649 research outputs found
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
Faster Binary Mean Computation Under Dynamic Time Warping
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means
Making the Dynamic Time Warping Distance Warping-Invariant
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 warping-invariance contributes to the inconsistency mentioned above
and to a strange behavior. To eliminate these peculiarities, we convert the
dtw-distance to a warping-invariant semi-metric, called time-warp-invariant
(twi) distance. Empirical results suggest that the error rates of the twi and
dtw nearest-neighbor classifier are practically equivalent in a Bayesian sense.
However, the twi-distance requires less storage and computation time than the
dtw-distance for a broad range of problems. These results challenge the current
practice of applying the dtw-distance in nearest-neighbor classification and
suggest the proposed twi-distance as a more efficient and consistent option.Comment: arXiv admin note: substantial text overlap with arXiv:1808.0996
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