Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Yet, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied.

We thank all the reviewers for their valuable comments. We carefully address all the raised issues accordingly below. We appreciate your positive feedback. Thank you for the comments. We will proofread and improve the readability.

Thefirsttwocolumns showresults for two different step-sizes, and the third one using the best step-size chosen retrospectively. The plots show the final ELBO achieved after trainingfor40000stepsvs. stepsizeused. Figure 11: VI using a diagonal Gaussian, with the best step-size chosen retrospectively. Bayesian logistic regression: We use a subset of700 rows of thea1a dataset. In this case the posterior p(z|x) has dimensionality d = 120.

Part qualification is crucial in additive manufacturing (AM) because it ensures that additively manufactured parts can be consistently produced and reliably used in critical applications. Part qualification aims at verifying that an additively manufactured part meets performance requirements; therefore, predicting the complex stress-strain behaviors of additively manufactured parts is critical. We develop a dynamic time warping (DTW)-transfer learning (TL) framework for additive manufacturing part qualification by transferring knowledge of the stress-strain behaviors of additively manufactured low-cost polymers to metals. Specifically, the framework employs DTW to select a polymer dataset as the source domain that is the most relevant to the target metal dataset. Using a long short-term memory (LSTM) model, four source polymers (i.e., Nylon, PLA, CF-ABS, and Resin) and three target metals (i.e., AlSi10Mg, Ti6Al4V, and carbon steel) that are fabricated by different AM techniques are utilized to demonstrate the effectiveness of the DTW-TL framework. Experimental results show that the DTW-TL framework identifies the closest match between polymers and metals to select one single polymer dataset as the source domain. The DTW-TL model achieves the lowest mean absolute percentage error of 12.41% and highest coefficient of determination of 0.96 when three metals are used as the target domain, respectively, outperforming the vanilla LSTM model without TL as well as the TL model pre-trained on four polymer datasets as the source domain.

Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Yet, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied.

However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Y et, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied. In this paper, we show that the joint alignment problem can be transformed into a network flow problem and thus can be exactly and efficiently solved by the max flow algorithm, with a guarantee of global optimality.

Another popular measure, known as Mahalanobis distance, can be viewed as the distorted Euclidean distance.

Solar-flare forecasting has been extensively researched yet remains an open problem. In this paper, we investigate the contributions of elastic distance measures for detecting patterns in the solar-flare dataset, SWAN-SF. We employ a simple $k$-medoids clustering algorithm to evaluate the effectiveness of advanced, high-dimensional distance metrics. Our results show that, despite thorough optimization, none of the elastic distances outperform Euclidean distance by a significant margin. We demonstrate that, although elastic measures have shown promise for univariate time series, when applied to the multivariate time series of SWAN-SF, characterized by the high stochasticity of solar activity, they effectively collapse to Euclidean distance. We conduct thousands of experiments and present both quantitative and qualitative evidence supporting this finding.

Abstract--Time series are high-dimensional and complex data objects, making their efficient search and indexing a longstanding challenge in data mining. Building on a recently introduced similarity measure, namely Multiscale Dubuc Distance (MDD), this paper investigates its comparative strengths and limitations relative to the widely used Dynamic Time Warping (DTW). MDD is novel in two key ways: it evaluates time series similarity across multiple temporal scales and avoids point-to-point alignment. We demonstrate that in many scenarios where MDD outperforms DTW, the gains are substantial, and we provide a detailed analysis of the specific performance gaps it addresses. We provide simulations, in addition to the 95 datasets from the UCR archive, to test our hypotheses. Finally, we apply both methods to a challenging real-world classification task and show that MDD yields a significant improvement over DTW, underscoring its practical utility. Time series, or more generally, ordered high-dimensional data types, have become increasingly prevalent with the rise of powerful computational tools and machine learning techniques. In this study, we adopt the term time series as an umbrella label for all such sequential data. A central challenge in analyzing time series lies in defining and measuring similarity. Similarity is inherently subjective, shaped by the specific goals and nuances of a given application. The existing literature has produced a rich landscape of similarity measures, each tailored to specific assumptions and use cases.