Exact Mean Computation in Dynamic Time Warping Spaces

Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational problem, so far solved by several heuristic and inexact strategies. We spot some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for benchmarking and evaluating known heuristics). Based on this dynamic program, we empirically study properties like uniqueness and length of a mean. Moreover, experimental evaluations reveal substantial deficits of state-of-the-art heuristics in terms of their output quality. We also give an exact polynomial-time algorithm for the special case of binary time series

Dynamic Dynamic Time Warping

The Dynamic Time Warping (DTW) distance is a popular similarity measure for polygonal curves (i.e., sequences of points). It finds many theoretical and practical applications, especially for temporal data, and is known to be a robust, outlier-insensitive alternative to the \frechet distance. For static curves of at most $n$ points, the DTW distance can be computed in $O(n^2)$ time in constant dimension. This tightly matches a SETH-based lower bound, even for curves in $\mathbb{R}^1$. In this work, we study \emph{dynamic} algorithms for the DTW distance. Here, the goal is to design a data structure that can be efficiently updated to accommodate local changes to one or both curves, such as inserting or deleting vertices and, after each operation, reports the updated DTW distance. We give such a data structure with update and query time $O(n^{1.5} \log n)$, where $n$ is the maximum length of the curves. As our main result, we prove that our data structure is conditionally \emph{optimal}, up to subpolynomial factors. More precisely, we prove that, already for curves in $\mathbb{R}^1$, there is no dynamic algorithm to maintain the DTW distance with update and query time~\makebox{$O(n^{1.5 - \delta})$} for any constant $\delta > 0$, unless the Negative-$k$-Clique Hypothesis fails. In fact, we give matching upper and lower bounds for various trade-offs between update and query time, even in cases where the lengths of the curves differ.Comment: To appear at SODA2

Feature Trajectory Dynamic Time Warping for Clustering of Speech Segments

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 applied as a similarity measure in the agglomerative hierarchical clustering of speech segments. Experiments using MFCC and PLP parametrisations extracted from TIMIT and from the Spoken Arabic Digit Dataset (SADD) show consistent and statistically significant improvements in the quality of the resulting clusters in terms of F-measure and normalised mutual information (NMI).Comment: 10 page

PERANCANGAN PROGRAM APLIKASI PEMBELAJARAN BAHASA ISYARAT DENGAN METODE DYNAMIC TIME WARPING

PERANCANGAN PROGRAM APLIKASI PEMBELAJARAN BAHASA ISYARAT DENGAN METODE DYNAMIC TIME WARPING - pembelajaran bahasa isyarat, pola gerakan, sensor kinect, dynamic time warping, depth sensor