A method for aligning sequences in a way that is insensitive to arbitrary "warping" (stretching or shifting) along the time (or "time") axis. Wikipedia article

• Standard DTW. This algorithm requires O(MN) time and memory, where M, N are the lengths of the two sequences to be aligned.
• FastDTW (Salvador & Chan, Intelligent Data Analysis 2007), which works by coarsening until DTW is easy, and then stepping back to the finest scales one at a time in a way that lets us search only "a radius" around the best DTW path from the next coarser scale.

• [*] Restricted DTW, where only a parallelogram is explored, not the full rectangular space. (This is a speed/memory optimization.)
• [*] FastDTW (Salvador & Chan, Intelligent Data Analysis 2007), which works by coarsening until DTW is easy, and then stepping back to the finest scales one at a time in a way that lets us search only "a radius" around the best DTW path from the next coarser scale.
• [*] Improve FastDTW code by creating a WindowedMatrix type, so that element access can be easier in the dtwwindowed code.
• Consider implementing SparseDTW paper on arXiv
• DTW Barycenter Averaging (see paper by Petitjean et al. 2011).
• Possibly a "spectrum aligner" where the data being warped are histograms. (Does this affect anything? Maybe not needed.)
• Learn the terminology and actually get proper references in place!
• Some demonstration examples.