is developed using matrix theory. We then address the problem of finding the theoretical minimum number of views that are necessary for reconstructing an object with quadric surfaces. Next, we reconstruct the conic edges by finding their matrix representations in 3D space. This effectively constructs a model corresponding to the three views. Finally, volume information is searched within the wireframe model to form the final solids. The novelty of our algorithm is in the use of the matrix representation of conics to assist in the 3D reconstruction, which increases both the efficiency and the reliability of the proposed approach.