A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proposes GDTW for aligning time series on different, incomparable spaces.
The paper proves compactness of warped product metrics on S²×S¹ with varying base metrics.
The paper explores null distance convergence 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.
Ricci flow converges to Taub-NUT metric under specific conditions.
Absolute index theorem for warped product manifolds.
Guided warping augments time series data by aligning features with a teacher.
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.
Proves curvature comparison for Riemannian bands in low dimensions.
Paper studies convergence of nonnegative scalar curvature metrics to a specific limit space.
The paper confirms a conjecture about manifolds with positive curvature.
Warped DLMs improve forecasting for count time series.
New rigidity results for warped product domains.
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.
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.
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.
The paper proves rigidity for warped product spaces with degenerate ends.
Algorithm detects lead-lag relationships in multivariate time series.
Time-warping improves RNN transfer learning for diverse 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.
For sequences of warped product metrics on a -torus satisfying the scalar curvature bound , 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 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…
Where dealing with temporal sequences it is fair to assume that the same kind of deformations that motivated the development of the Dynamic Time Warp algorithm could be relevant also in the calculation of the dot product ("convolution") in a 1-D convolution layer. In this work a method is proposed for aligning the conv…
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.
Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.
Paper proves convergence of warped product manifolds to a nonnegative scalar curvature limit.
Study compact 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.
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.
Paper introduces k-DTW for robust curve comparison.
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.
New examples challenge Geroch conjecture stability.
NTW aligns multiple time-series data efficiently using neural networks.
New method uses DTW to evaluate neural network forecasts of geomagnetic indices.