Related papers: Making the Dynamic Time Warping Distance Warping-I…

Elastic distances like dynamic time warping (DTW) are central to time series machine learning because they compare sequences under local temporal misalignment. Soft-DTW is an adaptation of DTW that can be used as a gradient-based loss by…

In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…

Quantifying similarities between time series in a meaningful way remains a challenge in time series analysis, despite many advances in the field. Most real-world solutions still rely on a few popular measures, such as Euclidean Distance…

This technical report details a family of time warp distances on the set of discrete time series. This family is constructed as an editing distance whose elementary operations apply on linear segments. A specific parameter allows…

Soft dynamic time warping (SDTW) is a differentiable loss function that allows for training neural networks from weakly aligned data. Typically, SDTW is used to iteratively compute and refine soft alignments that compensate for temporal…

The classification of time series data is a well-studied problem with numerous practical applications, such as medical diagnosis and speech recognition. A popular and effective approach is to classify new time series in the same way as…

Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an…

Full Waveform Inversion (FWI) is a powerful technique for estimating high-resolution subsurface velocity models by minimizing the discrepancy between modeled and observed seismic data. However, the oscillatory nature of seismic waveforms…

We offer to apply the powerful Dynamic Time Warping (DTW) algorithm to find the spreading rate variation by comparing profiles of marine magnetic anomalies with the synthetic field constructed by the magnetic polarity reference scale. For…

Many tasks in music information retrieval (MIR) involve weakly aligned data, where exact temporal correspondences are unknown. The connectionist temporal classification (CTC) loss is a standard technique to learn feature representations…

Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing.…

The concept of sample mean in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems and generalize centroid-based clustering algorithms. Its existence has neither been proved nor challenged.…

Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

In this work, we consider the problem of sequence-to-sequence alignment for signals containing outliers. Assuming the absence of outliers, the standard Dynamic Time Warping (DTW) algorithm efficiently computes the optimal alignment between…

In this paper, we propose a method of improving temporal Convolutional Neural Networks (CNN) by determining the optimal alignment of weights and inputs using dynamic programming. Conventional CNN convolutions linearly match the shared…

The quality of seismic-to-well tie is commonly quantified using the classical Pearson's correlation coefficient. However the seismic wavelet is time-variant, well logging and upscaling is only approximate, and the correlation coefficient…

Computing an accurate mean of a set of time series is a critical task in applications like nearest-neighbor classification and clustering of time series. While there are many distance functions for time series, the most popular distance…

We study the role of time-reversal symmetry on the dynamical response of nonlinear optical systems that behave as unidirectional ("one-way") devices. It is shown that lossless nonlinear materials, despite being nonreciprocal, are typically…

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…