This is the first time I'm asking a question on math section of stackexchange, so please excuse me if this isn't the right place for such a question.
I'm a programmer studying about an algorithm which embeds the notion of projection of points. Here is the concrete paperwork. In the spirit of math section, I'm not expecting from anyone to spend time on the algorithm itself, but I am interesting in a concrete part, that talks about these projections to speed up the algorithm. That part is located on page numerated as 225.
What confuses me is this - does the distance used in projection need to be Euclidean, or any other distance can be used?
Concretely, I'm interesting in something called Dynamic Time Warping as a distance measure. This distance measure is used mostly to find the similarities between to signals, where signals may be shifted or skewed. It finds the optimal alignment between the signals. It actually uses Euclidean distance measure to find distance between two points, but it creates a matrix which is used to find the best alignment.
Can anyone please explain would it be reasonable to use such a distance, and that the projections are still valid?
This projection is used to find the "most central object in cluster". On page 226 you could see how this projection is actually used.
Any help would be great, thanks.
The distance does not have to be Euclidean, but it cannot be DTW.
The distance needs to be a metric, and DTW is not a metric.
There are other ways to quickly cluster under DTW; for example, see "Dynamic Time Warping Averaging of Time Series allows Faster and more Accurate Classification" ICDM 2014
There are ways to approximately embed DTW into a metric space, but it is not clear that it is worth the effort.
Source: I have more papers on DTW than anyone else in the world. Eamonn