33:
20:
1438:. Optimal nonlinear time warping functions are computed by minimizing a measure of distance of the set of functions to their warped average. Roughness penalty terms for the warping functions may be added, e.g., by constraining the size of their curvature. The resultant warping functions are smooth, which facilitates further processing. This approach has been successfully applied to analyze patterns and variability of speech movements.
41:
1159:(GTW) is a generalized version of DTW that can align multiple pairs of time series or sequences jointly. Compared with aligning multiple pairs independently through DTW, GTW considers both the alignment accuracy of each sequence pair (as DTW) and the similarity among pairs (according to the data structure or assigned by user). This can result in better alignment performance when the similarity among pairs exists.
1681:, which uses a time-normalization effect, where the fluctuations in the time axis are modeled using a non-linear time-warping function. Considering any two speech patterns, we can get rid of their timing differences by warping the time axis of one so that the maximal coincidence is attained with the other. Moreover, if the warping function is allowed to take any possible value,
1148:
contrast, ADTW employs an additive penalty that is incurred each time that the path is warped. Any amount of warping is allowed, but each warping action incurs a direct penalty. ADTW significantly outperforms DTW with windowing when applied as a nearest neighbor classifier on a set of benchmark time series classification tasks.
1430:, time series are regarded as discretizations of smooth (differentiable) functions of time. By viewing the observed samples as smooth functions, one can utilize continuous mathematics for analyzing data. Smoothness and monotonicity of time warp functions may be obtained for instance by integrating a time-varying
1413:
DTW-AROW (DTW with
Additional Restrictions on Warping) is a generalization of DTW to handle missing values. DTW-AROW obtains both a distance and a warping path; hence, can simply be replaced by DTW to handle missing values in many applications. DTW-AROW has the same time and memory complexity as DTW.
779:
The DTW algorithm produces a discrete matching between existing elements of one series to another. In other words, it does not allow time-scaling of segments within the sequence. Other methods allow continuous warping. For example, Correlation
Optimized Warping (COW) divides the sequence into uniform
585:
int DTWDistance(s: array , t: array ) { DTW := array for i := 0 to n for j := 0 to m DTW := infinity DTW := 0 for i := 1 to n for j := 1 to m cost := d(s, t) DTW := cost + minimum(DTW,
1147:
Amerced
Dynamic Time Warping (ADTW) is a variant of DTW designed to better control DTW's permissiveness in the alignments that it allows. The windows that classical DTW uses to constrain alignments introduce a step function. Any warping of the path is allowed within the window and none beyond it. In
1112:
In a survey, Wang et al. reported slightly better results with the LB_Improved lower bound than the LB_Keogh bound, and found that other techniques were inefficient. Subsequent to this survey, the LB_Enhanced bound was developed that is always tighter than LB_Keogh while also being more efficient to
1108:
A common task, retrieval of similar time series, can be accelerated by using lower bounds such as LB_Keogh, LB_Improved, LB_Enhanced, LB_Webb or LB_Petitjean. However, the Early
Abandon and Pruned DTW algorithm reduces the degree of acceleration that lower bounding provides and sometimes renders it
1452:
DTW and related warping methods are typically used as pre- or post-processing steps in data analyses. If both observed sequences contain random variation in their values, shape of observed sequences and random temporal misalignment, the warping may overfit to noise leading to biased results. A
780:
segments that are scaled in time using linear interpolation, to produce the best matched warping. The segment scaling causes potential creation of new elements, by time-scaling segments either down or up, and thus produces a more sensitive warping than DTW's discrete matching of raw elements.
69:
and decelerations during the course of an observation. DTW has been applied to temporal sequences of video, audio, and graphics data — indeed, any data that can be turned into a one-dimensional sequence can be analyzed with DTW. A well-known application has been automatic
1121:
Averaging for dynamic time warping is the problem of finding an average sequence for a set of sequences. NLAAF is an exact method to average two sequences using DTW. For more than two sequences, the problem is related to the one of the
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and requires heuristics. DBA is currently a reference method to average a set of sequences consistently with DTW. COMASA efficiently randomizes the search for the average sequence, using DBA as a local optimization process.
2049:
Thomas Prätzlich, Jonathan
Driedger, and Meinard MĂĽller (2016). Memory-Restricted Multiscale Dynamic Time Warping. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp.
64:
for measuring similarity between two temporal sequences, which may vary in speed. For instance, similarities in walking could be detected using DTW, even if one person was walking faster than the other, or if there were
486:
In addition to a similarity measure between the two sequences, a so called "warping path" is produced. By warping according to this path the two signals may be aligned in time. The signal with an original set of points
770:
cost := d(s, t) DTW := cost + minimum(DTW, // insertion DTW, // deletion DTW) // match return DTW }
467:
is the match that satisfies all the restrictions and the rules and that has the minimal cost, where the cost is computed as the sum of absolute differences, for each matched pair of indices, between their values.
23:
Dynamic time warping between two piecewise linear functions. The dotted line illustrates the time-warp relation. Notice that several points in the lower function are mapped to one point in the upper function, and
1685:
distinction can be made between words belonging to different categories. So, to enhance the distinction between words belonging to different categories, restrictions were imposed on the warping function slope.
1484:
C++ library implements Fast
Nearest-Neighbor Retrieval algorithms under the GNU General Public License (GPL). It also provides a C++ implementation of dynamic time warping, as well as various lower bounds.
36:
Two repetitions of a walking sequence recorded using a motion-capture system. While there are differences in walking speed between repetitions, the spatial paths of limbs remain highly similar.
1677:
Due to different speaking rates, a non-linear fluctuation occurs in speech pattern versus time axis, which needs to be eliminated. DP matching is a pattern-matching algorithm based on
1625:) Dynamic Programming algorithm and bases on Numpy. It supports values of any dimension, as well as using custom norm functions for the distances. It is licensed under the MIT license.
1388:
920:
1507:) requirement for the standard DTW algorithm. FastDTW uses a multilevel approach that recursively projects a solution from a coarser resolution and refines the projected solution.
982:
503:(warped). This finds applications in genetic sequence and audio synchronisation. In a related technique sequences of varying speed may be averaged using this technique see the
454:
1317:
1534:) with a comprehensive coverage of the DTW algorithm family members, including a variety of recursion rules (also called step patterns), constraints, and substring matching.
1470:
C++ library with Python bindings implements Early
Abandoned and Pruned DTW as well as Early Abandoned and Pruned ADTW and DTW lower bounds LB_Keogh, LB_Enhanced and LB_Webb.
1008:
1257:
1091:
1567:
743:
2672:
Yurtman, Aras; Soenen, Jonas; Meert, Wannes; Blockeel, Hendrik (2023). Koutra, Danai; Plant, Claudia; Gomez
Rodriguez, Manuel; Baralis, Elena; Bonchi, Francesco (eds.).
2027:
Stan
Salvador, Philip Chan, FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space. KDD Workshop on Mining Temporal and Sequential Data, pp. 70–80, 2004.
2883:
Nakagawa, Seiichi; Nakanishi, Hirobumi (1988-01-01). "Speaker-Independent
English Consonant and Japanese Word Recognition by a Stochastic Dynamic Time Warping Method".
2037:
322:
942:. This algorithm can also be adapted to sequences of different lengths. Despite this improvement, it was shown that a strongly subquadratic running time of the form
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method is often used in time series classification. Although DTW measures a distance-like quantity between two given sequences, it doesn't guarantee the
3397:
586:// insertion DTW, // deletion DTW) // match return DTW }
1410:
in time series. Simple preprocessing methods such as dropping or interpolating missing values do not provide a good estimate of the DTW distance.
2151:
Tan, Chang Wei; Petitjean, Francois; Webb, Geoffrey I. (2019). "Elastic bands across the path: A new framework and methods to lower bound DTW".
110:
The mapping of the indices from the first sequence to indices from the other sequence must be monotonically increasing, and vice versa, i.e. if
104:
The first index from the first sequence must be matched with the first index from the other sequence (but it does not have to be its only match)
32:
2335:
Petitjean, F. O.; Ketterlin, A.; Gançarski, P. (2011). "A global averaging method for dynamic time warping, with applications to clustering".
107:
The last index from the first sequence must be matched with the last index from the other sequence (but it does not have to be its only match)
2979:
Raket LL, Sommer S, Markussen B (2014). "A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data".
2709:
Lucero, J. C.; Munhall, K. G.; Gracco, V. G.; Ramsay, J. O. (1997). "On the Registration of Time and the Patterning of Speech Movements".
475:
in the time dimension to determine a measure of their similarity independent of certain non-linear variations in the time dimension. This
1457:. In human movement analysis, simultaneous nonlinear mixed-effects modeling has been shown to produce superior results compared to DTW.
1453:
simultaneous model formulation with random variation in both values (vertical) and time-parametrization (horizontal) is an example of a
3336:
Myers, C. S.; Rabiner, L. R. (1981). "A Comparative Study of Several Dynamic Time-Warping Algorithms for Connected-Word Recognition".
2289:
Gupta, L.; Molfese, D. L.; Tammana, R.; Simos, P. G. (1996). "Nonlinear alignment and averaging for estimating the evoked potential".
2936:
Juang, B. H. (September 1984). "On the hidden Markov model and dynamic time warping for speech recognition #x2014; A unified view".
2260:
Wang, Xiaoyue; et al. (2010). "Experimental comparison of representation methods and distance measures for time series data".
1957:
Herrmann, Matthieu; Webb, Geoffrey I. (2021). "Early abandoning and pruning for elastic distances including dynamic time warping".
860:
are the lengths of the two input sequences. The 50 years old quadratic time bound was broken in 2016: an algorithm due to Gold and
2497:
1105:
Fast techniques for computing DTW include Early Abandoned and Pruned DTW, PrunedDTW, SparseDTW, FastDTW, and the MultiscaleDTW.
756:// adapt window size (*) for i := 0 to n for j:= 0 to m DTW := infinity DTW := 0
1491:
library is a Java implementation of DTW and a FastDTW implementation that provides optimal or near-optimal alignments with an
3418:
3386:
3107:
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2178:
1930:
1885:
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Howell, P.; Anderson, A.; Lucero, J. C. (2010). "Speech motor timing and fluency". In Maassen, B.; van Lieshout, P. (eds.).
3485:
1610:
software package implements DTW and nearest-neighbour classifiers, as well as their extensions (hubness-aware classifiers).
1322:
Recent work has shown that tuning of this distance measure can be useful for tuning DTW performance. Specifically, tuning
699:, i.e. the end point is within the window length from diagonal. In order to make the algorithm work, the window parameter
1706:
Dynamic time warping is used in finance and econometrics to assess the quality of the prediction versus real-world data.
2802:
1011:
1819:
Gold, Omer; Sharir, Micha (2018). "Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier".
3490:
83:
2559:"The great time series classification bake off: a review and experimental evaluation of recent algorithmic advances"
101:
Every index from the first sequence must be matched with one or more indices from the other sequence, and vice versa
1775:
Olsen, NL; Markussen, B; Raket, LL (2018), "Simultaneous inference for misaligned multivariate functional data",
1649:
Is a Julia implementation of DTW and related algorithms such as FastDTW, SoftDTW, GeneralDTW and DTW barycenters.
1548:
Python library implements the Manhattan and Euclidean flavoured DTW measures including the LB_Keogh lower bounds.
2522:
Sakoe, Hiroaki; Chiba, Seibi (1978). "Dynamic programming algorithm optimization for spoken word recognition".
1740:
511:
1750:
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used to score matches between pairs of values across the two sequences. The original definition of DTW used
867:
3480:
2413:"Querying and mining of time series data: experimental comparison of representations and distance measures"
1735:
3430:"Addressing Big Data Time Series: Mining Trillions of Time Series Subsequences Under Dynamic Time Warping"
2820:"Speech production variability in fricatives of children and adults: Results of functional data analysis"
2746:"Toward a Comprehensive Framework for the Spatiotemporal Statistical Analysis of Longitudinal Shape Data"
2616:"Parameterizing the cost function of dynamic time warping with application to time series classification"
1730:
522:
This example illustrates the implementation of the dynamic time warping algorithm when the two sequences
2919:
945:
391:
3246:
3200:"Decoupling and recoupling in the crude oil price benchmarks: An investigation of similarity patterns"
3199:
1262:
3016:"Separating timing, movement conditions and individual differences in the analysis of human movement"
1094:
2380:"Summarizing a set of time series by averaging: From Steiner sequence to compact multiple alignment"
987:
3307:
Sakoe, H.; Chiba (1978). "Dynamic programming algorithm optimization for spoken word recognition".
1510:
1427:
2040:. Proceedings of the International Conference on Music Information Retrieval (ISMIR), pp. 192—197.
1205:
1052:
2673:
1640:
706:
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Mastroeni, Loretta; Mazzoccoli, Alessandro; Quaresima, Greta; Vellucci, Pierluigi (2021-02-01).
1516:
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can achieve state-of-the-art performance when using dynamic time warping as a distance measure.
3288:
3247:"Modelling bursts and chaos regularization in credit risk with a deterministic nonlinear model"
2615:
1755:
1156:
301:
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Webb, Geoffrey I.; Petitjean, Francois (2021). "Tight lower bounds for Dynamic Time Warping".
1113:
compute. LB_Petitjean is the tightest known lower bound that can be computed in linear time.
1698:. Several techniques are used to counter this defense, one of which is dynamic time warping.
1559:-normalized Euclidean distance similar to the popular UCR-Suite on CUDA-enabled accelerators.
1431:
79:
16:
An algorithm for measuring similarity between two temporal sequences, which may vary in speed
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139:
113:
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Dynamic Time Warping. In Information Retrieval for Music and Motion, chapter 4, pages 69-84
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2002:
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549:
359:
327:
49:
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Rabiner, Lawrence; Juang, Biing-Hwang (1993). "Chapter 4: Pattern-Comparison Techniques".
2557:
Bagnall, Anthony; Lines, Jason; Bostrom, Aaron; Large, James; Keogh, Eamonn (2016-11-23).
2496:
Wang, Yizhi; Miller, David J; Poskanzer, Kira; Wang, Yue; Tian, Lin; Yu, Guoqiang (2016).
8:
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used to search for the most likely path through the HMM is equivalent to stochastic DTW.
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75:
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2464:
2348:
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2118:
2095:
Lemire, D. (2009). "Faster Retrieval with a Two-Pass Dynamic-Time-Warping Lower Bound".
1745:
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uses Greedy DTW (implemented in JavaScript) as part of LaTeX symbol classifier program.
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Java library implements the UltraFastWWSearch algorithm for fast warping window tuning.
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823:
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Ding, Hui; Trajcevski, Goce; Scheuermann, Peter; Wang, Xiaoyue; Keogh, Eamonn (2008).
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Durrleman, S; Pennec, X.; Trouvé, A.; Braga, J.; Gerig, G. & Ayache, N. (2013).
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Keogh, E.; Ratanamahatana, C. A. (2005). "Exact indexing of dynamic time warping".
1976:
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We can easily modify the above algorithm to add a locality constraint (differences
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90:
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2680:. Lecture Notes in Computer Science. Cham: Springer Nature Switzerland: 221–237.
2473:
2448:
2356:
2238:
2126:
1856:"Quadratic Conditional Lower Bounds for String Problems and Dynamic Time Warping"
1555:
C++/CUDA library implements subsequence alignment of Euclidean-flavoured DTW and
457:
3215:
3133:"Financial markets' deterministic aspects modeled by a low-dimensional equation"
2674:"Estimating Dynamic Time Warping Distance Between Time Series with Missing Data"
3320:
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implements DTW to match mel-frequency cepstral coefficients of audio signals.
3445:
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We sometimes want to add a locality constraint. That is, we require that if
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861:
66:
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2449:"Amercing: An intuitive and effective constraint for dynamic time warping"
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space in a naive implementation, the space consumption can be reduced to
456:. In this formulation, we see that the number of possible matches is the
94:
3294:
Vintsyuk, T. K. (1968). "Speech discrimination by dynamic programming".
1523:
136:
are indices from the first sequence, then there must not be two indices
1911:"Tight Hardness Results for LCS and Other Sequence Similarity Measures"
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1798:
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implements DTW to match two 1-D arrays or 2-D speech files (2-D array).
1552:
1527:
1481:
472:
19:
2843:
2302:
1909:
Abboud, Amir; Backurs, Arturs; Williams, Virginia Vassilevska (2015).
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2678:
Machine Learning and Knowledge Discovery in Databases: Research Track
1614:
1545:
74:, to cope with different speaking speeds. Other applications include
61:
3197:
2795:
Speech Motor Control: New Developments in Basic and Applied Research
2614:
Herrmann, Matthieu; Tan, Chang Wei; Webb, Geoffrey I. (2023-04-16).
2153:
Proceedings of the 2019 SIAM International Conference on Data Mining
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1971:
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2015:
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2015 IEEE 56th Annual Symposium on Foundations of Computer Science
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2015 IEEE 56th Annual Symposium on Foundations of Computer Science
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1519:(Java) a package for time series classification using DTW in Weka.
3085:"Ultra fast warping window optimization for Dynamic Time Warping"
1574:
2003:
Speeding Up All-Pairwise Dynamic Time Warping Matrix Calculation
3131:
Orlando, Giuseppe; Bufalo, Michele; Stoop, Ruedi (2022-02-01).
2818:
Koenig, Laura L.; Lucero, Jorge C.; Perlman, Elizabeth (2008).
2607:
2498:"Graphical Time Warping for Joint Alignment of Multiple Curves"
3083:
Tan, Chang Wei; Herrmann, Matthieu; Webb, Geoffrey I. (2021).
2920:"From Dynamic Time Warping (DTW) to Hidden Markov Model (HMM)"
3309:
IEEE Transactions on Acoustics, Speech, and Signal Processing
2524:
IEEE Transactions on Acoustics, Speech, and Signal Processing
2410:
44:
DTW between a sinusoid and a noisy and shifted version of it.
2016:
SparseDTW: A Novel Approach to Speed up Dynamic Time Warping
3014:
Raket LL, Grimme B, Schöner G, Igel C, Markussen B (2016).
2334:
1639:
CUDA Python library implements a state of the art improved
1538:
2743:
2671:
2708:
2038:
An Efficient Multiscale Approach to Audio Synchronization
1632:
Python library implements DTW in the time-series context.
1603:
C++ real-time gesture-recognition toolkit implements DTW.
1017:
While the dynamic programming algorithm for DTW requires
3092:
2021 IEEE International Conference on Data Mining (ICDM)
2556:
2288:
2036:
Meinard MĂĽller, Henning Mattes, and Frank Kurth (2006).
2569:(3). Springer Science and Business Media LLC: 606–660.
2495:
659:). However, the above given modification works only if
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1774:
1390:makes DTW focus more on low amplitude effects when
3374:
3130:
2377:
1853:
1777:Journal of the Royal Statistical Society, Series C
1643:using only linear memory with phenomenal speedups.
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3434:ACM Transactions on Knowledge Discovery from Data
3245:Orlando, Giuseppe; Bufalo, Michele (2021-12-10).
2882:
2711:Journal of Speech, Language, and Hearing Research
2502:Advances in Neural Information Processing Systems
1499:) time and memory complexity, in contrast to the
922:time and space for two input sequences of length
530:are strings of discrete symbols. For two symbols
3472:
3007:
2972:
2824:The Journal of the Acoustical Society of America
2150:
1062:
3082:
2613:
1768:
1577:C# library implements DTW with various options.
1142:
89:In general, DTW is a method that calculates an
2447:Herrmann, Matthieu; Webb, Geoffrey I. (2023).
2014:Al-Naymat, G., Chawla, S., Taheri, J. (2012).
2001:Silva, D. F., Batista, G. E. A. P. A. (2015).
1326:in a family of distance functions of the form
3381:. Englewood Cliffs, N.J.: PTR Prentice Hall.
3244:
2797:. Oxford University Press. pp. 215–225.
2442:
2440:
2206:
2146:
2144:
1689:
246:We can plot each match between the sequences
3372:
3335:
2938:AT&T Bell Laboratories Technical Journal
2446:
1956:
788:The time complexity of the DTW algorithm is
745:(see the line marked with (*) in the code).
2291:IEEE Transactions on Biomedical Engineering
1854:Bringmann, Karl; KĂĽnnemann, Marvin (2015).
1701:
766:for i := 1 to n for j :=
3306:
2521:
2517:
2515:
2437:
2202:
2200:
2198:
2141:
1818:
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1401:
1394:is small and large amplitude effects when
1167:DTW is sensitive to the distance function
3453:
3428:Rakthanmanon, Thanawin (September 2013).
3174:
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3059:
3049:
3031:
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2472:
2428:
2395:
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1970:
1867:
1788:
1694:Unstable clocks are used to defeat naive
1421:
1416:An open-source implementation of DTW-AROW
1151:
510:This is conceptually very similar to the
3293:
2750:International Journal of Computer Vision
2378:Petitjean, F. O.; Gançarski, P. (2012).
1663:has Python and C implementations of DTW.
761:for j := max(1, i-w) to min(m, i+w)
542:is a distance between the symbols, e.g.
39:
31:
18:
2512:
2195:
1460:
162:in the other sequence, such that index
3473:
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2330:
2328:
2094:
1617:Python library implements the classic
1383:{\displaystyle d(x,y)=|x-y|^{\gamma }}
1130:
915:{\displaystyle O({N^{2}}/\log \log N)}
97:) with certain restriction and rules:
3289:Dynamic Time Warping Algorithm Review
2935:
2667:
2665:
2663:
2661:
1952:
1950:
1445:(HMM) and it has been shown that the
1162:
774:
504:
2259:
1566:machine learning library implements
748:int DTWDistance(s: array , t: array
2620:Data Mining and Knowledge Discovery
2563:Data Mining and Knowledge Discovery
2489:
2325:
2262:Data Mining and Knowledge Discovery
1959:Data Mining and Knowledge Discovery
1596:: a GPL Java implementation of DBA.
1116:
1100:
13:
3377:Fundamentals of speech recognition
3350:10.1002/j.1538-7305.1981.tb00272.x
3281:
2950:10.1002/j.1538-7305.1984.tb00034.x
2658:
1947:
1513:(Java) published to Maven Central.
1012:Strong exponential time hypothesis
977:{\displaystyle O(N^{2-\epsilon })}
93:between two given sequences (e.g.
14:
3502:
2062:Knowledge and Information Systems
1259:. In time series classification,
517:
449:{\displaystyle (0,1),(1,0),(1,1)}
82:. It can also be used in partial
2917:
1312:{\displaystyle d(x,y)=(x-y)^{2}}
388:, such that each step is one of
3238:
3191:
3124:
3076:
2929:
2911:
2876:
2811:
2786:
2737:
2702:
2404:
2371:
2282:
2253:
2088:
2053:
2043:
1667:
1601:Gesture Recognition Toolkit|GRT
1434:, thus being a one-dimensional
752:) { DTW := array
2897:10.1080/03772063.1988.11436710
2030:
2021:
2008:
1995:
1902:
1847:
1821:ACM Transactions on Algorithms
1812:
1541:Python library implements DTW.
1370:
1355:
1348:
1336:
1300:
1287:
1281:
1269:
1245:
1231:
1224:
1212:
1189:
1177:
1080:
1077:
1065:
1059:
1036:
1027:
1003:{\displaystyle \epsilon >0}
971:
952:
909:
874:
807:
798:
725:
711:
681:
667:
634:
620:
568:
554:
443:
431:
425:
413:
407:
395:
375:
363:
343:
331:
1:
3338:Bell System Technical Journal
1761:
1751:Nonlinear mixed-effects model
1455:nonlinear mixed-effects model
783:
495:(original) is transformed to
3100:10.1109/ICDM51629.2021.00070
3051:10.1371/journal.pcbi.1005092
3001:10.1016/j.patrec.2013.10.018
2686:10.1007/978-3-031-43424-2_14
2474:10.1016/j.patcog.2023.109333
2384:Theoretical Computer Science
2357:10.1016/j.patcog.2010.09.013
2239:10.1016/j.patcog.2021.107895
2127:10.1016/j.patcog.2008.11.030
1441:Another related approach is
1252:{\displaystyle d(x,y)=|x-y|}
1143:Amerced Dynamic Time Warping
1137:nearest-neighbour classifier
1086:{\displaystyle O(\min(N,M))}
7:
3486:Machine learning algorithms
3216:10.1016/j.eneco.2020.105036
2981:Pattern Recognition Letters
1731:Multiple sequence alignment
1709:
738:{\displaystyle |n-m|\leq w}
471:The sequences are "warped"
10:
3507:
3321:10.1109/tassp.1978.1163055
3158:10.1038/s41598-022-05765-z
3020:PLOS Computational Biology
2638:10.1007/s10618-023-00926-8
2536:10.1109/tassp.1978.1163055
2171:10.1137/1.9781611975673.59
1981:10.1007/s10618-021-00782-4
1741:Needleman–Wunsch algorithm
1690:Correlation power analysis
1517:time-series-classification
768:max(1, i-w) to min(m, i+w)
754:w := max(w, abs(n-m))
512:Needleman–Wunsch algorithm
3411:10.1007/978-3-540-74048-3
3263:10.1016/j.frl.2021.102599
2762:10.1007/s11263-012-0592-x
2575:10.1007/s10618-016-0483-9
2508:. Curran Associates, Inc.
2397:10.1016/j.tcs.2011.09.029
2074:10.1007/s10115-004-0154-9
864:enables computing DTW in
601:with the best alignment.
317:{\displaystyle M\times N}
3491:Multivariate time series
3396:MĂĽller, Meinard (2007).
3251:Finance Research Letters
2885:IETE Journal of Research
2430:10.14778/1454159.1454226
1736:Wagner–Fischer algorithm
1702:Finance and econometrics
1679:dynamic programming (DP)
1428:functional data analysis
1418:is available in Python.
1010:cannot exist unless the
703:must be adapted so that
593:is the distance between
3446:10.1145/2513092.2500489
2723:10.1044/jslhr.4005.1111
1673:Spoken-word recognition
1641:Time Warp Edit Distance
1402:Handling missing values
1756:Graphical time warping
1422:Alternative approaches
1384:
1313:
1253:
1196:
1195:{\displaystyle d(x,y)}
1157:Graphical Time Warping
1152:Graphical Time Warping
1095:Hirschberg's algorithm
1087:
1043:
1004:
978:
936:
916:
854:
834:
814:
739:
689:
652:, a window parameter.
642:
576:
450:
382:
350:
318:
292:
266:
236:
222:is matched with index
216:
196:
182:is matched with index
176:
156:
155:{\displaystyle l>k}
130:
129:{\displaystyle j>i}
45:
37:
29:
1647:DynamicAxisWarping.jl
1432:radial basis function
1385:
1314:
1254:
1197:
1088:
1044:
1042:{\displaystyle O(NM)}
1005:
979:
937:
917:
855:
835:
815:
813:{\displaystyle O(NM)}
740:
690:
688:{\displaystyle |n-m|}
643:
641:{\displaystyle |i-j|}
577:
575:{\displaystyle |x-y|}
451:
383:
381:{\displaystyle (M,N)}
351:
349:{\displaystyle (1,1)}
319:
293:
267:
237:
217:
197:
177:
157:
131:
80:signature recognition
43:
35:
22:
3094:. pp. 589–598.
1923:10.1109/FOCS.2015.14
1878:10.1109/FOCS.2015.15
1716:Levenshtein distance
1461:Open-source software
1330:
1319:has become popular.
1263:
1206:
1171:
1053:
1021:
988:
946:
926:
868:
844:
824:
792:
758:for i := 1 to n
707:
695:is not greater than
663:
648:is not greater than
616:
550:
392:
360:
328:
302:
276:
250:
226:
206:
186:
166:
140:
114:
54:dynamic time warping
50:time series analysis
3481:Dynamic programming
3149:2022NatSR..12.1693O
3042:2016PLSCB..12E5092R
2993:2014PaReL..38....1R
2836:2008ASAJ..124.3158K
2465:2023PatRe.13709333H
2453:Pattern Recognition
2349:2011PatRe..44..678P
2337:Pattern Recognition
2231:2021PatRe.11507895W
2209:Pattern Recognition
2119:2009PatRe..42.2169L
2097:Pattern Recognition
1443:hidden Markov model
1131:Supervised learning
481:triangle inequality
291:{\displaystyle 1:N}
265:{\displaystyle 1:M}
76:speaker recognition
3137:Scientific Reports
2622:. Springer: 1–22.
1917:. pp. 59–78.
1862:. pp. 79–97.
1799:10.1111/rssc.12276
1726:Sequence alignment
1594:Sequence averaging
1530:) and R packages (
1406:DTW cannot handle
1380:
1309:
1249:
1192:
1163:Distance functions
1124:multiple alignment
1083:
1039:
1000:
974:
932:
912:
850:
830:
810:
775:Warping properties
735:
685:
638:
572:
477:sequence alignment
446:
378:
346:
314:
288:
262:
232:
212:
192:
172:
152:
126:
72:speech recognition
46:
38:
30:
3440:(3): 10:1–10:31.
3420:978-3-540-74047-6
3388:978-0-13-015157-5
3109:978-1-6654-2398-4
2918:Fang, Chunsheng.
2844:10.1121/1.2981639
2695:978-3-031-43424-2
2303:10.1109/10.486255
2180:978-1-61197-567-3
1932:978-1-4673-8191-8
1887:978-1-4673-8191-8
1526:provides Python (
1475:UltraFastMPSearch
1447:Viterbi algorithm
935:{\displaystyle N}
853:{\displaystyle M}
833:{\displaystyle N}
235:{\displaystyle k}
215:{\displaystyle j}
195:{\displaystyle l}
175:{\displaystyle i}
3498:
3467:
3457:
3424:
3404:
3392:
3380:
3369:
3344:(7): 1389–1409.
3332:
3303:
3275:
3274:
3242:
3236:
3235:
3204:Energy Economics
3195:
3189:
3188:
3178:
3160:
3128:
3122:
3121:
3089:
3080:
3074:
3073:
3063:
3053:
3035:
3011:
3005:
3004:
2976:
2970:
2969:
2944:(7): 1213–1243.
2933:
2927:
2926:
2924:
2915:
2909:
2908:
2880:
2874:
2873:
2863:
2830:(5): 3158–3170.
2815:
2809:
2808:
2790:
2784:
2783:
2773:
2741:
2735:
2734:
2717:(5): 1111–1117.
2706:
2700:
2699:
2669:
2656:
2655:
2653:
2652:
2631:
2611:
2605:
2604:
2594:
2554:
2548:
2547:
2519:
2510:
2509:
2493:
2487:
2486:
2476:
2444:
2435:
2434:
2432:
2423:(2): 1542–1552.
2417:Proc. VLDB Endow
2408:
2402:
2401:
2399:
2375:
2369:
2368:
2332:
2323:
2322:
2286:
2280:
2279:
2277:
2257:
2251:
2250:
2224:
2204:
2193:
2192:
2164:
2148:
2139:
2138:
2112:
2103:(9): 2169–2180.
2092:
2086:
2085:
2057:
2051:
2047:
2041:
2034:
2028:
2025:
2019:
2012:
2006:
1999:
1993:
1992:
1974:
1965:(6): 2577–2601.
1954:
1945:
1944:
1906:
1900:
1899:
1871:
1851:
1845:
1844:
1816:
1810:
1809:
1792:
1772:
1746:Fréchet distance
1721:Elastic matching
1684:
1397:
1393:
1389:
1387:
1386:
1381:
1379:
1378:
1373:
1358:
1325:
1318:
1316:
1315:
1310:
1308:
1307:
1258:
1256:
1255:
1250:
1248:
1234:
1201:
1199:
1198:
1193:
1117:Average sequence
1101:Fast computation
1092:
1090:
1089:
1084:
1048:
1046:
1045:
1040:
1009:
1007:
1006:
1001:
983:
981:
980:
975:
970:
969:
941:
939:
938:
933:
921:
919:
918:
913:
893:
888:
887:
886:
859:
857:
856:
851:
839:
837:
836:
831:
819:
817:
816:
811:
769:
765:
762:
759:
755:
751:
744:
742:
741:
736:
728:
714:
694:
692:
691:
686:
684:
670:
658:
647:
645:
644:
639:
637:
623:
611:
608:is matched with
607:
600:
596:
592:
581:
579:
578:
573:
571:
557:
545:
541:
505:average sequence
455:
453:
452:
447:
387:
385:
384:
379:
355:
353:
352:
347:
323:
321:
320:
315:
297:
295:
294:
289:
271:
269:
268:
263:
242:, and vice versa
241:
239:
238:
233:
221:
219:
218:
213:
201:
199:
198:
193:
181:
179:
178:
173:
161:
159:
158:
153:
135:
133:
132:
127:
3506:
3505:
3501:
3500:
3499:
3497:
3496:
3495:
3471:
3470:
3421:
3402:
3389:
3284:
3282:Further reading
3279:
3278:
3243:
3239:
3196:
3192:
3129:
3125:
3110:
3087:
3081:
3077:
3026:(9): e1005092.
3012:
3008:
2977:
2973:
2934:
2930:
2922:
2916:
2912:
2881:
2877:
2816:
2812:
2805:
2791:
2787:
2742:
2738:
2707:
2703:
2696:
2670:
2659:
2650:
2648:
2612:
2608:
2555:
2551:
2520:
2513:
2494:
2490:
2445:
2438:
2409:
2405:
2376:
2372:
2333:
2326:
2287:
2283:
2258:
2254:
2205:
2196:
2181:
2149:
2142:
2093:
2089:
2058:
2054:
2048:
2044:
2035:
2031:
2026:
2022:
2013:
2009:
2000:
1996:
1955:
1948:
1933:
1907:
1903:
1888:
1852:
1848:
1833:10.1145/3230734
1817:
1813:
1773:
1769:
1764:
1712:
1704:
1692:
1682:
1675:
1670:
1463:
1424:
1404:
1395:
1391:
1374:
1369:
1368:
1354:
1331:
1328:
1327:
1323:
1303:
1299:
1264:
1261:
1260:
1244:
1230:
1207:
1204:
1203:
1172:
1169:
1168:
1165:
1154:
1145:
1133:
1119:
1103:
1054:
1051:
1050:
1022:
1019:
1018:
989:
986:
985:
959:
955:
947:
944:
943:
927:
924:
923:
889:
882:
878:
877:
869:
866:
865:
845:
842:
841:
825:
822:
821:
793:
790:
789:
786:
777:
772:
767:
763:
760:
757:
753:
749:
724:
710:
708:
705:
704:
702:
698:
680:
666:
664:
661:
660:
656:
651:
633:
619:
617:
614:
613:
609:
605:
598:
594:
590:
587:
567:
553:
551:
548:
547:
543:
539:
537:
533:
529:
525:
520:
458:Delannoy number
393:
390:
389:
361:
358:
357:
329:
326:
325:
303:
300:
299:
298:as a path in a
277:
274:
273:
251:
248:
247:
227:
224:
223:
207:
204:
203:
187:
184:
183:
167:
164:
163:
141:
138:
137:
115:
112:
111:
17:
12:
11:
5:
3504:
3494:
3493:
3488:
3483:
3469:
3468:
3425:
3419:
3393:
3387:
3370:
3333:
3304:
3291:
3283:
3280:
3277:
3276:
3237:
3190:
3123:
3108:
3075:
3006:
2971:
2928:
2910:
2875:
2810:
2804:978-0199235797
2803:
2785:
2736:
2701:
2694:
2657:
2606:
2549:
2511:
2488:
2436:
2403:
2370:
2324:
2297:(4): 348–356.
2281:
2252:
2194:
2179:
2140:
2087:
2068:(3): 358–386.
2052:
2042:
2029:
2020:
2007:
1994:
1946:
1931:
1901:
1886:
1846:
1811:
1783:(5): 1147–76,
1766:
1765:
1763:
1760:
1759:
1758:
1753:
1748:
1743:
1738:
1733:
1728:
1723:
1718:
1711:
1708:
1703:
1700:
1696:power analysis
1691:
1688:
1674:
1671:
1669:
1666:
1665:
1664:
1657:
1650:
1644:
1633:
1626:
1611:
1604:
1597:
1591:
1584:
1578:
1571:
1560:
1549:
1542:
1535:
1520:
1514:
1508:
1485:
1478:
1471:
1462:
1459:
1436:diffeomorphism
1423:
1420:
1408:missing values
1403:
1400:
1377:
1372:
1367:
1364:
1361:
1357:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1306:
1302:
1298:
1295:
1292:
1289:
1286:
1283:
1280:
1277:
1274:
1271:
1268:
1247:
1243:
1240:
1237:
1233:
1229:
1226:
1223:
1220:
1217:
1214:
1211:
1191:
1188:
1185:
1182:
1179:
1176:
1164:
1161:
1153:
1150:
1144:
1141:
1132:
1129:
1118:
1115:
1102:
1099:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1038:
1035:
1032:
1029:
1026:
999:
996:
993:
973:
968:
965:
962:
958:
954:
951:
931:
911:
908:
905:
902:
899:
896:
892:
885:
881:
876:
873:
849:
829:
809:
806:
803:
800:
797:
785:
782:
776:
773:
747:
734:
731:
727:
723:
720:
717:
713:
700:
696:
683:
679:
676:
673:
669:
649:
636:
632:
629:
626:
622:
584:
570:
566:
563:
560:
556:
535:
531:
527:
523:
519:
518:Implementation
516:
445:
442:
439:
436:
433:
430:
427:
424:
421:
418:
415:
412:
409:
406:
403:
400:
397:
377:
374:
371:
368:
365:
345:
342:
339:
336:
333:
313:
310:
307:
287:
284:
281:
261:
258:
255:
244:
243:
231:
211:
191:
171:
151:
148:
145:
125:
122:
119:
108:
105:
102:
86:applications.
84:shape matching
15:
9:
6:
4:
3:
2:
3503:
3492:
3489:
3487:
3484:
3482:
3479:
3478:
3476:
3465:
3461:
3456:
3451:
3447:
3443:
3439:
3435:
3431:
3426:
3422:
3416:
3412:
3408:
3401:
3400:
3394:
3390:
3384:
3379:
3378:
3371:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3334:
3330:
3326:
3322:
3318:
3314:
3310:
3305:
3301:
3297:
3292:
3290:
3287:Pavel Senin,
3286:
3285:
3272:
3268:
3264:
3260:
3256:
3252:
3248:
3241:
3233:
3229:
3225:
3221:
3217:
3213:
3209:
3205:
3201:
3194:
3186:
3182:
3177:
3172:
3168:
3164:
3159:
3154:
3150:
3146:
3142:
3138:
3134:
3127:
3119:
3115:
3111:
3105:
3101:
3097:
3093:
3086:
3079:
3071:
3067:
3062:
3057:
3052:
3047:
3043:
3039:
3034:
3029:
3025:
3021:
3017:
3010:
3002:
2998:
2994:
2990:
2986:
2982:
2975:
2967:
2963:
2959:
2955:
2951:
2947:
2943:
2939:
2932:
2921:
2914:
2906:
2902:
2898:
2894:
2890:
2886:
2879:
2871:
2867:
2862:
2857:
2853:
2849:
2845:
2841:
2837:
2833:
2829:
2825:
2821:
2814:
2806:
2800:
2796:
2789:
2781:
2777:
2772:
2767:
2763:
2759:
2755:
2751:
2747:
2740:
2732:
2728:
2724:
2720:
2716:
2712:
2705:
2697:
2691:
2687:
2683:
2679:
2675:
2668:
2666:
2664:
2662:
2647:
2643:
2639:
2635:
2630:
2625:
2621:
2617:
2610:
2602:
2598:
2593:
2588:
2584:
2580:
2576:
2572:
2568:
2564:
2560:
2553:
2545:
2541:
2537:
2533:
2529:
2525:
2518:
2516:
2507:
2503:
2499:
2492:
2484:
2480:
2475:
2470:
2466:
2462:
2458:
2454:
2450:
2443:
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2426:
2422:
2418:
2414:
2407:
2398:
2393:
2389:
2385:
2381:
2374:
2366:
2362:
2358:
2354:
2350:
2346:
2342:
2338:
2331:
2329:
2320:
2316:
2312:
2308:
2304:
2300:
2296:
2292:
2285:
2276:
2271:
2267:
2263:
2256:
2248:
2244:
2240:
2236:
2232:
2228:
2223:
2218:
2214:
2210:
2203:
2201:
2199:
2190:
2186:
2182:
2176:
2172:
2168:
2163:
2158:
2154:
2147:
2145:
2136:
2132:
2128:
2124:
2120:
2116:
2111:
2106:
2102:
2098:
2091:
2083:
2079:
2075:
2071:
2067:
2063:
2056:
2046:
2039:
2033:
2024:
2017:
2011:
2004:
1998:
1990:
1986:
1982:
1978:
1973:
1968:
1964:
1960:
1953:
1951:
1942:
1938:
1934:
1928:
1924:
1920:
1916:
1912:
1905:
1897:
1893:
1889:
1883:
1879:
1875:
1870:
1865:
1861:
1857:
1850:
1842:
1838:
1834:
1830:
1826:
1822:
1815:
1808:
1804:
1800:
1796:
1791:
1786:
1782:
1778:
1771:
1767:
1757:
1754:
1752:
1749:
1747:
1744:
1742:
1739:
1737:
1734:
1732:
1729:
1727:
1724:
1722:
1719:
1717:
1714:
1713:
1707:
1699:
1697:
1687:
1680:
1662:
1661:DTAI Distance
1658:
1655:
1651:
1648:
1645:
1642:
1638:
1634:
1631:
1627:
1624:
1620:
1616:
1612:
1609:
1605:
1602:
1598:
1595:
1592:
1589:
1585:
1582:
1581:Sketch-a-Char
1579:
1576:
1572:
1569:
1565:
1561:
1558:
1554:
1550:
1547:
1543:
1540:
1536:
1533:
1529:
1525:
1521:
1518:
1515:
1512:
1509:
1506:
1502:
1498:
1494:
1490:
1486:
1483:
1479:
1476:
1472:
1469:
1465:
1464:
1458:
1456:
1450:
1448:
1444:
1439:
1437:
1433:
1429:
1419:
1417:
1411:
1409:
1399:
1375:
1365:
1362:
1359:
1351:
1345:
1342:
1339:
1333:
1320:
1304:
1296:
1293:
1290:
1284:
1278:
1275:
1272:
1266:
1241:
1238:
1235:
1227:
1221:
1218:
1215:
1209:
1186:
1183:
1180:
1174:
1160:
1158:
1149:
1140:
1138:
1128:
1125:
1114:
1110:
1109:ineffective.
1106:
1098:
1096:
1074:
1071:
1068:
1056:
1033:
1030:
1024:
1015:
1013:
997:
994:
991:
966:
963:
960:
956:
949:
929:
906:
903:
900:
897:
894:
890:
883:
879:
871:
863:
847:
827:
804:
801:
795:
781:
764:DTW := 0
746:
732:
729:
721:
718:
715:
677:
674:
671:
653:
630:
627:
624:
602:
583:
564:
561:
558:
515:
513:
508:
506:
502:
498:
494:
490:
484:
482:
478:
474:
469:
466:
465:optimal match
461:
459:
440:
437:
434:
428:
422:
419:
416:
410:
404:
401:
398:
372:
369:
366:
340:
337:
334:
311:
308:
305:
285:
282:
279:
259:
256:
253:
229:
209:
189:
169:
149:
146:
143:
123:
120:
117:
109:
106:
103:
100:
99:
98:
96:
92:
91:optimal match
87:
85:
81:
77:
73:
68:
67:accelerations
63:
59:
55:
51:
42:
34:
27:
21:
3437:
3433:
3405:. Springer.
3398:
3376:
3341:
3337:
3315:(1): 43–49.
3312:
3308:
3299:
3295:
3254:
3250:
3240:
3207:
3203:
3193:
3140:
3136:
3126:
3091:
3078:
3023:
3019:
3009:
2984:
2980:
2974:
2941:
2937:
2931:
2913:
2891:(1): 87–95.
2888:
2884:
2878:
2827:
2823:
2813:
2794:
2788:
2756:(1): 22–59.
2753:
2749:
2739:
2714:
2710:
2704:
2677:
2649:. Retrieved
2619:
2609:
2566:
2562:
2552:
2530:(1): 43–49.
2527:
2523:
2505:
2501:
2491:
2456:
2452:
2420:
2416:
2406:
2387:
2383:
2373:
2340:
2336:
2294:
2290:
2284:
2265:
2261:
2255:
2212:
2208:
2152:
2100:
2096:
2090:
2065:
2061:
2055:
2045:
2032:
2023:
2010:
1997:
1962:
1958:
1914:
1904:
1859:
1849:
1824:
1820:
1814:
1780:
1776:
1770:
1705:
1693:
1676:
1668:Applications
1622:
1618:
1556:
1511:FastDTW fork
1504:
1500:
1496:
1492:
1451:
1440:
1425:
1412:
1405:
1321:
1166:
1155:
1146:
1134:
1120:
1111:
1107:
1104:
1016:
787:
778:
654:
603:
588:
521:
509:
500:
496:
492:
491:(original),
488:
485:
473:non-linearly
470:
462:
324:matrix from
245:
88:
57:
53:
47:
25:
3296:Kibernetika
3143:(1): 1693.
2155:: 522–530.
95:time series
78:and online
3475:Categories
3257:: 102599.
3210:: 105036.
3033:1601.02775
2651:2023-04-17
2629:2301.10350
2459:: 109333.
2343:(3): 678.
2222:2102.07076
2215:: 107895.
2162:1808.09617
1972:2102.05221
1869:1502.01063
1790:1606.03295
1762:References
1528:dtw-python
1482:lbimproved
1398:is large.
784:Complexity
499:(warped),
202:and index
26:vice versa
3358:0005-8580
3271:1544-6123
3232:230536868
3224:0140-9883
3167:2045-2322
3118:246291550
2958:0748-612X
2905:0377-2063
2852:0001-4966
2646:1573-756X
2583:1384-5810
2483:256182457
2390:: 76–91.
2275:1012.2789
2247:231925247
2110:0811.3301
2082:207056701
1989:235313990
1683:very less
1654:Multi_DTW
1615:simpledtw
1524:DTW suite
1376:γ
1363:−
1294:−
1239:−
992:ϵ
984:for some
967:ϵ
964:−
904:
898:
730:≤
719:−
675:−
628:−
562:−
507:section.
483:to hold.
309:×
62:algorithm
3464:31607834
3366:12857347
3329:17900407
3302:: 81–88.
3185:35105929
3070:27657545
2870:19045800
2780:23956495
2601:30930678
2544:17900407
2365:14850691
2319:28688330
2268:: 1–35.
2189:52120426
2050:569—573.
1941:16094517
1841:52070903
1807:88515233
1710:See also
1588:MatchBox
820:, where
750:, w: int
60:) is an
3455:6790126
3176:8807815
3145:Bibcode
3061:5033575
3038:Bibcode
2989:Bibcode
2987:: 1–7.
2966:8461145
2861:2677351
2832:Bibcode
2771:3744347
2731:9328881
2592:6404674
2461:Bibcode
2345:Bibcode
2311:8626184
2227:Bibcode
2135:8658213
2115:Bibcode
1896:1308171
1630:tslearn
1553:cudadtw
1489:FastDTW
1014:fails.
612:, then
544:d(x, y)
540:d(x, y)
3462:
3452:
3417:
3385:
3364:
3356:
3327:
3269:
3230:
3222:
3183:
3173:
3165:
3116:
3106:
3068:
3058:
2964:
2956:
2903:
2868:
2858:
2850:
2801:
2778:
2768:
2729:
2692:
2644:
2599:
2589:
2581:
2542:
2481:
2363:
2317:
2309:
2245:
2187:
2177:
2133:
2080:
1987:
1939:
1929:
1894:
1884:
1839:
1805:
1637:cuTWED
1608:PyHubs
1564:JavaML
1396:γ
1392:γ
1324:γ
1093:using
862:Sharir
657:marked
589:where
3403:(PDF)
3362:S2CID
3325:S2CID
3228:S2CID
3114:S2CID
3088:(PDF)
3028:arXiv
2962:S2CID
2923:(PDF)
2624:arXiv
2540:S2CID
2479:S2CID
2361:S2CID
2315:S2CID
2270:arXiv
2243:S2CID
2217:arXiv
2185:S2CID
2157:arXiv
2131:S2CID
2105:arXiv
2078:S2CID
1985:S2CID
1967:arXiv
1937:S2CID
1892:S2CID
1864:arXiv
1837:S2CID
1827:(4).
1803:S2CID
1785:arXiv
1546:pydtw
1468:tempo
3460:PMID
3415:ISBN
3383:ISBN
3354:ISSN
3267:ISSN
3220:ISSN
3181:PMID
3163:ISSN
3104:ISBN
3066:PMID
2954:ISSN
2901:ISSN
2866:PMID
2848:ISSN
2799:ISBN
2776:PMID
2727:PMID
2690:ISBN
2642:ISSN
2597:PMID
2579:ISSN
2307:PMID
2266:2010
2175:ISBN
1927:ISBN
1882:ISBN
1659:The
1652:The
1635:The
1628:The
1613:The
1606:The
1599:The
1586:The
1575:ndtw
1573:The
1562:The
1551:The
1544:The
1539:mlpy
1537:The
1522:The
1487:The
1480:The
1473:The
1466:The
995:>
840:and
597:and
534:and
526:and
463:The
272:and
147:>
121:>
3450:PMC
3442:doi
3407:doi
3346:doi
3317:doi
3259:doi
3212:doi
3171:PMC
3153:doi
3096:doi
3056:PMC
3046:doi
2997:doi
2946:doi
2893:doi
2856:PMC
2840:doi
2828:124
2766:PMC
2758:doi
2754:103
2719:doi
2682:doi
2634:doi
2587:PMC
2571:doi
2532:doi
2469:doi
2457:137
2425:doi
2392:doi
2388:414
2353:doi
2299:doi
2235:doi
2213:115
2167:doi
2123:doi
2070:doi
1977:doi
1919:doi
1874:doi
1829:doi
1795:doi
1568:DTW
1532:dtw
1426:In
1063:min
901:log
895:log
591:DTW
356:to
58:DTW
48:In
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