Amercing: An Intuitive, Elegant and Effective Constraint for Dynamic Time Warping
This addresses the need for more intuitive and effective constraints in time series alignment for applications in classification, though it appears incremental as it builds on existing DTW variants.
The authors tackled the problem of overly permissive alignments in Dynamic Time Warping (DTW) by introducing Amerced Dynamic Time Warping (ADTW), a variant that penalizes warping with a fixed additive cost, and demonstrated its effectiveness on a standard time series classification benchmark.
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++.