Proposes GDTW for aligning time series on different, incomparable spaces.
problem Dynamic time warping requires comparable spaces, but time series can live on different, incomparable spaces.
method Gromov dynamic time warping (GDTW) considers intra-relational geometry to avoid comparability requirements.
result Demonstrates effectiveness of GDTW in aligning, combining, and comparing time series on incomparable spaces.
The paper proves compactness of warped product metrics on S²×S¹ with varying base metrics.
problem Proving compactness of warped product metrics on S²×S¹ with nonnegative scalar curvature.
method Using Gromov-Sormani MinA scalar curvature compactness conjecture, the paper proves a uniform diameter bound for the base surfaces, compactness of the base warping functions, and convergence of the metrics.
result The metrics converge to a limit metric with nonnegative scalar curvature in the distributional sense.
The paper explores null distance convergence for warped product spacetimes.
problem Defining convergence for sequences of spacetimes as metric spaces.
method Using the null distance to define convergence of spacetimes.
result Optimal convergence theorem for warped product spacetimes.
The goal of dynamic time warping is to transform or warp time in order to approximately align two signals together. We pose the choice of warping function as an optimization problem with several terms in the objective. The first term measures the misalignment of the time-warped signals. Two additional regularization te…
RNNs compute by warping neural representations over time.
problem Understanding how RNNs perform task computations.
method Developed a Riemannian geometric framework to derive the manifold topology and geometry of RNNs.
result Dynamic warping is a fundamental feature of RNN computations.
Ricci flow converges to Taub-NUT metric under specific conditions.
problem Analyzing convergence of Ricci flow solutions to Taub-NUT metric.
method Study of Ricci flow starting from a specific metric on R4. result Ricci flow converges to Taub-NUT metric in infinite time under certain conditions.
Absolute index theorem for warped product manifolds.
problem Equivariant index computation for manifolds with warped product structures.
method Warped product structure, Fredholm operator, Atiyah-Segal-Singer index theorem.
result Equivariant relative index theorem for manifolds with warped product structures.
Guided warping augments time series data by aligning features with a teacher.
problem Small time series datasets limit neural network performance.
method Guided warping with a discriminative teacher to augment data deterministically.
result Significant improvement in performance on various time series datasets.
The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant. The lack of warpin…
Dynamic Time Warping improves regression accuracy on spectroscopy data.
problem Improving regression accuracy on spectroscopy data with DTW when data is across multiple wavelengths.
method Illustrated DTW's effectiveness on spectroscopy time-series data, showing its benefits in improving regression accuracy when only a single wavelength is considered. DTW combined with k-Nearest Neighbour reveals similarities and differences at the time-series level.
result DTW improves regression accuracy on spectroscopy data, especially when considering a single wavelength.
Proves curvature comparison for Riemannian bands in low dimensions.
problem Curvature comparison in Riemannian bands with lower bounds.
method Uses warped products over scalar-flat manifolds with log-concave warping.
result Scalar and mean curvature comparison results proven.
Paper studies convergence of nonnegative scalar curvature metrics to a specific limit space.
problem Understanding convergence of nonnegative scalar curvature metrics.
method Analyzes a sequence of warped product metrics on $\Sph^2 imes \Sph^1$.
result Sequence converges to an extreme limit space in specific senses.
The paper confirms a conjecture about manifolds with positive curvature.
problem Estimating the width of manifolds with positive sectional curvature.
method Establishing an optimal Lipschitz lower bound for functions on manifolds.
result Characterization of doubly warped product metrics with positive constant curvature.
A new method aligns convolution filters for temporal sequences using Dynamic Time Warp.
problem Improving deep learning models' ability to handle temporal sequence data.
method Integrates Dynamic Time Warp algorithm into 1-D convolution layers for better alignment of input and filter.
result Exceeds or matches standard 1-D convolution layers in time series classification tasks.
Warped DLMs improve forecasting for count time series.
problem Limited options for modeling count time series data.
method Introduces a semiparametric methodology using warping of Gaussian DLMs.
result Demonstrates improved forecasting capabilities for count time series.
New rigidity results for warped product domains.
problem Scalar curvature rigidity of domains in warped products.
method Developed a new connection on a twisted spinor bundle and associated Dirac operator.
result Obtained Llarull type scalar curvature rigidity for a general class of domains in a warped product.
Dynamic time warping (DTW) can be used to compute the similarity between two sequences of generally differing length. We propose a modification to DTW that performs individual and independent pairwise alignment of feature trajectories. The modified technique, termed feature trajectory dynamic time warping (FTDTW), is a…
Proposes a new method for time series classification and clustering.
problem Overfitting and information loss in dynamic time warping.
method Generalized time warping operator integrated with dictionary learning.
result Improves dictionary learning, classification, and clustering performance.
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining applications. This article converts the dtw-distance to a semi-metric and shows that its…
Study shows curvature rigidity of specific metric types.
problem Curvature rigidity of specific metric types.
method Spin geometry based arguments.
result Scalar curvature rigidity of specific metric types.
Update rules for learning in dynamic time warping spaces are based on optimal warping paths between parameter and input time series. In general, optimal warping paths are not unique resulting in adverse effects in theory and practice. Under the assumption of squared error local costs, we show that no two warping paths …
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…
Study extends null distance concept to Lorentzian length spaces for spacetime analysis.
problem Understanding spacetime convergence and topology in Lorentzian geometry.
method Extend null distance concept to Lorentzian length spaces, study Gromov-Hausdorff convergence.
result First results on compatibility of null distance with synthetic curvature bounds in warped product Lorentzian length spaces.
The paper proves rigidity for warped product spaces with degenerate ends.
problem Proving rigidity for warped product spaces with degenerate ends.
method Analyzing scalar curvature for specific classes of warped product spaces.
result Proves scalar curvature extremality and rigidity for certain degenerate spaces.
Algorithm detects lead-lag relationships in multivariate time series.
problem Understanding temporal dependencies between time series.
method Cluster-driven methodology based on dynamic time warping.
result Robust detection of lead-lag relationships in lagged multi-factor models.
Time-warping improves RNN transfer learning for diverse time scales.
problem Transfer learning for RNNs with varying time scales.
method Time-warping rescales time in LSTM models for better transfer.
result Time-warping maintains accuracy in transferring RNNs between different time scales.
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different temporal graphs. To this end, we propose to study dynamic time warping on temporal …
Valid inference method for DTW distance for abnormal time-series detection.
problem Statistical inference on DTW distance under uncertain conditions.
method Conditional selective inference framework to derive valid p-values.
result First method to provide valid p-values for DTW distance.
For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj≥−j1, uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the Gromov-Hausdorff and the Sormani-Wenger Intrin…
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. This article presents sufficient conditions for existence of a sample mean in DT…
We explore the distinctions between Lp convergence of metric tensors on a fixed Riemannian manifold versus Gromov-Hausdorff, uniform, and intrinsic flat convergence of the corresponding sequence of metric spaces. We provide a number of examples which demonstrate these notions of convergence do not agree even for two…
The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantiz…
TS-K-means improves financial data clustering with dynamic time warping.
problem Inadequate handling of temporal dependencies in financial time series data.
method Integrates Dynamic Time Warping into Time Series K-means for financial data.
result TS-K-means outperforms traditional K-means in financial data analysis.
Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.
problem Time series classification
method Diffeomorphic Time Warping (DiffTW)
result Outperforms DTW on 60 out of 86 datasets
Paper proves convergence of warped product manifolds to a nonnegative scalar curvature limit.
problem Proving convergence of sequences of manifolds with nonnegative scalar curvature.
method Warped product manifolds with diverging circular fibers, proving convergence in W1,p sense. result Sequence converges to an extreme limit space with nonnegative scalar curvature.
Study compact sequences of warped product circles over spheres with nonnegative scalar curvature.
problem Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature.
method Proved subsequence convergence to a W1,p Riemannian metric for all p<2 with nonnegative scalar curvature in the distributional sense. result Proved compactness of sequences of warped product circles over spheres with nonnegative scalar curvature.
In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-v…
This paper improves forecasts for diverse time series by averaging similar ones.
problem Forecasting challenges in heterogeneous time series.
method Dynamic Time Warping to find similar time series, k-Nearest Neighbor averaging.
result Averaging improves forecasts of simple models.
Studying the impact of climate change on precipitation is constrained by finding a way to evaluate the evolution of precipitation variability over time. Classical approaches (feature-based) have shown their limitations for this issue due to the intermittent and irregular nature of precipitation. In this study, we prese…
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scalar curvature and area of minimal surfaces bounded below should have subsequences which converge in the intrinsic flat sense to limit spaces which have nonnegative generalized scalar curvature and Euclidean tangent cones a…
Recent automated crop mapping via supervised learning-based methods have demonstrated unprecedented improvement over classical techniques. However, most crop mapping studies are limited to same-year crop mapping in which the present year's labeled data is used to predict the same year's crop map. Classification accurac…
The study constructs AdS manifolds from Gromov-Thurston manifolds.
problem Creating hyperbolic and anti-de Sitter structures from Gromov-Thurston manifolds.
method Explicit correspondence between quasifuchsian AdS manifolds and compact quotients of Ø(2d,2)/U(d,1).
result Existence of quasifuchsian AdS manifolds and hyperbolic ends with specified boundary.
Paper introduces k-DTW for robust curve comparison.
problem Robust dissimilarity measure for polygonal curves.
method Introduces k-Dynamic Time Warping (k-DTW) as a novel dissimilarity measure.
result k-DTW is more robust to outliers and has stronger metric properties than DTW.
Measuring similarities between unlabeled time series trajectories is an important problem in domains as diverse as medicine, astronomy, finance, and computer vision. It is often unclear what is the appropriate metric to use because of the complex nature of noise in the trajectories (e.g. different sampling rates or out…
Paper proposes a new efficient transport-based dissimilarity measure for time series classification.
problem Classifying time series with warping distortions.
method Defining a problem statement, proposing an Optimal Transport-based dissimilarity measure.
result The proposed method can solve the time series classification problem with reduced computational cost.
New examples challenge Geroch conjecture stability.
problem Stability of the Geroch conjecture in warped products.
method Constructing warped-product manifolds with specific curvature properties.
result First counterexample to Sormani's conjecture on stability.
NTW aligns multiple time-series data efficiently using neural networks.
problem Multiple sequence alignment for time-series analyses.
method Neural time warping that relaxes the MSA to a continuous optimization problem.
result NTW successfully aligns a hundred time-series and outperforms existing methods.
New method uses DTW to evaluate neural network forecasts of geomagnetic indices.
problem Evaluation metrics fail to capture persistence behavior in neural network forecasts.
method Dynamic Time Warping (DTW) to measure time series similarity, training neural networks to remove persistence.
result DTW reveals persistence behavior in neural network forecasts, confirming visual inspection.