Best path/local distance

[Sandy F]

To clarify, is the local distance in DTW the geometric distance between the vectors at each point in the grid? And this would mean that the unknown word and reference word that are most similar would have the most similar vectors, and therefore the shortest local distances/total distance?

Is DTW repeated on the unknown word for each reference word until a best path is found?

[Simon]

Correct, the local distance in DTW is the geometric distance between the pair of feature vectors at a given point in the grid.

We hope that the total distance (usually denoted D), which is the sum of local distances, will be lowest for the template that actually corresponds to what was said in the unknown word.

For a single, given unknown word, DTW is repeated once for every template. In each case, DTW finds the best path that aligns the unknown word with the current template being tried. This results in a separate value for D for each template. We then compare all those D values and pick the lowest.

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