Quaternion Dynamic Time Warping

Dynamic time warping (DTW) is used for the comparison and processing of nonlinear signals and constitutes a widely researched field of study. The method has been initially designed for, and applied to, signals representing audio data. Afterwords it has been successfully modified and applied to many other fields of study. In this paper, we present the results of researches on the generalized DTW method designed for use with rotational sets of data parameterized by quaternions. The need to compare and process quaternion time series has been gaining in importance recently. Three-dimensional motion data processing is one of the most important applications here. Specifically, it is applied in the context of motion capture, and in many cases all rotational signals are described in this way. We propose a construction of generalized method called quaternion dynamic time warping (QDTW), which makes use of specific properties of quaternion space. It allows for the creation of a family of algorithms that deal with the higher order features of the rotational trajectory. This paper focuses on the analysis of the properties of this new approach. Numerical results show that the proposed method allows for efficient element assignment. Moreover, when used as the measure of similarity for a clustering task, the method helps to obtain good clustering performance both for synthetic and real datasets.