论文标题
时间序列之间的可区分差异
Differentiable Divergences Between Time Series
论文作者
论文摘要
众所周知，计算可变大小的时间序列之间的差异是具有挑战性的。虽然动态的时间扭曲（DTW）通常用于此目的，但它在任何地方都不可区分，并且在用作“损失”时会导致不良的本地Optima。 Soft-DTW解决了这些问题，但这不是一个积极的差异：由于熵正则化引入的偏见，它可能是负面的，并且在时间序列相等时不会最小化。我们在本文中提出了一种新的分歧，称为软dtw Divergence，旨在纠正这些问题。我们研究其特性；特别是，在地面成本的条件下，我们表明这是一个有效的差异：当且仅当两个时间序列相等时，它是非负的且最小化的。我们还通过进一步消除熵偏见提出了一种新的“尖锐”变体。与84个时间序列分类数据集的DTW和Soft-DTW相比，我们展示了时间序列上的分歧，并显示出显着的准确性提高。
Computing the discrepancy between time series of variable sizes is notoriously challenging. While dynamic time warping (DTW) is popularly used for this purpose, it is not differentiable everywhere and is known to lead to bad local optima when used as a "loss". Soft-DTW addresses these issues, but it is not a positive definite divergence: due to the bias introduced by entropic regularization, it can be negative and it is not minimized when the time series are equal. We propose in this paper a new divergence, dubbed soft-DTW divergence, which aims to correct these issues. We study its properties; in particular, under conditions on the ground cost, we show that it is a valid divergence: it is non-negative and minimized if and only if the two time series are equal. We also propose a new "sharp" variant by further removing entropic bias. We showcase our divergences on time series averaging and demonstrate significant accuracy improvements compared to both DTW and soft-DTW on 84 time series classification datasets.
