Dynamic Time Warping (DTW), and its constrained (CDTW) and weighted (WDTW) variants, are time series distances with a wide range of applications. They minimize the cost of non-linear alignments between series. CDTW and WDTW have been introduced because DTW is too permissive in its alignments. However, CDTW uses a crude step function, allowing unconstrained flexibility within the window, and none beyond it. WDTW's multiplicative weight is relative to the distances between aligned points along a warped path, rather than being a direct function of the amount of warping that is introduced. In this paper, we introduce Amerced Dynamic Time Warping (ADTW), a new, intuitive, DTW variant that penalizes the act of warping by a fixed additive cost. Like CDTW and WDTW, ADTW constrains the amount of warping. However, it avoids both abrupt discontinuities in the amount of warping allowed and the limitations of a multiplicative penalty. We formally introduce ADTW, prove some of its properties, and discuss its parameterization. We show on a simple example how it can be parameterized to achieve an intuitive outcome, and demonstrate its usefulness on a standard time series classification benchmark. We provide a demonstration application in C++.
翻译:动态时间转换(DTW)及其限制(CDTW)和加权(WDTW)变体是具有广泛应用范围的时间序列距离,它们最大限度地降低了序列间非线性调整的成本。 CDTW和WDTW之所以被引入,是因为DTW过于宽松。 但是,CDTW使用粗糙的步步函数,允许窗口内没有限制的灵活性,而没有超出它的范围。 WDTW的倍增权重与扭曲路径上对齐点之间的距离有关,而不是引入的扭曲量的直接功能。 在本文中,我们正式引入了ADTW(ADTW), 即动态时间转换(ADTW),这是一个新的、直观的、DTW变体的变体,它用固定的添加成本来惩罚战争行为。 与CDTW和W一样,ADTW限制了战争的幅度。 然而,它避免了扭曲允许的幅度的突然中断和多重复制处罚的限度。 我们正式引入了ADTTW, 证明它的一些特性的特性, 证明了它的特性的动态时间转换(ADTW) 标准的标准化, 我们展示了它的一个标准的分类。