Interpretation of the Dynamic Time Warping (DTW) graph

Question

How can I interpret ate the DTW graph.

I understood the algorithm behind DTW, but I struggle to interpret ate the graph.

When I compute the DTW for a signal that is the same signal but shifted in time, my result will be a diagonal, straight line from top right to bottom left. When the signal does not match exactly, I would see some deviation from the ideal diagonal line.

But how to be exact about the outcome?

I try to explain my issue from a different perspective

When I calculate the standard Euclidean distance I can say as bigger the value as bigger the error, but what about the values calculated with DTW?

Answer 1

The graph plots two things:

• the optimal warping path;
• the accumulated cost matrix (which looks like a heat map).

To interpret the graph, suppose we draw some other path from bottom left to top right. We think of points on our path as matches between the two signals. Different paths correspond to different ways to match the signals. The more our path passes high-cost regions, the higher the error between the two signals when matched in this way. The optimal warping path, which we get on the graph, is the one with the smallest error we can get.