Linear Time Warping, alignment issues

[s1735009]

If we need to stretch our sequence of feature vectors, won’t we inevitably get vectors that mismatch the template equally?

If one vector in the unknown sequence maps to two vectors in the template, how do we choose an alignment?
In the case in my diagram, how do we decide between the red or green alignment?
Is there a more formal protocol than “by eye” in a tie situation?

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[Simon]

The choice between red and green could be arbitrary, but it would be better to choose whichever gives you the lowest global distance (as in DTW).

There are many problems with pattern matching using exemplars, whether using linear or dynamic alignment, and the HMM will solve most of them. For example, the number of local distances summed together might vary with different alignments, making it hard to fairly compare them

Holmes & Holmes Chapter 8 details various solutions that were proposed for some of these problems, such as introducing ad-hoc penalties, or placing restrictions on how paths move through the grid (e.g., slope constraints). These all demonstrate that the method has many problems and ad-hoc design decisions.

[Author]

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