Sequence Alignment with Dirichlet Process Mixtures

We present a probabilistic model for unsupervised alignment of high-dimensional time-warped sequences based on the Dirichlet Process Mixture Model (DPMM). We follow the approach introduced in (Kazlauskaite, 2018) of simultaneously representing each data sequence as a composition of a true underlying function and a time-warping, both of which are modelled using Gaussian processes (GPs) (Rasmussen, 2005), and aligning the underlying functions using an unsupervised alignment method. In (Kazlauskaite, 2018) the alignment is performed using the GP latent variable model (GP-LVM) (Lawrence, 2005) as a model of sequences, while our main contribution is extending this approach to using DPMM, which allows us to align the sequences temporally and cluster them at the same time. We show that the DPMM achieves competitive results in comparison to the GP-LVM on synthetic and real-world data sets, and discuss the different properties of the estimated underlying functions and the time-warps favoured by these models.