  Clustering of time series data exhibits a number of challenges not present in
other settings, notably the problem of registration (alignment) of observed
signals. Typical approaches include pre-registration to a user-specified
template or time warping approaches which attempt to optimally align series
with a minimum of distortion. For many signals obtained from recording or
sensing devices, these methods may be unsuitable as a template signal is not
available for pre-registration, while the distortion of warping approaches may
obscure meaningful temporal information. We propose a new method for automatic
time series alignment within a clustering problem. Our approach, Temporal
Registration using Optimal Unitary Transformations (TROUT), is based on a novel
dissimilarity measure between time series that is easy to compute and
automatically identifies optimal alignment between pairs of time series. By
embedding our new measure in a optimization formulation, we retain well-known
advantages of computational and statistical performance. We provide an
efficient algorithm for TROUT-based clustering and demonstrate its superior
performance over a range of competitors.
