In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. The number of HMMs and the number of topics are both automatically determined. The sticky prior avoids redundant states and makes our HDP-HMM more effective to model multimodal observations. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. The sources and sinks in the scene are learnt by clustering endpoints (origins and destinations) of trajectories. The semantic motion regions are learnt using the points in trajectories. On combining the learnt sources and sinks, the learnt semantic motion regions, and the learnt sequence of atomic activities, the action represented by a trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

In this paper, we address the problem of human action recognition through combining global temporal dynamics and local visual spatio-temporal appearance features. For this purpose, in the global temporal dimension, we propose to model the motion dynamics with robust linear dynamical systems (LDSs) and use the model parameters as motion descriptors. Since LDSs live in a non-Euclidean space and the descriptors are in non-vector form, we propose a shift invariant subspace angles based distance to measure the similarity between LDSs. In the local visual dimension, we construct curved spatio-temporal cuboids along the trajectories of densely sampled feature points and describe them using histograms of oriented gradients (HOG). The distance between motion sequences is computed with the Chi-Squared histogram distance in the bag-of-words framework. Finally we perform classification using the maximum margin distance learning method by combining the global dynamic distances and the local visual distances. We evaluate our approach for action recognition on five short clips data sets, namely Weizmann, KTH, UCF sports, Hollywood2 and UCF50, as well as three long continuous data sets, namely VIRAT, ADL and CRIM13. We show competitive results as compared with current state-of-the-art methods.

In this paper, we formulate human action recognition as a novel Multi-Task Sparse Learning(MTSL) framework which aims to construct a test sample with multiple features from as few bases as possible. Learning the sparse representation under each feature modality is considered as a single task in MTSL. Since the tasks are generated from multiple features associated with the same visual input, they are not independent but inter-related. We introduce a Beta process(BP) prior to the hierarchical MTSL model, which efficiently learns a compact dictionary and infers the sparse structure shared across all the tasks. The MTSL model enforces the robustness in coefficient estimation compared with performing each task independently. Besides, the sparseness is achieved via the Beta process formulation rather than the computationally expensive L1 norm penalty. In terms of non-informative gamma hyper-priors, the sparsity level is totally decided by the data. Finally, the learning problem is solved by Gibbs sampling inference which estimates the full posterior on the model parameters. Experimental results on the KTH and UCF sports datasets demonstrate the effectiveness of the proposed MTSL approach for action recognition.

In this paper, a new nonparametric Bayesian model called Sticky Multimodal Dual Hierarchical Dirichlet Process Hidden Markov Model (SMD-HDP-HMM) is proposed for mining activities from a collection of time series. An activity is modeled as an HMM where each state corresponds to an atomic activity. By extensively using Dirichlet Process (DP), multiple HMMs sharing a common set of states are learned and the numbers of HMMs and states are both automatically determined. Each time series is modeled to be generated by one of the HMMs such that all time series are clustered into activities. Simultaneously state sequences for time series are learned and each of them is decomposed into a sequence of atomic activities. Experimental results on KTH activity dataset demonstrate the advantage of our method.

Trajectory analysis is the basis for many applications, such as indexing of motion events in videos, activity recognition, and surveillance. In this paper, the Dirichlet process mixture model (DPMM) is applied to trajectory clustering, modeling, and retrieval. We propose an incremental version of a DPMM-based clustering algorithm and apply it to cluster trajectories. An appropriate number of trajectory clusters is determined automatically. When trajectories belonging to new clusters arrive, the new clusters can be identified online and added to the model without any retraining using the previous data. A time-sensitive Dirichlet process mixture model (tDPMM) is applied to each trajectory cluster for learning the trajectory pattern which represents the time-series characteristics of the trajectories in the cluster. Then, a parameterized index is constructed for each cluster. A novel likelihood estimation algorithm for the tDPMM is proposed, and a trajectory-based video retrieval model is developed. The tDPMM-based probabilistic matching method and the DPMM-based model growing method are combined to make the retrieval model scalable and adaptable. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our algorithm.