Dynamic Time Warping (DTW) is a popular time series distance measure that aligns the points in two series with one another. These alignments support warping of the time dimension to allow for processes that unfold at differing rates. The distance is the minimum sum of costs of the resulting alignments over any allowable warping of the time dimension. The cost of an alignment of two points is a function of the difference in the values of those points. The original cost function was the absolute value of this difference. Other cost functions have been proposed. A popular alternative is the square of the difference. However, to our knowledge, this is the first investigation of both the relative impacts of using different cost functions and the potential to tune cost functions to different tasks. We do so in this paper by using a tunable cost function {\lambda}{\gamma} with parameter {\gamma}. We show that higher values of {\gamma} place greater weight on larger pairwise differences, while lower values place greater weight on smaller pairwise differences. We demonstrate that training {\gamma} significantly improves the accuracy of both the DTW nearest neighbor and Proximity Forest classifiers.

翻译：动态时间规整（DTW）是一种流行的时序距离度量方法，它通过将两条序列中的点彼此对齐来实现。这种对齐支持对时间维度的扭曲，从而允许以不同速率展开的过程。该距离是在时间维度任何允许扭曲下，所得对齐的最小成本总和。两个点对齐的成本是这些点数值之差的函数。原始成本函数采用差值的绝对值，其他成本函数也被提出。一种常用的替代方案是差值的平方。然而，据我们所知，这是首次研究不同成本函数的相对影响，以及针对不同任务调整成本函数的潜力。本文通过使用带有参数γ的可调成本函数λγ来实现这一点。我们表明，较高的γ值会赋予较大的逐对差值更高权重，而较低的γ值会赋予较小的逐对差值更高权重。我们证明，训练γ能显著提升DTW最近邻分类器和邻近森林分类器的准确率。