  The clustering for functional data with misaligned problems has drawn much
attention in the last decade. Most methods do the clustering after those
functional data being registered and there has been little research using both
functional and scalar variables. In this paper, we propose a simultaneous
registration and clustering (SRC) model via two-level models, allowing the use
of both types of variables and also allowing simultaneous registration and
clustering. For the data collected from subjects in different unknown groups, a
Gaussian process functional regression model with time warping is used as the
first level model; an allocation model depending on scalar variables is used as
the second level model providing further information over the groups. The
former carries out registration and modeling for the multi-dimensional
functional data (2D or 3D curves) at the same time. This methodology is
implemented using an EM algorithm, and is examined on both simulated data and
real data.
