Soft-DTW: a Differentiable Loss Function for Time-Series

2017-03-05 · ICML 2017 8 · Marco Cuturi, Mathieu Blondel

We propose in this paper a differentiable learning loss between time series, building upon the celebrated dynamic time warping (DTW) discrepancy. Unlike the Euclidean distance, DTW can compare time series of variable size and is robust to shifts or dilatations across the time dimension. To compute DTW, one typically solves a minimal-cost alignment problem between two time series using dynamic programming. Our work takes advantage of a smoothed formulation of DTW, called soft-DTW, that computes the soft-minimum of all alignment costs. We show in this paper that soft-DTW is a differentiable loss function, and that both its value and gradient can be computed with quadratic time/space complexity (DTW has quadratic time but linear space complexity). We show that this regularization is particularly well suited to average and cluster time series under the DTW geometry, a task for which our proposal significantly outperforms existing baselines. Next, we propose to tune the parameters of a machine that outputs time series by minimizing its fit with ground-truth labels in a soft-DTW sense.

📄 PDF Abstract BibTeX arXiv:1703.01541

Code (9)

mblondel/soft-dtw 공식 구현

Maghoumi/DeepNAG pytorch

PeteWe/ts_similarity_tensorflow tf

baggepinnen/DynamicAxisWarping.jl

jihyeonseong/SoM-TP pytorch

keonlee9420/Soft-DTW-Loss pytorch

khdlr/softdtw_jax jax

lyprince/sdtw_pytorch pytorch

yueyaog/TSGEM_Clustering

Tasks

Dynamic Time WarpingTime SeriesTime Series Analysis

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