Dynamic Time Wrapping (DTW) is a widely used algorithm for measuring
similarities between two time series. It is especially valuable in a wide
variety of applications, such as clustering, anomaly detection, classification,
or video segmentation, where the time-series have different timescales, are
irregularly sampled, or are shifted. However, it is not prone to be considered
as a loss function in an end-to-end learning framework because of its
non-differentiability and its quadratic temporal complexity. While
differentiable variants of DTW have been introduced by the community, they
still present some drawbacks: computing the distance is still expensive and
this similarity tends to blur some differences in the time-series. In this
paper, we propose a fast and differentiable approximation of DTW by comparing
two architectures: the first one for learning an embedding in which the
Euclidean distance mimics the DTW, and the second one for directly predicting
the DTW output using regression. We build the former by training a siamese
neural network to regress the DTW value between two time-series. Depending on
the nature of the activation function, this approximation naturally supports
differentiation, and it is efficient to compute. We show, in a time-series
retrieval context on EEG datasets, that our methods achieve at least the same
level of accuracy as other DTW main approximations with higher computational
efficiency. We also show that it can be used to learn in an end-to-end setting
on long time series by proposing generative models of EEGs.

提出了一种快速且可微分的 DTW 近似算法，分别采用学习嵌入和回归直接预测 DTW 输出的两种结构，可用于时间序列检索和 EEG 数据集生成模型的端到端学习。