# 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.

## 1 Answer

Just follow the instructions:

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

'deletion', 'insertion' and 'match' refer to the deletion of the period of observation, insertion of another period with the same observation ('elongating the observation') and keeping the period observation without changes.

The warped version of the shorter sequence $$[1, 1, 2, 2, 3, 5]$$ thus will be

$$[1, \color{red}{1}, 2, \color{red}{2}, 3, 5, \color{green}{5}, \color{green}{5}, \color{green}{5}] = [1, 2, 3, 5, 5, 5, 5]$$

where the deleted observations are colored in red and inserted are colored in green.