# DTW find the warped sequences

I have these 2 sequences:

s1 = [1, 2, 3, 5, 5, 5, 6]
s2 = [1, 1, 2, 2, 3, 5]


And have calculated the DTW matrix as:

+------+------+------+------+------+------+------+------+
|      |   0  |   1  |   1  |   2  |   2  |   3  |   5  |
+------+------+------+------+------+------+------+------+
|   0  |   0  |  inf |  inf |  inf |  inf |  inf |  inf |
+------+------+------+------+------+------+------+------+
|   1  |  inf |   0  |   0  |   1  |   2  |   4  |   8  |
+------+------+------+------+------+------+------+------+
|   2  |  inf |   1  |   1  |   0  |   0  |   1  |   4  |
+------+------+------+------+------+------+------+------+
|   3  |  inf |   3  |   3  |   1  |   1  |   0  |   2  |
+------+------+------+------+------+------+------+------+
|   5  |  inf |   7  |   7  |   4  |   4  |   2  |   0  |
+------+------+------+------+------+------+------+------+
|   5  |  inf |  11  |  11  |   7  |   7  |   4  |   0  |
+------+------+------+------+------+------+------+------+
|   5  |  inf |  15  |  15  |  10  |  10  |   6  |   0  |
+------+------+------+------+------+------+------+------+
|   6  |  inf |  20  |  20  |  14  |  14  |   9  |   1  |
+------+------+------+------+------+------+------+------+


Now I need to generate the warped sequences, but I couldn't find how to do this.

I know this is the path:

And that

• A horizontal move represents deletion
• A vertical move represents insertion
• A diagonal move represents match

What how do I get the warped sequences?

The matrix and sequences where taken from here since I don't want to publish the ones I'm using.

The warped version of the shorter sequence $$[1, 1, 2, 2, 3, 5]$$ thus will be
$$[1, \color{red}{1}, 2, \color{red}{2}, 3, 5, \color{green}{5}, \color{green}{5}, \color{green}{5}] = [1, 2, 3, 5, 5, 5, 5]$$