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.
Traditional methods mainly focus on clustering synchronous (or aggregated) time series with discrete time-lagged variables @cite_21 @cite_41 @cite_35 . These methods rely on probabilistic mixture models @cite_36 , extracting features from sequential data and then learning clusters via a Gaussian mixture model (GMM) @cite_39 @cite_19 . Recently, a mixture model of Markov chains is proposed in @cite_26 , which learns potential clusters from aggregate data. For asynchronous event sequences, most of the existing clustering methods can be categorized into feature-based methods, clustering event sequences from learned or predefined features. Typical examples include the Gaussian process-base multi-task learning method in @cite_3 and the multi-task multi-dimensional Hawkes processes in @cite_24 . Focusing on Hawkes processes, the feature-based mixture models in @cite_43 @cite_44 @cite_12 combine Hawkes processes with Dirichlet processes @cite_47 @cite_30 . However, these methods aim at modeling clusters of events or topics hidden in event sequences (i.e., sub-sequence clustering), which cannot learn clusters of event sequences. To our knowledge, the model-based clustering method for event sequences has been rarely considered.
@cite_30 @cite_35 @cite_26 @cite_41 @cite_36 @cite_21 @cite_3 @cite_39 @cite_24 @cite_19 @cite_43 @cite_44 @cite_47 @cite_12
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How to cluster event sequences generated via different point processes is an interesting and important problem in statistical machine learning. To solve this problem, we propose and discuss an effective model-based clustering method based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. The proposed model generates the event sequences with different clusters from the Hawkes processes with different parameters, and uses a Dirichlet process as the prior distribution of the clusters. We prove the identifiability of our mixture model and propose an effective variational Bayesian inference algorithm to learn our model. An adaptive inner iteration allocation strategy is designed to accelerate the convergence of our algorithm. Moreover, we investigate the sample complexity and the computational complexity of our learning algorithm in depth. Experiments on both synthetic and real-world data show that the clustering method based on our model can learn structural triggering patterns hidden in asynchronous event sequences robustly and achieve superior performance on clustering purity and consistency compared to existing methods. The task of event coreference resolution plays a critical role in many natural language processing applications such as information extraction, question answering, and topic detection and tracking. In this article, we describe a new class of unsupervised, nonparametric Bayesian models with the purpose of probabilistically inferring coreference clusters of event mentions from a collection of unlabeled documents. In order to infer these clusters, we automatically extract various lexical, syntactic, and semantic features for each event mention from the document collection. Extracting a rich set of features for each event mention allows us to cast event coreference resolution as the task of grouping together the mentions that share the same features they have the same participating entities, share the same location, happen at the same time, etc.. Some of the most important challenges posed by the resolution of event coreference in an unsupervised way stem from a the choice of representing event mentions through a rich set of features and b the ability of modeling events described both within the same document and across multiple documents. Our first unsupervised model that addresses these challenges is a generalization of the hierarchical Dirichlet process. This new extension presents the hierarchical Dirichlet process's ability to capture the uncertainty regarding the number of clustering components and, additionally, takes into account any finite number of features associated with each event mention. Furthermore, to overcome some of the limitations of this extension, we devised a new hybrid model, which combines an infinite latent class model with a discrete time series model. The main advantage of this hybrid model stands in its capability to automatically infer the number of features associated with each event mention from data and, at the same time, to perform an automatic selection of the most informative features for the task of event coreference. The evaluation performed for solving both within-and cross-document event coreference shows significant improvements of these models when compared against two baselines for this task. Statistical models based on Markov chains, especially mixtures of Markov chains, have recently been studied and demonstrated to be effective in various data mining applications such as tourist flow analysis, animal migration modeling, and transportation administration. Nevertheless, the research so far has mainly focused on analyzing data at individual levels. Due to security and privacy reasons, however, the observations in practice usually consist of coarse-grained statistics of individual data, a.k.a. aggregate data, rendering learning mixtures of Markov chains an even more challenging problem. In this work, we show that this challenging problem, although intractable in its original form, can be solved approximately by posing structural constraints on the transition matrices. The proposed structural constraints include specifying active state sets corresponding to the chains and adding a pairwise sparse regularization term on transition matrices. Based on these two structural constraints, we propose a constrained least-squares method to learn mixtures of Markov chains. We further develop a novel iterative algorithm that decomposes the overall problem into a set of convex subproblems and solves each subproblem efficiently, making it possible to effectively learn mixtures of Markov chains from aggregate data. We propose a framework for generating synthetic data and analyze the complexity of our algorithm. Additionally, the empirical results of the convergence and the robustness of our algorithm are also presented. These results demonstrate the effectiveness and efficiency of the proposed algorithm, comparing with traditional methods. Experimental results on real-world data sets further validate that our algorithm can be used to solve practical problems. In this paper, we model multi-agent events in terms of a temporally varying sequence of sub-events, and propose a novel approach for learning, detecting and representing events in videos. The proposed approach has three main steps. First, in order to learn the event structure from training videos, we automatically encode the sub-event dependency graph, which is the learnt event model that depicts the conditional dependency between sub-events. Second, we pose the problem of event detection in novel videos as clustering the maximally correlated sub-events using normalized cuts. The principal assumption made in this work is that the events are composed of a highly correlated chain of sub-events that have high weights (association) within the cluster and relatively low weights (disassociation) between the clusters. The event detection does not require prior knowledge of the number of agents involved in an event and does not make any assumptions about the length of an event. Third, we recognize the fact that any abstract event model should extend to representations related to human understanding of events. Therefore, we propose an extension of CASE representation of natural languages that allows a plausible means of interface between users and the computer. We show results of learning, detection, and representation of events for videos in the meeting, surveillance, and railroad monitoring domains.