科研成果详情

As spherical data (i.e. L normalized vectors) are often encountered in a variety of real-life applications (such as gesture recognition, gene expression analysis, etc.), sequential spherical data modeling has become an important research topic in recent years. Hidden Markov models (HMMs), as probabilistic graph models, have shown their effectiveness in modeling sequential data in previous research works. In this article, we propose a nonparametric hidden Markov model (NHMM) for modeling time series or sequential spherical data vectors. In our model, the emission distribution of each hidden state obeys a mixture of von Mises (VM) distributions which has better capability for modeling spherical data than other popular distributions (e.g. the Gaussian distribution). As we construct our NHMM by leveraging a Bayesian nonparametric model namely the Dirichlet process, the amount of hidden states and the number of mixture components for each state can be automatically adjusted according to observed data set. In addition, to handle high-dimensional data sets which may contain irrelevant or noisy features, feature selection, which is the process of selecting the “best” feature subset for describing the given data set, is adopted in our framework. In our case, an unsupervised localized feature selection method is incorporated with the developed NHMM, which results in a unified framework that can simultaneously perform data modeling and feature selection. Our model is learned by theoretically developing a convergence-guaranteed algorithm through variational Bayes. The advantages of our model are demonstrated by conducting experiments on both synthetic and real-world sequential data sets.