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.

翻译：时间序列数据分组显示的是其他环境所没有的若干挑战,特别是观测到的信号的登记(调整)问题。典型的方法包括预先登记用户指定的模板或时间扭曲方法,这些模板或时间扭曲方法试图以最优化的方式对序列进行最起码的扭曲。对于从记录或遥感装置获得的许多信号,这些方法可能不适合作为预登记所用的模板信号,而扭曲方法的扭曲可能掩盖有意义的时间信息。我们提出了在集群问题中自动时间序列调整的新方法。我们的方法,即使用最佳单位转换(TROUT)进行的时间序列登记,是基于一种新颖的不同尺度,即易于计算和自动确定时间序列之间的最佳一致。通过将我们的新尺度嵌入优化公式,我们保留了计算和统计绩效的众所周知的优势。我们为基于TROUT的集群提供了一种高效算法,并展示其在一系列竞争者中的优异性表现。