Dynamic Time Warping in Python / C (using ctypes)
The Dynamic Time Warping (DTW)[1,2] is a time-normalisation algorithm initially designed to eliminate timing differences between two speech patterns. This normalisation, or correction, is done by warping the time axis of one time series to match the other. The correction (time warping) makes it easier to compare two signals in a similar way to the method human beings use[3].
Example of 2D trajectory-matching generated by the DTW method. Although looking perfect in the figure on the left, the cardioid was modified to have a constant value zone from time step $50$ to $150$. The DTW correctly matches the values as can be seen as a straight blue line in the Accumulated Distance plot (right).
Above is presented an example where a cardioid is compared to a circle. The cardioid also had a time delay inserted (values were kept constant). The DTW calculates the distance (here the Euclidean one) between all the points of the two time series and, then, generates another matrix with the accumulated distances. The total distance defined by the path formed with the minimum values of the accumulated distance (right-hand side of the figure) can be easily applied to compare different shapes.
This version of the algorithm uses a C kernel, supporting multidimensional arrays and Euclidean distance, to speed up the calculations with a Python wrapper as the user interface. More details and sample code can be found in this Jupyter notebook:
if you are not happy with my explanations above, one of the best explanations about how the DTW works I've found on a presentation by Elena Tsiporkova.
dtw_python
execute make
.sudo make install
.dtw_python
directory anymore and you can test it using the jupyter notebook.