  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.
