Abstract
Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.
Highlights
Trajectory recognition is important and meaningful in many practical applications, such as human activities recognition [1], speech recognition [2], handwritten character recognition [3] and navigation task with mobile robot [4]
We propose a variational BP-Hidden Markov model (HMM) for trajectory recognition, in which the way of the data modeling and the inference method are novel compared with the previous sampled Beta process HMMs (BP-HMMs)
Different from the sampled BP-HMM which uses the Indian buffet process (IBP) construction for the BP to lend it to a Gibbs sampler, we use the stick-breaking construction for the BP to adapt to variational inference
Summary
Trajectory recognition is important and meaningful in many practical applications, such as human activities recognition [1], speech recognition [2], handwritten character recognition [3] and navigation task with mobile robot [4]. From the perspective of performance, the classification procedure in the sampled BPHMM [1] is too rough to make full use of the trained model, in which the state transition matrix for each class is calculated by averaging the transition matrixes of all the trajectories. This will lead to the loss of information, especially when the training set has some ambiguous trajectories. We propose a variational BP-HMM for trajectory recognition, in which the way of the data modeling and the inference method are novel compared with the previous sampled BP-HMM.
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