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 convex clustering problem. Our approach, Temporal Registration using Optimal Unitary Transformations (TROUT), is based on a novel distance metric between time series that is easy to compute and automatically identifies optimal alignment between pairs of time series. By embedding our new metric in a convex 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.
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