This article introduces the Variable Markov Oracle (VMO) data structure for multivariate time series indexing. VMO can identify repetitive fragments and find sequential similarities between observations. VMO can also be viewed as a combination of online clustering algorithms with variable-order Markov constraints. The authors use VMO for gesture query-by-content and gesture following. A probabilistic interpretation of the VMO query-matching algorithm is proposed to find an analogy to the inference problem in a hidden Markov model (HMM). This probabilistic interpretation extends VMO to be not only a data structure but also a model for time series. Query-by-content experiments were conducted on a gesture database that was recorded using a Kinect 3D camera, showing state-of-the-art performance. The query-by-content experiments' results are compared to previous works using HMM and dynamic time warping. Gesture following is described in the context of an interactive dance environment that aims to integrate human movements with computer-generated graphics to create an augmented reality performance
