Sequence Alignment with Dirichlet Process Mixtures
This work addresses the challenge of aligning and clustering time-series data in an unsupervised manner, representing an incremental improvement over existing methods.
The paper tackles the problem of unsupervised alignment of high-dimensional time-warped sequences by extending a prior approach using Dirichlet Process Mixture Models (DPMM) to simultaneously align and cluster sequences, achieving competitive results compared to GP-LVM on synthetic and real-world datasets.
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.