We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to a cluster is generated via the same Hawkes process with specific parameters, and different clusters correspond to different Hawkes processes. The prior distribution of the Hawkes processes is controlled via a Dirichlet distribution. We learn the model via a maximum likelihood estimator (MLE) and propose an effective variational Bayesian inference algorithm. We specifically analyze the resulting EM-type algorithm in the context of inner-outer iterations and discuss several inner iteration allocation strategies. The identifiability of our model, the convergence of our learning method, and its sample complexity are analyzed in both theoretical and empirical ways, which demonstrate the superiority of our method to other competitors. The proposed method learns the number of clusters automatically and is robust to model misspecification. Experiments on both synthetic and real-world data show that our method can learn diverse triggering patterns hidden in asynchronous event sequences and achieve encouraging performance on clustering purity and consistency.
SUMMARY In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a,b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties. Producing attractive trailers for videos needs human expertise and creativity, and hence is challenging and costly. Different from video summarization that focuses on capturing storylines or important scenes, trailer generation aims at producing trailers that are attractive so that viewers will be eager to watch the original video. In this work, we study the problem of automatic trailer generation, in which an attractive trailer is produced given a video and a piece of music. We propose a surrogate measure of video attractiveness named fixation variance, and learn a novel self-correcting point process-based attractiveness model that can effectively describe the dynamics of attractiveness of a video. Furthermore, based on the attractiveness model learned from existing training trailers, we propose an efficient graph-based trailer generation algorithm to produce a max-attractiveness trailer. Experiments demonstrate that our approach outperforms the state-of-the-art trailer generators in terms of both quality and efficiency. 