Editing Dynamic time warping (section)

== Average sequence ==
Averaging for dynamic time warping is the problem of finding an average sequence for a set of sequences. 
NLAAF<ref>{{Cite journal | last1 = Gupta | first1 = L. | last2 = Molfese | first2 = D. L. | last3 = Tammana | first3 = R. | last4 = Simos | first4 = P. G. | title = Nonlinear alignment and averaging for estimating the evoked potential | doi = 10.1109/10.486255 | journal = IEEE Transactions on Biomedical Engineering | volume = 43 | issue = 4 | pages = 348–356 | year = 1996 | pmid =  8626184| s2cid = 28688330 }}</ref> is an exact method to average two sequences using DTW.
For more than two sequences, the problem is related to that of [[multiple alignment]] and requires heuristics.
DBA<ref name="DBA">{{Cite journal | last1 = Petitjean | first1 = F. O. | last2 = Ketterlin | first2 = A. | last3 = Gançarski | first3 = P. | doi = 10.1016/j.patcog.2010.09.013 | title = A global averaging method for dynamic time warping, with applications to clustering | journal = Pattern Recognition | volume = 44 | issue = 3 | pages = 678 | year = 2011 | bibcode = 2011PatRe..44..678P }}</ref> is currently a reference method to average a set of sequences consistently with DTW.
COMASA<ref>{{Cite journal | last1 = Petitjean | first1 = F. O. | last2 = Gançarski | first2 = P. | doi = 10.1016/j.tcs.2011.09.029 | title = Summarizing a set of time series by averaging: From Steiner sequence to compact multiple alignment | journal = Theoretical Computer Science | volume = 414 | pages = 76–91 | year = 2012 | doi-access = free }}</ref> efficiently randomizes the search for the average sequence, using DBA as a local optimization process.